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Diode Laser Spectroscopy

1. Glass ND Filter Figure 3 Turning mirrors added to setup D Understanding the Functions of the Beams We are now ready to add the important 50 50 beam splitter as shown in Figure 4 But first let s talk about the motivation for all the beams flying around The initial 1090 9096 beamsplitter has generated two weak probe beams and you ve seen that each of them passing through the cell to a photodetector is a probe of the transmission of the cell But the stronger beam transmitted through the 10 90 beamsplitter has now been brought around to the far side of the cell and is ready to be sent through the cell in the opposite direction of the probe beams and overlapping one of the two probe beams inside the cell You want to overlap the beam going to Detector 1 The stronger beam is called the pump beam and what it pumps is the atoms being probed by only one of the two probe beams Because we are using a 50 50 beamsplitter only half the pump beam is sent through the cell and only half of the probe beam gets through to the photodetector PD1 The important function of the 50 50 BS however is to create the desired anti parallelism of the pump beam and one of the probe beams Rev 2 0 11 09 There are two fine points to observe in Figure 4 First note the upper adjustment knob on the 50 50 BS mount is on the side such that the probe beam can pass through the mount You should also observe that the mount is placed such that the
2. B Setting up the Absorption Cell Assembly the cell takes a while to get to optimum temperature so you want to have it heating up while you do other things 1 Slide the Absorption Cell Assembly into the Magnetic Field Coils and secure it 2 Place the assembly on the breadboard so that the laser beam will go through the cell Put it eight inches or so away so that you have room to work between it and the laser 3 Connect both cables from the cell assembly to the back of the controller You will notice that the polarity of the banana plug heater wires does not matter The polarity of the blue thermocouple connector however does matter It will only plug into the blue receptacle one way 4 When the power is turned on the Cell Temperature controller LED display on front panel will first reset and then display the cell temperature In five or ten minutes the cell temperature will be close to its factory established set point temperature of 50 C You may check and or change the cell temperature set point as follows a Press the leftmost button on the cell temperature controller It is marked by a circular arrow The temperature controller will read SP1 b Press the rightmost button on the cell temperature controller The cell set point temperature in degrees C will now be displayed c You can press the up down arrow buttons to change the set point Start with a temperature of 50 C d Press the rightmost button The display
3. Rev 2 0 12 09 Table 2 lists the various control terms and the standard values that the unit was shipped with Once the changes have been made the top cover should be reinstalled before the power is applied to the electronics Control Standard Parameter Fauanon Values Value E Rxtl 20 KQ B Gain P G Rxt1 Rxt6 10k 10k un E Integral I iazo Roa Raro EAT AME Lacu gee Rxt4 0 Derivative D D 10uF Rxt3 Rxt5 100k eor is D 10 sec Table 2 PID Default values Rev 2 0 12 09 I C LASER CURRENT CONTROLLER The amount of current determines in part the gain of the laser Below the threshold current the overall gain is less than one and the light coming from the diode is incoherent and broadband similar to light from an LED At currents above the threshold the light coming from the diode becomes coherent narrow band laser light and the intensity increases linearly with the current Increasing the current also increases the temperature of the diode This changes the wavelength of the laser in a manner similar to that of external heating As discussed in Chapter 1 Section IIB the small scale local slope of the steps in Figure 7 makes it possible to estimate that a current noise of 0 5 uA would produce a laser line width of about 1 MHz See Chapter 1 pages 6 amp 7 Figure 7 wavelength versus current for a bare diode I C 1 Specifications Current Range 0 100 mA Curre
4. Figure 19 shows the amount of light transmitted by the polarizer The linear polarizers work well at laser powers of 2mW and below At powers between 2 mW and 30 mW they show transient behavior With laser powers above 30mW they can be permanently damaged SINGLE PARALLEL PERCENT TRANSMITTANCE s 17 45 37 10 X 40 CROSSED 450 500 750 890 850 50 600 650 700 WAVELENGTH NM Figure 19 Percent Transmittance of Linear Polarizers 5 30 Rev 2 0 12 09 IV E QUARTER WAVELENGTH PLATE IN ROTATABLE MOUNT Diameter 50 mm optical thickness 200 5 nm When properly oriented the quarter wave plate allows linearly polarized light to be converted to circularly polarized light The plate has two optical axes at 90 degrees to each other with different indices of refraction along each axis Light travels at different speeds along each axis The axes are called the fast axis and slow axis To produce circularly polarized light monochromatic linearly polarized light is placed incident to the plate at 45 to each axis If the plate is of the correct thickness then the phase lag along the slow axis causes the light exiting the plate to be circularly polarized The optical thickness of the plate may not be the desired value Tuning the optical thickness retardation can be accomplished by rotating the plate about the vertical axis Rotation about the slow axis increases the retardation and about the fast axis decreas
5. V Experimental Properties of Mode Degenerate Interferometers In this section we consider some of the practical aspects of mode degenerate interferometers As discussed in the preceding section the confocal in terferometer is the most useful of the mode degen erate interferometers because it has the highest finesse Most of the discussion in this section is spe cifically but not inevitably related to the confocal interferometer PIEZOELECTRIC SPACER V MWERERRRRRRRERRRURE A Anh a evens V NN BAM ff VA DETECTOR j Ypy efe eer 3 Seanning confocal interferometer Figure 3 shows a typical scanning confocal inter ferometer It comprises two spherical mirrors sep arated by a distance equal to their radius of curva ture The back surfaces of the mirrors are made such that the mirrors are self collimating that is a plane wavefront incident on the interferometer will be transformed into a spherical wavefront whose radius of curvature matches that of the transverse modes of the interferometer The con cave surfaces of the mirrors are coated with high reflectance multilayer films and the convex sur faces are coated with anti reflection films to eliminate spurious interferometer resonances in volving the back surfaces of the mirrors The mirrors are mounted in cells which are sep arated by a piezoelectric spacer By applying a po tential difference of a few hundred volts to the piez
6. or 4 a Output spectrum of a helium neon laser operating simultaneously in two transverse modes b Output spectrum of a helium neon laser operating in a single transverse mode The vertical sensitivity and horizontal dispersion are the same for both a and b 5 a Output spectrum from a free running argon ion laser b Output spectrum from a self phase locked argon jon laser The vertical sensitivity and horizontal dispersion are the same for both a and b The other application of scanning spherical mir ror interferometers that we consider is their use in studying phase locking phenomena Figure 5 Shows the output spectrum of a single transverse mode argon ion laser when it is a free running and b self phase locked Note that the output spectrum is quite different for the two cases The spectrum shown in Figure 6 a is somewhat blurred because of the erratic mode hopping dur ing the exposure time This mode hopping is char acteristic of lasers whose mode spacing is less than the homogeneous linewidth In Figure 6 b the output spectrum is constant in time Do glas C Sinclair April 1968 References 1 R L Fork D R Herriott and H Kogelnik A Sean ning Spherical Mirror Interferometer for Spectral Anal ysis of Laser Radiation Appl Optics 3 1471 1964 P Connes Increase of the Product of Luminosity and Resolving Power of Interferometers by Using a Path Differen
7. 0 to 5 The first and last of these correspond to the positions A and C in Figure 3 Label your plots You will be trying to reproduce these curves in the lab Check your calculations by comparing with the one calculated curve in Figure 5 below Why does Aw 0 Io go to 0 25 for large To Amazingly enough the generality of the Kramers Kronig relations says that the above calculations relating ng 1 and amp are true for a Doppler broadened gas as well as for atoms at rest Because of this scanning the laser over the Gaussian profile of the Doppler broadened gas will give results which are qualitatively similar to those you calculated in Problem 2 for the atoms natural Lorentzian profile II LABORATORY EXERCISES The Clausius Clapeyron Relation Before launching into the main part of the lab we ll get warmed up by first measuring just the resonant absorption as a function of the rubidium cell temperature Heating the cell increases the rubidium vapor density and thus increases the absorption The rubidium vapor in the cell is in equilibrium with a small bit of solid rubidium on the cell wall and the vapor pressure is given by the Clausius Clapeyron relation p T pees poe T where po is a constant T is the cell temperature in Kelvin L is the latent heat of vaporization per mole is the latent heat per atom R is the gas constant and k is Boltzmann s constant This equation is derived from rather fundamental thermodynamic rela
8. 3 Saturated absorption spectrum for atoms with a single ground state and two closely spaced excited states 1 Probe Transmission 02 04 06 O08 4000 2000 0 v vy MHz 2000 4000 Fig 4 Saturated absorption spectrum for atoms with a single excited state that can decay into either of two closely spaced excited states operates for a short period of time as the atoms travel through the laser beams If you think about it a while you can see there are two velocity classes of atoms that are responsible for the dip For one velocity class the pump laser excites g1 e which tends to pump atoms into g2 Then the probe laser which excites g2 e for these atoms sees extra absorption For the other velocity class the pump laser excites g2 e gl gets overpopulated and again the probe laser which now excites g1 e for these atoms sees more absorption Rev 2 0 11 09 IV QUANTITATIVE PICTURE OF SATURATED ABSORPTION SPECTROSCOPY 2 LEVEL ATOMS One can fairly easily write down the basic ideas needed to calculate a crude saturated absorption spectrum for 2 level atoms which demonstrates much of the underlying physics The main features are 1 the transmission of the probe laser beam through the cell is e and c v is the optical depth of the vapor 2 the contribution to t v from one velocity class of atoms is given by dt v v P P F v v dn v where P is the relative population of the ground state P
9. As is the case for a Fabry Perot etalon the surface figure must be accurate to roughly the transmission wavelength divided by the finesse In order to minimize the requirements on the surface figure of the mirrors the diameter of the incoming laser beam should be approximately equal to the diameter of the TEM mode of the interferometer Spherical aberration of the mirrors gives rise to a fundamental limitation on the amount of mode mismatch that can be tolerated in a mode degen erate interferometer The theory of Hermite Gaussian mode structure in spherical mirror inter ferometers is based on the paraxial optics approxi mation If a mode degenerate interferometer is illuminated too far off axis the paraxial optics approximation cannot be used to describe its be havior The dominant aberration which enters the theory is spherical aberration The amount of spherical aberration in the interferometer depends on the radius of curvature and separation of the mirrors For a confocal interferometer one can show that the path difference variation caused by spherical aberration for rays entering the interferometer parallel to the axis but displaced from it by a dis tance h is given by ht a If we demand that this path difference variation be less than the transmission wavelength of the interferometer divided by the finesse we find that the incoming beam must have a radius h given by h QE 18 A 17 F
10. PRINT ut V Select Folder 1 F 4 About 2j Save All CHivi00v CH2 200VBy M100ms Ext S 00mV 23 Oct 04 00 22 10Hz Figure 11 Expanded Scan Showing Four Absorption Lines Operating point The depth of the lines depends on the length of the Rb cell and the atomic density the latter depending on cell temperature You can explore this by changing the cell temperature 3 You can see in the above that the background intensity changes considerably with the scan This is because you are now scanning the laser intensity via the current together with the laser frequency via the piezo You can correct for this effect in a number of ways One way is to digitally record a spectrum with the cell in place and then record a second spectrum with the cell removed and finally divide the two signals in software This has the advantage that only a single photodetector is needed but the disadvantage that the two traces are not recorded simultaneously Another way to accomplish this is by using a second photodiode as in the following layout Rev 2 0 11 09 Detector 2 to INPUT CCD Camera Photo diode Detector X X ND Filter Holder with Gelatin Filters 10 09 9q epoip oloud J
11. This depends on the properties of the semiconductor material from which the laser is made in particular the band gap The medium gain shows a broad peak in frequency space whose position depends mainly on laser temperature Since we are aiming for the rubidium atomic transition we must set the laser temperature using the temperature controller so that it operates near 780 nm the wavelength of the rubidium resonance lines This temperature is recorded on the antistatic bag in which each diode is shipped The temperature for the diode that was shipped in your laser is listed on the data sheet included in your manual A plot of Wavelength versus Temperature for a typical laser is shown in Figure 6 The overall slope of this data is about 0 23 nm C which should be about equal for all the Sanyo diodes From this slope and the temperature set point for 780 nm you can determine an appropriate temperature for any desired wavelength for that specific diode Once this is done the medium gain curve is so broad that it is unimportant for determining the precise wavelength of the laser Rev 2 0 11 09 780 5 780 0 779 5 779 0 778 5 Wavelength nm 778 0 777 5 12 14 16 18 20 22 24 26 Temperature C Figure 6 Output wavelength of a free running i e no external optical feedback Sanyo DL 7140 200S diode laser as a function of diode temperature The behavior of other diode lasers is similar 2 The internal cavity The di
12. When operating the laser at a temperature below the local dew point condensation may be a problem In such cases it is advisable to put tape over the un used hole and tape a piece of glass microscope slide or cover slip over the hole through which the laser beam exits Though better than no braid at all we believe that this is the weak link in the thermal stability chain as it relates to wavelength stability When operating at temperatures far from room temp there is a significant temperature difference between the movable mirror mount section that holds the grating and the rest of the mirror mount about 6 C at a 60 C set point 5 3 Rev 2 0 12 09 I B 3 Laser Temperature Electronics The TEC is a Melcor model CP1 127 08 with dimensions of 30 mm by 30 mm a maximum current voltage of 2 3A 15 4V and a cooling power of 21 4 Watts The TEC transfers heat between the cold plate and heat sink When run in reverse direction the cold plate becomes a hot plate and the heat sink a heat source Temperature is sensed with a 10k thermistor used in a bridge circuit see Figure 3 An instrument amplifier generates an error voltage that is the difference between the set point voltage and the voltage across the thermistor A PID circuit conditions the error signal into a control voltage that operates the TEC through a power amplifier The entire circuit is bipolar so that both cooling and heating may be accomplished Analysis of the brid
13. can be derived from one another is an example of the more general Kramers Kronig relations A full quantum mechanical treatment also yields the same relation for the absorption and refractive index of a gas near an atomic resonance An electromagnetic wave in the medium propagates according to e twt nkz e Fnosz e i ot knoz 1 where k w c From this it can be seen that no corresponds to the usual index of refraction equal to c v while amp describes the attenuation of the wave Then the complex electric field amplitude can be written Eo exp 7 after passing through the cell where Ep is the initial field amplitude and T w knok w L ik no w 1 L where we have taken out the constant phase shift kL Using no 1 2Awk y this becomes i2kA wisL TY marg asin Q o Q 5 0 5 Aw y Figure 3 Plot of the absorption nox and refractive index change no 1 for a gas near an atomic resonance Note the index change is proportional to the first derivative of the absorption 2 Tw knok w L 229 2G Av zd where To is the optical depth at line center defined from the intensity and not field and G w is the normalized line profile 2 77 4 G Aw Aw Aw 72 4 We can write the electric field in linearly polarized light as E 2 S Ee tK E pipet and circularly polarized light 1 on d E EO Ege et k2 i Ege era ke 5 y 1 r Em E i iE 2 1 j PU E
14. instrumental bandwidth is known as the resolving power or Q quality factor of the etalon We thus have 2zvd The Fabry Perot etalon although it is a versatile tool for the high resolution spectroscopy of ordi O nary light sources is of limited usefulness in ana lyzing laser mode structure The reason for this is that an ordinary Fabry Perot etalon does not have sufficient resolving power to be very useful in ana lyzing laser beams A typical gas laser transition has a Doppler line width of a few gigahertz The various modes of the laser are typically separated by a few tens of mega hertz In order for an interferometer to be useful in analyzing laser mode spectra it should have a free spectral range which is larger than the Doppler linewidth and an instrumental bandwidth which is small compared to the frequency differ ences between the various modes of the laser in short it should have a high finesse For analyzing laser mode spectra it is usually desirable to employ an interferometer having a finesse of at least one hundred It is very difficult to make Fabry Perot etalons which have a finesse of 100 A typical value for the finesse of a Fabry Perot etalon is 30 although it is possible to obtain somewhat higher values with high quality instruments Two principal factors limit the finesse of Fabry Perot etalons The surface figure of the mirrors must be flat to approximately the transmission wavelength divi
15. is limited by the number of oscillating longitudinal modes As mentioned above the scanning spherical mirror interferometer is a powerful tool for study ing the mode structure of gas lasers There are however other methods which are used to study laser mode structure The most common of these employs a radio frequency spectrum analyzer When a laser beam is detected by a photodetector the output eurrent from the photodetector will con tain signals at the difference frequencies between the various modes of the laser beam By measuring the frequencies and amplitudes of the various dif ference frequency signals some characteristics of the optical spectra can be deduced Radio frequency measurements have some advan tages and some disadvantages over direct optical frequency measurements such as those obtained from scanning spherical mirror interferometers Radio frequency measurements usually have high er resolution than optical frequency measurements On the other hand conventional radio frequency measurements do not give complete information about the optical mode spectra Consider the case of a laser beam containing two modes one large in amplitude and one small in am plitude If such a beam is detected by a photode tector the output current will contain a signal which oscillates at a frequency equal to the differ ence frequency between the two modes However there will be no way to determine whether the strong mode i
16. 3 Set up the two channel oscilloscope that you will use for these experiments Run a BNC cable from the RAMP OUTPUT of the RAMP GENERATOR module to an oscilloscope Run a second cable from the RAMP GENERATOR SYNC OUTPUT to the scope trigger Observe the output on the scope as you adjust the RAMP GENERATOR settings Rev 2 0 11 09 4 Use The RAMP GENERATOR and PIEZO CONTROLLER to Set the Frequency Sweep a Turn the ramp amplitude down and connect the RAMP OUTPUT from the oscilloscope to the modulation input connection on the PIEZO CONTROLLER MODULE This is a good place to use one of the short BNC cables that came with the system b Connect the MONITOR OUTPUT of the PIEZO to Channel 1 of the oscilloscope Turn the piezo OUTPUT OFFSET knob to zero The OUTPUT OFFSET changes the DC level of the monitor output It does not change the voltage applied to the piezo stack This control is used when locking the laser to an absorption feature and is not needed here c Set the ramp generator frequency to about 10 Hz Turn the piezo ATTENUATOR knob to one 1 Set the ramp generator AMPLITUDE knob to ten 10 and use the DC OFFSET knob of piezo controller to produce a large amplitude triangle wave that is not clipped at the top or bottom The piezo MONITOR OUTPUT should have a signal that runs from about 3 volts to about 8 volts Operating note The PIEZO CONTROLLER drives a small piezoelectric stack that moves the optical feedback grating This sca
17. 87Rb 28 85Rb 72 Figure 8 More rubidium level diagrams showing the hyperfine splittings of the ground and excited states II LABORATORY EXERCISES The goal of this section is first to observe and record saturated absorption spectra for as many of the Page 8 Photodiode Figure 9 Recommended set up to get the laser running on the rubidium resonance lines rubidium lines as you can and then to see how well you can measure the P3 2 hyperfine splitting of STRb using a auxiliary interferometer as a length standard Remember that eye safety is important First of all the laser operates at 780 nm which is very close to being invisible Thus you can shine a beam into your eye without noticing it Also the laser power is about 20 milliwatts and all that power is concentrated in a narrow beam Looking directly at the Sun puts about 1 milliwatt into your eye and that much power is obviously painful It is certainly possible to cause permanent eye damage using the Ph76 laser if you are not careful Therefore be careful ALWAYS WEAR LASER GOGGLES WHEN THE LASER IS ON As long as you keep the goggles on your eyes will be protected Week 1 Getting the Laser On Resonance The first step is to get the laser turned on and tuned to hit the rubidium lines We see in Figure 7 that the lines span about 8 GHz which can be compared with the laser frequency of v c 4 x 10 Hz Thus to excite the atoms at all the laser frequency
18. AAS ea 0 75 X 0 75 Collimation Epi Tube Hold d RA ube Holde AW SS Set Sorews i7 E a NY SN CD S3 PZT Stack WD A E Ball tipped Set Screw Grating Grating Holder Figure 7 Overview of Laser Head Rev 2 0 12 09 I D 1 Laser Diode The diode is a Sanyo DL 7140 201S infrared laser diode with a nominal wavelength of 785 nm and a maximum output power of 70 mW The data sheet is included at the end of this section The data sheet shows the output power as a function of current for different laser temperatures The point where the power rises sharply is called the threshold current and is the start of lasing action There are also graphs of the threshold current as a function of temperature When the diode is placed in an aligned optical system the threshold current is reduced below that for the bare diode When the laser beam is viewed on a white card with the CCD camera you can observe the threshold as a sudden brightening of the beam spot Measuring or just observing this threshold condition will be used in the following section for aligning the grating and correctly positioning the lens Section I D 2 c If you notice that the laser experiments are not functioning properly even though they did previously you might have a damaged diode that needs to be replaced Diode lasers rarely burn out completely before they lose the ability to function adequately in the laser lab Thus it is not alwa
19. By reducing the laser current and adjusting the Piezo DC LEVEL you should be able to get a nice scan showing the 85a and 87a features This is shown in Figure 10 Tek AE Tria d M Pos 40 00ms SAVE REC Action NAA PRINT Mode hop dele NESSUN OO eee eee See eee i TERE oe EE Select Folder About Save All Sr ee Pere Pee Pee Pere Pee ree CH1 500mw CH2 2 00VBy M 10 0ms Ext 8 00mV 22 Oct 04 21 44 lt 10Hz Figure 10 Scan improved by adjustments to laser current and piezo DC level Rev 2 0 11 09 I Using Simultaneous Current and Piezo Modulation to produce a larger scan range without mode hops See the Diode Laser Physics section for an explanation 1 Set the laser CURRENT ATTENUATOR knob to zero Attach the BNC splitter F connector to the RAMP OUTPUT on the RAMP GENERATOR Plug one BNC from the RAMP OUTPUT to the MODULATION INPUT of the PIEZO CONTROLLER and the second BNC from RAMP OUTPUT to the CURRENT MODULATION INPUT 2 Turn the ramp generator amplitude up to maximum and watch what happens when you turn up the current attenuator knob With some tweaking you should be able to produce a full trace over the Rb spectrum The oscilloscope invert function has been used to show the trace in what looks more like an absorption spectrum in the Figure 11 Note the correspondence to the expected atomic Rb spectrum shown in Figure 8 Tek Ju Mod MPos4o Ums SAVE PEC 4
20. Glass X X Coils Figure 12 Apparatus set up to use two detectors J Using Two Photodiode Detectors to Compare a Beam directly from the Laser to one that has passed through rubidium vapor 1 You will need to place the 50 50 Beam splitter in a mirror mount Please refer to the Optics section in the Apparatus Chapter of the manual if you are unfamiliar with putting optical components into mounts 2 With this experimental configuration you will detect two simultaneous signals one with and one without the Rb absorption and then subtract the spectra You will use the Detector electronics on the Laser Diode Controller To Oscilloscope Chan 1 FREQUENCY RANGE DC OFFSET 45 9 PE og og 12 SE 8 01 Ten oy Js x goi ok 4 1 0 2 Frequency Xj Multiplier coarse FINE Laser eu 100V Full Scale Temperature Indicator 9 2 3 A S 2 258 Laser Diode Temperature o 2 8 1 4 0 1 o 5 Above Set Pt o 10 0 ATTENUATOR AMPLITUDE OFFSET ATTENUATOR OUTPUT Temperature e OFFSET MODULATION Set Point MODULATION MONITOR Below Set Pt OUTPUT To Oscilloscope Trigger From From PD 2 PD 1 Figure 13 Controller Modules showing connections for using two photodiode detectors 3 Connect the BNC from the Photodiode Detector 1 to the right most DETECTOR INPUT This will invert the signal from PD 1 so that absorptions will show as dips Set the BALANCE knob above the
21. In addition to spikes at fj f2 and f5 there will be crossover spikes at fj5 f23 and fj3 Fabry Perot Cavity FP1 A INSTRUCTOR S MANUAL A PRODUCT OF TEACHSPIN INC TeachSpin Inc 2495 Main Street Suite 409 Buffalo NY 14214 2153 Phone 716 885 4701 Fax 716 836 1077 WWW TeachSpin com TeachSpin Inc FABRY PEROT CAVITY INSTRUCTOR S MANUAL INDEX The Basics e Overview of the Physics e Unpacking your Instrument e Setting Up the Fabry Perot Cavity for the First Time e Appendix A The Poor Man s Optical Isolator Fabry Perot Cavities and FM Spectroscopy Courtesy of California Institute of Technology e Background Detailed analysis of the physics e Laboratory Exercises e References Scanning Spherical Mirror Interferometers for the Analysis of Laser Mode Structure Spectra Physics Laser Technical Bulletin Rev 2 0 11 09 Instruction Manual for TeachSpin s Fabry Perot Cavity Introduction The Fabry Perot Interferometer is a resonant cavity for light which has many uses in the world of optics TeachSpin s Fabry Perot Cavity was designed specifically to calibrate the frequency scale of a tunable laser It can be used with any tunable laser operating in a wavelength range of 740 820 nm As an appendix we have included a manual written by California Institute of Technology Professors Kenneth Libbrecht and Eric Black of the California Institute of Technology with whom TeachSpin collaborated in b
22. L 0 giving J 1 2 and the ground state 7 9 2 For the first excited state we have 5 1 2 and L 1 giving J 1 2 or J 3 2 so there are two excited states P j2 and P3 5 Spin orbit coupling lifts splits the otherwise degenerate P 2 and P3 5 levels See any good quantum mechanics or atomic physics text for a discussion of spin orbit coupling The dominant term in the interaction between the nuclear spin and the electron gives rise to the magnetic hyperfine splitting this is described in many quantum mechanics textbooks The form of the interaction Page 7 term in the atomic Hamiltonian is Hpy c J I which results in an energy splitting AE SIFE 1 I I 1 J J 4 1 where F I J is the total angular momentum quantum number including nuclear spin and C is the hyperfine structure constant Figures 7 and 8 shows the lower S and P energy levels for Rb and Rb including the hyperfine splitting F 3 SPs 2 1 0 09 87a S 85a a b 3 rt 87b H F 2 07 5Sip os 85b F 1 87Rb EET 2 0 2 4 Detuning GHz Figure 7 Left Level diagrams for the D2 lines of the two stable rubidium isotopes Right Typical absorption spectrum for a rubidium vapor cell with the different lines shown 267 MHz 121 MHz 5P 2 5P 3 32 157 MHz 32 63 MHz 72 MHz 29 MHz 2 3 5P 5P 1 12 2 1 2 D2 780 2 nm D2 780 2 nm D1 794 8 nm D1 794 8 nm 2 3 5815 6835 MHz 5815 3036 MHz 1 2
23. See picture at step 15 You will use the allen wrench as a lever to gently move through the horizontal modes b Watch the oscilloscope display as you gently push on the end of the allen wrench You should be able to identify six to eight modes in which the Rb absorption is still visible on the oscilloscope You want to set the Side knob in the middle of this mode pattern c You might notice that the modes at the ends have a shorter and more erratic scan over the Rb absorption You do not need to make an exact adjustment with the Side knob as the Piezo DC OFFSET voltage can be used to fine tune to the mode With proper alignment and laser current adjustment you should be able to set a scan that covers the first three lines in the absorption spectrum 87b 85b and 85a as shown in Figure 9 3 12 Rev 2 0 11 09 M Pos 40 00ms SAVE REC Action Save All mode hop TNT 2 87h Select Folder i About extra feature Save All CHI 50 mv CH2 2 00VBy Mi10 0ms Ext 8 00m 22 Oct 04 21 48 lt 10Hz Figure 9 Scan showing first three absorption lines 2 You may notice a few extra features at the ends of a scan right before a mode hop These feature look like and are replicas of the strong 85b and 87b absorptions and appear near where you would expect to find the 87a absorption The extra features are associated with relaxation oscillations in the diode laser See Diode Laser Physics Section
24. a crude picture but it can be helpful in understanding the confocal cavity It shows you in a rough way how the output spectrum might be insensitive to alignment since the bow tie modes are excited no matter where the beam enters the cavity You will work with a confocal and non confocal cavity in the lab and hope fully this will all make good sense once you see it all in action FM Spectroscopy In the radio frequency domain there exists a substantial technology built up around amplitude modulation and frequency modulation of an electromagnetic carrier wave which gives us for example AM and FM radio broadcasting If one boosts the typical carrier wave frequency from 100 MHz Page 5 Input m gt Figure 4 Ray paths for a confocal Fabry Perot cavity the off axis scale is exaggerated FM radio to 500 THz optical the same ideas apply to AM and FM modulation of lasers The resulting optical technology has many applications the most dominant one being fiber optic communications Modulating the injection current to the diode laser is a very simple way to modulate the laser output both in frequency and amplitude Using non linear crystal modulators is another way to modulate a laser beam The basic idea is that one drives the laser with an injection current which consists of a large DC part and a small high frequency AC part on top The AC part produces both AM and FM modulation of the laser but we will ignore the smaller AM par
25. and techniques in precision spectroscopy that continue to be used and refined to this day photodiode probe ye N beam vapor cell pump beam Figure 1 The basic saturated absorption spectroscopy set up II QUALITATIVE PICTURE OF SATURATED ABSORPTION SPECTROSCOPY 2 LEVEL ATOMS Saturated absorption spectroscopy is one simple and frequently used technique for measuring narrow line atomic spectral features limited only by the natural linewidth I of the transition for the rubidium D lines I 6 MHz from an atomic vapor with large Doppler broadening of AV popp 1 GHz To see how saturated absorption spectroscopy works consider the experimental set up shown in Figure 1 Two lasers are sent through an atomic vapor cell from opposite directions one the probe beam is very weak while the other the pump beam is strong Both beams are derived from the same laser and therefore have the same frequency As the laser frequency is scanned the probe beam intensity is measured by a photodetector Figure 2 shows the spectra that might be recorded if 2 level atoms were in the vapor cell The upper plot gives the probe beam absorption without the pump beam Here one sees simple Doppler broadened absorption In our case the Doppler width is much larger than the natural linewidth Av popp gt gt I and the optical depth of the vapor is fairly small t v lt 1 Rev 2 0 11 09 1 The transmitted fraction of the probe is e w
26. and Series G W 1979 The Spectrum of Atomic Hydrogen Scientific American 240 94 March Milonni P and Eberly J 1988 Lasers Wiley Schmidt O Knaak K M Wynands R and Meschede D 1994 Cesium Saturation Spectroscopy Revisited How to Reverse Peaks and Oserve Narrow Resonances Appl Phys B 59 167 DIODE LASER SPECTROSCOPY GETTING STARTED OVERVIEW of the INSTRUMENT INITIAL SETUP FIRST EXPLORATIONS Rev 2 0 11 09 I Overview of the Instrument See the Apparatus Section 5 for details A The Laser TeachSpin s robust and reliable grating stabilized laser is both temperature and current regulated When the grating is in place it provides optical feedback that retroreflects the laser light to create an external cavity that stabilizes the laser to run at a controllable wavelength A piezo stack mounted in the grating support allows the grating position to be modulated by an applied voltage The laser temperature laser current and piezo stack modulation are determined by individual modules of the Laser Diode Controller A Plexiglas cover over the laser provides isolation from air currents and protects the knobs used to adjust the angle of the grating from accidental changes There are two holes in the cover to allow the laser beam to exit undisturbed both with and without the diffraction grating in place The grating can be removed to study the way the laser behaves without grating stabilization
27. as 10 of the output light scattered back into the laser may affect its frequency stability As shown in Figure 4 we overcome both these problems by using a diode laser with a small amount of controlled feedback from a diffraction grating Diffraction Grating Diode Laser CN TE EE Coating n J yat Collimating Lens Output Beam Figure 4 Basic configuration of the diode laser system A lens in front of the laser collimates the output into a nearly nondiverging elliptical beam After the lens the beam strikes a diffraction grating which is a holographic no blaze grating with 1800 lines mm Most of the light is directly reflected by the grating m 0 grating order but roughly 15 percent is reflected back into the laser m 1 order The grating forms an external cavity i e external to the laser s own internal semiconductor cavity which serves to frequency stabilize and line narrow the laser output see Wieman and Hollberg 1991 and references therein to understand how this happens With the simple addition of the diffraction grating the laser is much less sensitive to stray light feedback and its linewidth will be reduced to Av 1 MHz much smaller than the atomic transition linewidths we will be observing B Laser Tuning With grating feedback the frequency of the laser output depends on a number of factors In order for you to effectively tune the laser to an atomic transition it is helpful to un
28. be to minimize the intensity of the unwanted reflection Punch a hole in one of the viewing cards and place it upstream of the isolator Position the viewing card so that the incoming light goes through the hole Use the CCD camera to observe the reflection Warning there will be several reflections You should be able to see additional reflections for the linear polarizer and wave plate By tilting the elements in their optical mounts you can identify which reflection belongs to which element It is the reflection from the Fabry Perot mirror that we wish to reduce The other elements can be angled such that their reflections do not travel back into the laser Now that you have identified the reflection you wish to reduce rotate the wave plate in its own plane to minimize this reflection You will be rotating around the Z axis in the figure above By this process you will have adjusted the relative angles of the wave plate and polarizer to be 45 degrees Now try twisting the whole wave plate about the vertical axis using the optical mount that holds the optic to the table You will be rotating around the X axis in the figure above If you find a point were the reflection becomes a minimum then you are done You may however observe that the reflected spot only gets brighter as the wave plate is rotated You have the wrong axis in the vertical direction Rotate the wave plate in its own plane by 90 degrees bringing the other velocity axis into
29. beam going to Detector 1 passes through the 50 50 beam splitter but the beam going to Detector 2 misses both the beam splitter and the edge of the mount that is holding the BS With the 50 50 beam splitter in place we are ready to align the strong pump beam so that it is anti parallel to the weak probe beam going to detector 1 You may want to read the appendix that has a short discussion of the algorithm used to position a beam in space Remove the glass ND filter from the beam path This will make it easier to see the two beams Use the IR viewing card to observe the beams at position 1 which is right before the probe beam goes through the 50 50 BS The IR viewing card has a circular hole on its backside so that you can observe beams from both directions Use the adjustment screws on Mirror 1 or 2 to overlap the two beam spots at position 1 Detector 2 Detector 1 to INPUT to INPUT Photo Photo diode diode Detector Detector IR viewing card position 1 Over lap these two beams CCD Camera IR viewing card position 2 Glass ND Filter Figure 4 Aligning pump and probe beams Rev 2 0 11 09 Now move the IR viewing card to position 2 between the Rb cell and the 10 90 BS Use th
30. beamsplitter cube and two detectors arranged to capture the optical power exiting its two output faces Also displayed are the lab fixed transverse coordinate axes X and y and the cube fixed axes and fy much smaller transverse angular and wavelength extent than the acceptance limits of the beamsplitter and the two output beams from the beamsplitter are easily captured on modest area photodiodes Each photodiode current is sepa rately converted to a voltage so that two separate real time voltages proportional to powers in two orthogonal optical linear polarizations are simultaneously available for oscillo scope display The beamsplitter and the two photodiodes are all held together in a cylindrical structure forming a rigid analyzer that can be rotated about a mechanical axis co inciding with the laser beam to be analyzed Given a light beam exiting the Faraday medium of the form 4 it is easy to work out the response of the polariza tion analyzer just described The simplest case of pure Fara day rotation with no differential absorption yields a linearly polarized beam with polarization axis rotated by angle A0 from its original x direction So if in Fig 6 the analyzer s axes were rotated by 45 away from the X and y direc tions it is easy to see that the transmitted and deflected beams would be of equal amplitude in the absence of Fara day rotation but in the presence of Faraday rotation one beam would
31. by i 2v 2m pru H Ain A 7 3 725 Am J Phys Vol 64 No 6 June 1996 where is the vacuum wavelength of the light and the inci dent field propagates through a sample of length L to give the emergent field 2T E L t Eg exp B L X iy exp 27 ct E exp B L X iy exp s n L zi 4 In the usual case of equal attenuations for the two polariza tions B B p this reduces to E L t 2E exp BL X cos A0 y sin A6 T 27 n n exp i 7 2 which clearly represents a linearly polarized wave whose di rection of polarization has been rotated through the Faraday rotation angle A6 given by _ 2a ae z i 6 In Sec III we will see how this rotation signal A can be extracted from 4 even when differential attenuation is present The second stage of the theoretical derivation is to relate the macroscopic parameters n and to the microscopic be havior of the sample This can be achieved by assuming that the medium as a whole develops in response to the electric field E an electric polarization P given by P oXE 7 where for a dilute gas sample we do not need to distinguish between the incident and the local value of the electric field The electric susceptibility x defined by 7 is a dimen sionless complex and frequency dependent scalar quantity characterizing the sample Under this assumption Maxwell s equations give the relations
32. cavity axis At the mirrors the wave fronts are curved and coincide with the mirror surfaces so the wave reflects back upon itself Page 4 01 LJ 02 o Cl ie CD 83 11 21 22 Figure 3 Several Laguerre Gaussian modes which are the electromagnetic normal modes inside a Fabry Perot cavity The TEM mode called a doughnut mode is a superposition of two degenerate TEMo modes rotated 90 with respect to one another Confocal Resonators An interesting and useful degeneracy occurs if we choose the cavity length to be equal to the radius of curvature of the Fabry Perot mirrors L Rmirror In this case the mode fre quencies of the various transverse modes all become degenerate with a separation of c AL Avrgpr 2 see Yariv Section 4 6 for a derivation of this For this special case called a confocal cavity the spectrum will look just like that shown in Figure 2 except the mode spacing will be Avon focal c 4L The width of the transmission peaks Av r5 stays roughly the same in principle but in practice Av fwhm depends on how well the cavity is aligned and how precisely we have L Rmirror Another nice feature of the confocal cavity is that the cavity transmission is insensitive to laser align ment Figure 4 shows that each resonant mode in the confocal cavity can be thought of as a bow tie mode which traverses the cavity twice before retracing its path hence Av focal 4L This is
33. cavity free spectral range Gaussian beam profile with a Laguerre polynomial The modes are labeled by TEM where p and are integers labeling the radial and angular mode orders The intensity at a point r in polar coordinates is given by Ln r Top LE cos t6 e where p 2r u and TS is the associate Laguerre polynomial of order p and index The radial scale of the mode is given by t and modes preserve their general shape during propagation A sample of some Laguerre Gaussian modes is shown in Figure 3 This figure displays the transverse mode profiles the longitudinal profile of the mode is that of a standing wave inside the cavity which has some number n of nodes The various modes with different n p and in general all have different resonant frequencies The TEMoo mode has a simple Gaussian beam profile and this is the mode one usually wants to excite inside the cavity Lasers typically use this mode and thus generate Gaussian output beams As you will see in the lab however it is not always trivial to excite just the TEMoo mode inside a cavity Note that the mode shape shown in Figure 1 essentially shows w for a TEMoo mode as a function of position inside the cavity The mode has a narrow waist at the center of the cavity and diffraction causes the beam to expand away from the center At the waist the wavefronts of the electric field or equivalently the nodes of the standing wave are flat and perpendicular to the
34. data or to check the function of the different sections Rev 2 0 12 09 III Absorption Cell Assembly The absorption cell assembly consists of an outer glass cylinder several melamine foam insulation and support pieces the heater assembly a type T thermocouple sensor a cold finger and the Rb cell The heater is an aluminum cylinder about which is wound a bifilar heater wire The heater has a resistance of about fifty ohms 50 Q Wires from the heater and thermocouple plug into the back panel of the electrical box II A SPECIFICATIONS Maximum temperature 90 C 140 C with 1 2 hole foam inserts Temperature differential across Cell T 50 C min on bottom max on top 10 C 2 0 C with 1 2 hole foam inserts Heater resistance 50 Temperature Controller 1 Hz PWM PID Controller Resolution 0 1 C Regulation no air currents 0 2 C Rubidium Cell 25 mm Diameter and 25 mm Length natural isotopic Rb no buffer gas Foam Insulation Exploded view of Cold finger l S a ee Aluminum Alum Rb p Piece Heater Cell i j EN RS PIN eee Brass Glass Cylinder Cold finger Piece Figure 17 Cross section of Cell Heater Assembly PWD means Pulse Width Modulated output voltage pulse rolled off with a maximum frequency of 1 kHz PID is Proportional Integral Derivati
35. differ from one another only in their oscillation frequency trans verse modes differ from one another not only in their oscillation frequency but also in their field distribution in a plane perpendicular to the direc tion of propagation Corresponding to a given transverse mode are a number of longitudinal modes which have the same field distributions as the given transverse mode but differ in frequency it is not customary however to associate different iransverse modes with a given longitudinal mode Copyright 1968 by Spectra Physics Inc Most applications of gas lasers require that the laser operate in a single transverse mode More over in most cases the laser must operate in the lowest order TEM transverse mode The reason for this concerns the amount of power that can be focused in a diffraction limited beam more power can be focused in such a beam when the laser oper ates in the lowest order transverse mode than when it operates in high order transverse modes In many applieations of gas lasers the longitudi nal mode structure of the laser beam is also impor tant In holography for example the presence of several longitudinal modes limits the coherence length of the emitted light and hence the depth of field of holograms made with it In many commu nications experiments the presence of several lon gitudinal modes may give rise to distortion effects In some spectroscopic applications the resolution
36. ever want to try different makes of diode in your laser head With 9 mm diodes the aluminum adapter is not used 5 16 Rev 2 0 12 09 I D 4 a Replacing the Diode First turn off the AC power to the Laser Diode Controller Before removing the diode from the laser you must set up an electrostatically safe place to work This should include a grounded table surface and a grounded wrist strap Diode lasers are easily damaged by electrostatic voltages Loosen the two setscrews on the side of the collimation tube holder see Figure 7 and slide the collimation tube out of the holder Remove the three 2 56 socket head cap screws from the strain relief cap and set the cap and screws aside Unthread the strain relief body from the collimation tube and slide it over the cable Do not allow the cable to twist with the strain relief body but keep it fixed with respect to the collimation tube You will have to unbend the cable somewhat to slide the strain relief body over it Unplug the PCB and socket from the diode Electric Field Beam 5 6mm s Sockel 5 6mm ee Profile Diode into Socket Laser Figure 13 Diagram showing relation between cable bend diode pin out beam profile and laser light polarization With the spanner wrench provided unthread the retaining ring from the collimation tube and remove the diode laser and adapter Place the old diode aside perhaps in a bag marked old diode and remov
37. have found it difficult to reinstall the collimation tube in a repeatable manner This is why we favor the above procedure When reinstalling the grating it is not necessary to set the beam height or contact the piezo stack with the ball tipped setscrew These steps need only be done at the end once the correct lens position has been determined However you should attempt to install the grating holder in a reproducible manner pressing the grating holder against the 6 32 cap screws before tightening the screws as shown in Figure 11 Rev 2 0 12 09 LD 4 c 3 The lens position may be determined by a mark that has been placed on the end of the collimation tube near one of the spanner wrench keyways See the picture in Figure 15 Figure 15 also shows a series of measurements that were taken as a function of lens position The pictures show the relative position of the mark and keyway You should realize that the mark stays fixed as the lens and keyway are rotated though the picture appears to show the opposite You should notice in the picture that we are making very small changes in the lens position only a few degrees and that the threshold current is changing by a milliamp or less Start Thres 2 504V 28 0mA cw Spanner E Thres Wrench 3 011V Keyway 30 1mA END Thres 2 898V 29 0mA Figure 15 Picture of Scratch Mark on Collimation Tube and Diagram Showing Threshold Current Measurement as a Function of Lens Positi
38. in number and can be avoided by the proper choice of 65 By contrast the number of divergent lines associated with a false monopole moment is proportional to N and is unaffected by the choice of 65 In several figures including the dipole CFLD of Fig 1 a gaps on negative charges were avoided by setting 65 to a value very close to 0 producing an apparently divergent field line that eventually reappears at the opposite end of the diagram and terminates on a negative charge Edwin A Abbot Flatland A Romance of Many Dimensions by a Square Seeley amp Co London 1884 For a more technical discussion of two dimensional science see A K Dewdney The Planiverse Computer Con tact with a Two dimensional World Poseidon New York 1984 While this article was in press the authors were made aware of the recent note of T E Freeman One two or three dimensional fields Am J Phys 63 273 274 1995 Freeman shows a field line diagram with a false monopole moment and correctly observes that the distortion would disap pear in a two dimensional universe PBoundary clumping can be avoided in a distribution with one negative and several positive charges by reversing the sign of each charge A form of boundary clumping can be seen in charge distributions containing a single positive charge but the problem originates solely from numerical errors that are easily avoided The problem of distributing points uniformly on a sphere is
39. increase and the other decrease in amplitude This is the motivation for taking the difference of the two intensities as the experimental signal For a general orienta tion of the analyzer with the upper face s normal turned through angle from the x direction we can define the eigen axes of the beamsplitter to be sin cos 35 in the sense that light of pure linear polarization along D will be entirely deflected and light of pure linear polarization along f will be entirely transmitted by the polarizer Defin ing the signal of interest to be the difference in the power emerging from the two faces of the beamsplitter we have h x cos y sin 9 1 P S Pi P253 E L t n z ECL 0 m 36 Here E is the complex electric field incident on the beam splitter and we have used the result E 2 for the time averaged power of a field written in complex representation For an electric field of the form 4 the result that emerges is S 2E exp B B_ L cos 2 4 6 4 37 which depends on the same rotation angle A6 defined in 6 despite the presence of differential absorption 8 4 f For the natural choice 45 this simplifies to 731 Am J Phys Vol 64 No 6 June 1996 S 2E exp B L sin 24 0 38 This shows that a readily extracted experimental signal is directly related to the sine of twice the Faraday rotation angle A6 defined by 6 The meaning of the
40. interaction the effect on the valence electron of the magnetic moment of the nucleus And in fact these ground state hyperfine splittings are well known commercial rubidium atomic frequency standards operate at the 6 834 GHz frequency corresponding to the energy difference between the two Rb 87 ground states So that knowledge provides one way to calibrate the frequency scale along which the diode laser is being scanned There are direct optical methods for checking this calibration such as unequal arm Michelson interferometry or the use of a Fabry Perot resonator Page 5 shows a detailed energy level diagram for the 780 nm or D2 lines for both Rb 85 and Rb 87 The screen capture below it shows the transmitted power as a function of wavelength You can match the dips to the transitions which caused them Our energy level diagram does not include the D1 transitions which take place at 795 nm They are the key to the phenomenon of Optical Pumping another TeachSpin experiment With a calibrated frequency scale it also becomes clear that the four optical transitions you see are not infinitely narrow rather they each have a spectral width of about 0 5 GHz In ordinary spectroscopy such widths are nearly always due to the imperfect resolving power of the spectrometer in question but here it s not so the laser can be shown to be monochromatic to better than 0 01 GHz So what is causing this width It comes from the fact
41. is from the photodiode showing absorption dips due to the Rb vapor Because we have a negative going signal these appear as spikes If the laser scanned perfectly in frequency that is no mode hopping you would see just some fraction of the Rb absorption spectrum The energy levels of Rb and Rb and the Doppler broaden spectrum are show below F 4 F 3 5P55 3 2 M 2 1 8 1 0 M e o9 a S 85 a 2 2 b 2 a 87b mo E F 2 E07 5 F 3 Sip as 85b F 1 85 Rb 87Rb EA 2 0 2 4 Detuning GHz Figure 7 Energy level Diagrams Figure 8 Doppler broadened spectrum b The absorption dips in your trace are interrupted by various mode hops when the laser frequency jumps suddenly Refer to the Diode Laser Physics section for a discussion of mode hops Observe how the signal changes when you vary the laser current and the piezo drive parameters Please explore the parameter space H Horizontal Modes Final Horizontal Adjustment l Adjust the laser current and piezo voltage so that a nice absorption spectrum is centered on the oscilloscope This takes a little practice As with the vertical adjustment there are also horizontal modes These modes are slightly different in that turning the horizontal move through two or three of these modes by changing the piezo DC LEVEL voltage a Place the 5 64 allen wrench hex key in the back of the SIDE knob with the long arm of the allen wrench sticking out at about a 45 angle
42. is the most useful mode de generate interferometer it has the highest finesse of any mode degenerate interferometer The con centric interferometer which corresponds to l 1 is not mode degenerate the theory leading to equa tion 8 is not valid in the concentric limit Mode degenerate interferometers can also be an alyzed in terms of geometrical optics The condi tion expressed in equation 9 is equivalent to the condition that a ray launched in the cavity retrace its path after complete traversals of the cavity Thus from the standpoint of geometrical optics an Lfold mode degenerate interferometer appears to have an effective length which is times the ac tual distance between the mirrors A typical ray path for a confocal interferometer is shown in Fig ure 2 2 Ray paths in a confocal interferometer The factors which limit the performance of mode degenerate interferometers are the reflect ance of the mirrors the surface figure of the mir rors and the spherical aberration of the mirrors The limitation imposed by the reflectance of the mirrors is not usually serious It is now possible to obtain mirrors having a reflectance of greater than 998 In a confocal interferometer this corresponds to a finesse c f equation 16 of more than 7750 Such values of finesse have been realized experi mentally The surface figure requirement on the interfer ometer mirrors presents a somewhat more serious problem
43. it on and feed it into the RF Input BNC of the diode laser NOTE Do not disconnect the cable from its connection at the laser The laser is sensitive to static discharge which can easily burn out the diode Also turn the RF generator on first and then feed the output into the laser This helps avoid voltage spikes that may occur when you turn the generator on As you vary the oscillator frequency 27 and the amplitude which changes Aw and thus 3 you should observe the range of behavior you calculated Record several traces that correspond as closely as you can achieve to your three calculated plots You should get pretty good agreement if not check with the TA One significant difference between calculated and measured spectra is that the measured spectra may be asymmetric This is due to residual amplitude modulation of the laser which we did not include in our pure FM calculation Measure the Free Spectral Range Finally put two high frequency sidebands on your laser print out a spectrum and use the known sideband frequency to measure the free spectral range of the Fabry Perot cavity Compare with what you expect for a cavity length of 20 cm equal to the radius of curvature of the mirrors III REFERENCES Yariv A 1991 Optical Electronics Saunders College Publishing 4th ed Page 12 x Spectra Physics S o Laser Technical Bulletin ONumber 6 PUBLISHED BY SPECTRA PHYSICS INCORPORATED MOUNTAIN VIEW CA
44. leading coeffi cient 2E is clearly seen operationally by imagining zero absorption zero Faraday rotation and the analyzer set to the 0 or 90 positions since then 37 gives baseline sig nals S0 2E 39 Then if the analyzer is set to angle 45 e one readily finds S So exp B B_ L sin 2 4 8 e 40 which can be used in three ways The first application is a method for setting the angle to the desired 45 the proce dure is to turn off the magnetic field so that the Faraday rotation A is zero then the signal S is seen to vanish only when sin 2 0 i e when e 0 or 45 The second application is a method for measuring the Faraday rotation angle A directly if for any given laser frequency the ana lyzer is turned from the previously established 45 loca tion to that angle at which the observed signal S is driven to zero then 40 shows that 2 40 6 0 or e A6 41 i e the analyzer has just been turned through exactly the Faraday rotation angle A6 The third application is a way to get a real time display related to the instantaneous Faraday rotation as the laser is scanned this is obtained by rotating the analyzer to 45 by sending voltage signals propor tional to P and P to a dual trace oscilloscope and by ar ranging for a vertical deflection proportional to their differ ence and a horizontal deflection driven by the same low frequency oscillator tha
45. leave the laser in the middle of this vertical mode pattern as best you can It is not necessary to sit right on one of the mode maxima but only near the center of the mode pattern The correct mode maximum will be set later with the side horizontal adjustment knob and piezo voltage Note that finger pressure on the knob also changes the grating alignment so remove your fingers often during this adjustment If you find it difficult to turn the knob with a light touch then you can use the Allen wrench placed in the back of the knob as a lever for adjustment It is not critical for operation of your laser that you achieve near perfect vertical alignment of the grating You will get adequate laser performance by simply turning the TOP knob to the intensity maximum However it has been found that the better the alignment the better the operation of the laser Better operation being defined as wider mode hop free scans If you are not able to see any change in laser intensity as you adjust the Top knob then STOP Do not continue Most likely both the SIDE and TOP knobs have both been moved by accident or during shipping Please refer to Aligning the external cavity in the Apparatus section of the manual Rev 2 0 11 09 Operating note The TOP and SIDE knobs are used to align the grating with respect to the diode The lines on the grating run vertically Figure 2 shows the diode laser with the cover off and the 5 64 Allen wrench pla
46. magnetic field is strong only near the axis of the device which therefore has a small clear aperture Also too much light intensity will burn a spot in the Faraday crystal so one must be careful not to focus the diode laser to a tight spot inside the optical isolator Page 13 Ph 77 ADVANCED PHYSICS LABORATORY ATOMIC AND OPTICAL PHYSICS Interferometric Measurement of Resonant Absorption and Refractive Index in Rubidium I BACKGROUND In this lab you will observe the relation between resonant absorption and the refractive index in rubidium gas To see how these are related consider a simple model for a rubidium atom namely that of a single electron bound by a harmonic force acted upon by the electric field of an incident laser see for example Jackson 1975 pg 284 Marion and Heald 1980 pg 282 Although crude this model does allow us to write down the basic optical properties of a gas of atoms near an atomic resonance In this picture the equation of motion for the electron around the atom is m ye wee eE z t where y measures a phenomenological damping force If the electric field varies in time as Ee then the dipole moment contributed by one atom is p er e m wi w iwy E OXE where Xe is called the electric susceptibility If there are N atoms per unit volume then the complex dielectric constant of the gas is given by w eo 1 4rxe 1 d An N fe m wk w duy
47. mirrors in the interferometer setups IV B BEAM SPLITTERS The NIR 50 50 Beam splitter has been coated so that the reflection and transmission are both about 50 You should be aware that this is for unpolarized light and that there will be some polarization dependence The other three beam splitters are uncoated pieces of glass There will be reflections from both the front and back surfaces of the glass With the wedged beam splitter it is not easy to determine which surface a particular beam is coming from It is sometimes easier to use a visible laser to identify the beams The amount of reflection will also be polarization dependent IV C NEUTRAL DENSITY ND FILTERS All the ND filters are absorptive rather than reflective The glass ND filter can be used with any laser power The thin film Wratten ND filters should only be used with low power laser light 2 mW or less At laser powers up to 30 mW there is no permanent damage to the filters However above 2 mW of laser power we start to notice transient effects The power transmitted fluctuates by about 0 5 in a way that is reminiscent of a damped harmonic oscillator with a time constant of tens of seconds This is also true of the linear polarizers IV D LINEAR POLARIZER IN ROTATABLE MOUNT The linear polarizers have been marked such that when the tick mark is at 0 the light transmitted by the polarizer has a vertically polarized electric field The mark should be accurate to 5
48. of the diode Since the external cavity is much larger we have AVpsg c 2L 10 GHz for a 15 mm external cavity length See Section A 4 and Figure A 4 1 for the relevant dimensions This curve shifts by moving the grating position which we do either with the L R knob on the laser head or with the piezo electric transducer PZT in the grating mount In order to force the laser into single mode laser operation at a predetermined wavelength do e g an atomic resonance line the gain from each of the components should peak at Ao as shown in Figures 5 To get a more complete understanding of how these contributions interact how the laser tunes as the grating angle is changed we have tried to construct an accurate best guess picture of the shape of the various cavity modes in the laser This picture is shown in Figure 8 Referring back to Figure 5 the grating feedback and external cavity gains have been merged into the single solid line of Figure 8 The broad medium gain has been left out of the plot Figure 8 is a picture of the various cavity modes with all the gains having a maximum at the same frequency Grating Feedback and External Cavity Sees Internal Cavity 0 8 Gain 4 N 0 4 D 1 s i M 4 4 D D z 0 2 J N PN 0 0 Relative Frequency GHz Figure 8 Best guess picture internal cavity grating feed back and external cavity modes in the laser Re
49. or any of the optics during the measurements only adjust the laser settings a small amount in order to minimize Iout wo Make sure you measure especially carefully when Iout wo Lin is small Measure at temperatures from 25C to 75C in increments of 5 10C You don t need to wait a long time to reach some particular temperature exactly just make sure the temperature is fairly stable for each reading The temperature is stable enough if it changes by less than 0 1C in 10 seconds When you have the data you should get a straight line when you plot log log Iout wo Iin versus 1 T why see above Extract the latent heat of vaporation from the slope of this line Express you answer in Joules gram Also plot Iout wo Lin as a function of temperature along with a curve going through the data using the Clausius Clapeyron relation with the parameters you measured If you plot the fit from about T 10C to T 80C you can also see the low temperature structure of the absorption versus temperature The Kramers Kronig Relation Next move on to the main event of observing the Kramers Kronig relation in the lab by measuring Mach Zehnder spectra like those you calculated in Problem 2 The first thing you should do in the lab is check your calculations with your TA If your calculations aren t right the lab will make no sense at all The optical set up is shown in Figure 4 To begin the lab work set up the Mach Zehnder interferometer using the diode l
50. running laser Wavelength versus Injection Current at a fixed temperature The current affects a diode in two ways First increasing the current causes simple heating which changes the temperature of the diode and thus the wavelength in much the same way as heating the laser head directly With respect to wavelength modulating the current can be thought of as a means of rapidly changing the diode temperature This effect predominates for time scales longer than 1 ps and tunes at roughly 2 GHz mA as shown in Figure 7 The second means by which the current changes the free running laser wavelength is by changing the carrier concentration in the active region This modulates the optical path length of the diode with a tuning rate of about 200 MHz mA up to a maximum frequency that is set by the relaxation oscillation frequency of the diode typically several GHz Taken together Figures 5 7 demonstrate the interaction of several influences Figure 6 shows a plot of the wavelength of a free running laser as a function of temperature As the temperature is increased the maximum gain of both the medium and the internal cavity modes shown in Figure 5 will shift to longer wavelengths They do not however shift at the same rate This creates laser mode hops to different peaks of the cavity gain function In practice we would like to set the temperature and injection current so that the laser operates at the rubidium resonance frequency But as can b
51. scope gains to display the signals again The filter does a good job of reducing the back reflection because it attenuates the light both going from and returning to the laser Figure 4 shows the scope trace with the feedback reduced The PD gain of the FP PD has been increased to 10 MQ and the room lights have been turned off If you cannot reduce the room lights you can also try putting a black cloth or paper roof over the gap between the end of the cavity and the snout of the photodiode detector to reduce the amount of stray light entering the PD 7 TeachSpin Fabry Perot Manual Rev 2 0 11 09 We can see from Figure 4 that the attenuator has reduced feedback to the laser The rubidium absorption spectrum now shows that the laser is tuning smoothly and continuously in frequency Tek IM Trig d M Post 43 20rms SAVE REC Action Save Image Nu quud Mol me m vM DET m A NE E n a et ee Format UE 0 00d Sd Amt RAS IAS EE EE EG T Saving Images 2 prariargggdgggg P d d rg TIPP RP IEGE OI PUN MC EUER ME EE ONCE E RU PONE mer Folder roii ae ale ren pera ee eee Save TEROOOT BMP CHi 5 0mw CHz 1400VBy Mi 10 0rns Ext 200 uv 24 Jan 07 4 35 lt C10Hz Figure 4 FP with a glass neutral density filter in beam path FP PD gain 10 MO Rb abs PD gain 100 kQ Room lights off Tweak the two steering mirrors to maximize the transmission signal through the cavity Your oscilloscope traces should be
52. signal can be handled as a difference of two dispersion signals with dis tinct line centers The Doppler broadening of Lorentzian ab sorption signals leads to the well known Voigt profile and a recent article describes various methods for comput ing these Given the need to compute the broadening of both absorption and dispersion signals and given modern compu tational environments the best route to a solution seems to be via the complex error function The change of variable 2 yin 2 t Avp vo voo transforms the integral above into the standard form exp t dt 1 de n Av 2 or vost A vp 2Vin 2 t v 2 vo Avp 2 ln 24y Av 2 In 2 e d A where yo ee or t x C y 2 vin 2 Av Avp 3 Integrals of this form lack antiderivatives but are related to the complex error function w z defined by w z exp z erfe iz exp z2 1 erf iz In fact the latest integral above is given very simply by 2 In 2 x Avp v voo and y D A Van Baak 734 og y or t x Fo d tO m Re w x iy or Im w x iy Since the complex function w z or at least erf z is avail able as a library function in some modern numerical analysis packages and since the real and imaginary parts of w z simultaneously provide the broadening of the absorption and dispersion lineshapes respectively this computational method has been u
53. simple as the model introduced so far since the data show not one but rather four absorption dips The structure observed is readily explained in terms of the actual structure of the rubidium D line This line arises from the 5s 15 5p Pis transition out of the ground state the combination of the isotopic composition of natural rubidium and the hyperfine structure of the states involved give rise to the lines displayed The two inner lines arise from the 72 15 abundant Rb isotope and the outer ones from the 27 85 abundant Rb isotope The two inner lines are sepa rated by about 3 6 GHz the Rb ground state hyperfine splitting similarly the outer lines are separated by about 6 8 GHz For the purposes of this paper these splittings can be taken as well known and they serve as a convenient way to calibrate the optical frequency scale Each of the four ob served absorption dips is broadened by two mechanisms common to all is the room temperature Doppler broadening of about 0 51 GHz and different for each is the unresolved upper state hyperfine structure which ranges from 0 09 to 0 42 GHz for the various lines Clearly enough is known about rubidium to permit a com plete quantum mechanical calculation of absorption disper sion and Faraday rotation such calculations are simplified by the cylindrical symmetry of the problem which leaves the magnetic quantum number m p a good quantum number even in the presence of t
54. that Faraday rotation offers an indirect but vastly easier way to detect atomic dispersion even for opti cally thin samples and that the Faraday rotation signal can be followed right through resonance The absorption and dispersion signals thus far computed are shown in Fig 2 in which axes have been normalized to natural values The horizontal axis gives frequency in units of the natural linewidth Av so that the absorption sig nal reaches half maximum and the dispersion signal reaches its extrema at ordinate 1 2 The dispersion shaped signal gives n v 1 in the units shown for reference the room temperature number density of rubidium is near N 2 5X10 m so that at a resonant wavelength of 4970 78X 107 m the factor N Aj87 has value 15X10 This means the computed index of refraction is confined to the range 1 75X10 and it shows that the y lt 1 assump tion made above is retrospectively justified With all these preliminaries we can now calculate the Faraday rotation signal and its frequency dependence Given the separate resonant frequencies 13 for the oppositely di rected circularly polarized fields E we can form the differ ence of refractive indices called for in 6 and write D A Van Baak 726 0 8 0 6 0 4 0 2 eo 0 4 0 2 o 0 2 0 4 Dispersion n v 1 in units of Na 8x Attenuation f v in units of Bmax 0 6 3 2 1 0 1 2 3 Detuning v v in un
55. the laser head Lower frequency modulation DC to 500 kHz is possible via the current modulation input on the front panel of the electronics box We have also provided a SMA to BNC adapter Though we have not experienced any problems you should always use extreme caution when modulating the laser via the direct SMA input We always worry about turn on transients damaging the diode Before applying AC power to the RF signal generator we make sure that the output amplitude has been set to its smallest value Then after AC power is applied the output amplitude can be increased 11 TeachSpin Fabry Perot Manual Rev 2 0 11 09 Tek MIM Stop Id Pos 351 5ms SAVE REC 3 7 i A action BURNS ET RS Se apes ata ee H Figure 12a Low Amplitude Current ui qud LR SD ME D iac File Modulation AE E RE UE g Format DEC IN Tr m ok a EMP Modulation of diode laser current at About low amplitude and 5 MHz aoe frequency has put sidebands on the 2 teles laser s optical frequency These are Folder separated from the carrier Ey flys Gone Fob 1f od 7 frequency by 5 MHz and are em hh hi hh mh hh htt n aye X das ee a WP ME ME TERD1BMP revealed by their ability to excite the CHa Ao M iims Ext 138V FP cavity 25 Jan 0 0000 lt 10Hz Tek i E Ready M Pos2942ms SAVEFREC Figure 12b Increased Amplitude Modulation with larger amplitude Note that sidebands of order 1 are About now dominant and sideb
56. the piezo stack is the sum of the voltage set by the DC OFFSET controls and the voltage from the modulation input To avoid overdriving the stack both positive and negative voltage clamps have been built into the electronics These are 110V and 6V respectively When used with the triangle wave from the Ramp Generator the clamps may clip the triangle wave at the top or bottom depending on the DC OFFSET of the Piezo Control Thus it is essential that you monitor the output on an oscilloscope The maximum amplitude change when using the 10 V p p Ramp output is 50 Volts The DC OFFSET FINE control and OUTPUT OFFSET are only needed when side locking the laser to a spectral feature In normal operation both these controls should be set to zero Rev 2 0 12 09 LF RAMP GENERATOR The Ramp Generator provides a bipolar variable amplitude and frequency triangle wave The frequency may be changed from 1 mHz to 7 kHz The maximum amplitude is 10 Volts peak to peak plus and minus 5 volts about ground The highest frequency output of the generator is 7 kHz Though the dials would lead you to believe that 10 KHz was the highest frequency At frequencies of 1 kHz and higher the high frequency Fourier components of the triangle wave are attenuated and you will observe a rounded triangle wave The high frequencies have little use in taking data and are only used to investigate the frequency response of the Piezo and Current controller The long sweep
57. through because its wavelength is not resonant with rubidium atoms allowed transitions at 780 and 795 nm So the laser needs to be tuned to reach the resonant condition In practice this works through a hierarchy of mechanisms 0 is to pick the right semiconductor 1 is to hold the laser at the right temperature 2 isto vary the current driving the diode laser emission 3 is to use a diffraction grating to create optical feedback into the laser selectively for the desired wavelength 4 is to use a piezoelectric element to tilt the grating ever so slightly In fact mechanisms 2 and 4 are both electrically actuated so it s possible to treat a working diode laser system as a black box with a variable control voltage going in and a voltage dependent optical wavelength coming out Diode Laser Spectroscopy David Van Baak July 2009 The application of a sawtooth waveform to this black box will give an output beam whose optical frequency also undergoes a sawtooth in time i e it scans up and down in optical frequency And it s easy to accomplish the whole scan every 10 100 ms so the laser s frequency is agile as well as variable Now it s rarely possible to get a diode laser system to scan over any very long interval in wavelength even a scan from 780 to 795 nm for rubidium spectroscopy would be asking too much In fact it s time to think in terms of optical frequency instead such a scan would extend from 384 000 GHz down
58. through the coils and with three different polarizer angles The theory still needs work when the polarizer angle is zero probably because the theory is too simplistic for a multilevel atom But it gives reasonable results when the polarizer is not quite at zero angle 2 Analysis We have the complex index of refraction for an atomic gas given by n mno l 4 ik ngo Finok where ng and amp are real quantities given by 2n w w2 N fe m i uy AA n AUN fe mwo Aw 72 4 no 1 kgl caltech edu URL http www its caltech edu atomic Tek EIGT R E 198 Acqs j WI S00mV h2 i 00mV Ma 00ms Cha X 702mV 27 jul 2001 09 05 39 Figure 2 Transmitted light as a function of frequency scanning over all four rubidium absorption lines The B field is zero and the cell temperature is about 40 C The background slope comes from scanning the laser current together with the scan of the grating position 1 AAw Aw 2 4 2n N fwye m w w2 3202 x N frye 2muwo Aw y A Ay 2 Aw 72 4 near the atomic resonance where Aw w wo These are plotted in Figure 3 This is the index of refraction for a dilute atomic gas which of course is proportional to the atom density N Note that a relation ng 1 24Awk exists between the index of refraction and the attenuation which is independent of the oscillator strength of the atomic transition This relation showing that no v and amp v
59. times were incorporated for use in slow temperature sweeps of the laser The reset toggle switch stops the triangle wave generator and takes the output to the minimum value This is useful in starting and stopping slow sweeps The reset can also be used to disable the sweep This is useful when you are trying to observe the fringes while setting up an interferometer The SYNC output provides a 5 to 5 volt square wave that can be used to trigger an oscilloscope Ramp Generator Noise The rms noise on the ramp generator output is about 50 uV rms If you use the Ramp Generator to provide a simultaneous Current and Piezo sweep of the laser frequency while observing very narrow Doppler free features 12 MHz or less the lines will be slightly broader than when doing only a Piezo sweep If you wish to observe very narrow Doppler free features you should use the Ramp Generator to sweep the Piezo only Rev 2 0 12 09 II Photodiode Detectors and detector low pass dc level Electronics II A PHOTODIODE DETECTORS Photodiodes Photonic Detectors Model PDB C108 Active Area 0 25 Diameter Circle Responsivity about 0 6 A W 1 7 W A at 800nm Gain 10 MQ to 333 Q The photodiode detectors contain a current to voltage converter The switch on the back of the detector allows gain setting of 10 MQ to 333 in ten steps Table 3 lists the high frequency 3dB points and noise for the different detector gains The detectors have separate signal and power cabl
60. where f is a standard fudge factor called the oscillator strength of the transition Adding the oscillator strength factor makes this simple classical calculation agree with a more realistic quantum mechanical calculation The oscillator strength is of order unity for strong transitions like the S P rubidium lines and is much smaller for forbidden atomic transitions Both the oscillator strength and the damping factor y are difficult to calculate for real atoms since doing so requires quite a lot of detailed atomic physics Maxwell s equations MKS units for a propagating electromagnetic wave give us OE V E ue 0 Prag and we define an index of refraction n c v 4 eu eoug where v is the speed of wave propagation Assuming u Lg 1 and the above expression for the dielectric constant e eo we find ourselves with a complex index of refraction which we write n y e eg no 1 ik 2 where no and amp are real quantities Evaluating Eqn 1 gives Re vVe e0 mo Page 1 21 w w2 N fe m a PT CE TAwN fe mwo Aw y fA Im w e eo nok 2n NN fwye m w w2 Pu x N frye 2mwo AGREE where Aw w w These are plotted in Figure 1 This is the index of refraction for a dilute atomic gas 1 Se dem R R which of course is proportional to the atom density lt H 5 0 5 Aw y Figure 1 Plot of the absorption no amp and refractive index change no 1 for a gas near an a
61. where they do not absorb the probe beam in fact they increase the probe beam intensity via stimulated emission Thus at v 2v the probe absorption is ess than it was without the pump beam If the pump beam had infinite intensity half of the atoms would be in the excited state at any given time and there would be identically zero probe absorption One would say these atoms were completely saturated by the pump beam hence the name saturated absorption spectroscopy The advantage of this form of spectroscopy should be obvious one can measure sharp Doppler free features in a Doppler broadened vapor IIl QUALITATIVE PICTURE OF SATURATED ABSORPTION SPECTROSCOPY MULTI LEVEL ATOMS If the atoms in the absorption cell had a single ground state and two excited states typically an electronic level split by the hyperfine interaction and the separation of the excited states was less than the Doppler width then one would see a spectrum like that shown in Figure 3 The peaks on the left and right are ordinary saturated absorption peaks at v and v the two resonance frequencies The middle peak at v v 2 is called a cross over resonance Rev 2 0 11 09 If you think about it for a while you can see where the extra peak comes from It arises from atoms moving at velocities such that the pump is in resonance with one transition and the probe is in resonance with the other transition If you think about it a bit more you will see t
62. which you will calculate as a prelab problem are given by Tei He pea 5126 E Q eR 1 Re where E is the amplitude of the incident light and 6 2r L A is the phase shift of the light after propagating through the cavity we assume the index of refraction is unity inside the cavity The transmitted light intensity is then 2 2 I E Te Io Ei x 1 Red The cavity transmission peaks when e 1 or equivalently at frequencies Vm mc 2L where m is an integer c is the speed of light At these frequencies the cavity length is an integer number of half Page 1 Figure 1 The basic Fabry Perot cavity The curved surfaces of the mirrors are coated for high reflectivity while the flat surfaces are anti reflection coated and have negligible reflectivity The curved lines inside the cavity represent the shape of the resonance optical mode wavelengths of light Note that the peak transmission is J Io 1 regardless of R The separation between adjacent peaks called the free spectral range is given by AvrsR Vmqi Vm c 2L If the mirror reflectivity is high for our cavity mirrors it is approximately 99 5 percent then the trans mission peaks will be narrow compared with Avrsg The full width at half maximum Av fwhm i e the separation between two frequencies where the transmission is half the peak value is written as AV fwhm Avrsr F where F is called the cavity finesse If
63. will stop this feedback from getting into the laser but it is not essential for operation of the system Another technique to reduce feedback is to put more ND filters in the beam path An added filter attenuates the reflected beam twice once on the way out and again on the return trip Tek JL Stop M Pos 3470ms SAVE REC Action Save Image File Format BMP About Saving Images Select Folder Save TEKOO10 BMP cHi EA CAS Tey 7 12 Nov 08 0452 lt 10H2 Figure 6 When the anti parallelism is too close to perfect there is feedback into the laser that corrupts the frequency sweep The staircase appearance of the absorption profile is the indication of this If you have set up the second photodetector you will now be able to use an electronics trick to isolate the SAS features To preview this capability send the two photodetector signals to the two channels of an oscilloscope and adjust things until you can see what s similar about the two signals and what s different Now you are ready use the detector electronics section of your electronics box to isolate that difference You will be subtracting out most of the broad absorption signal Put the signal from Detector into the minus input and that from Detector 2 into the plus input of the detector section of the electronics box Attach the monitor output to the scope Set the plus balance control to zero and the minus balance control to one and ob
64. with optical isolator in place The turning point of piezo scan shown by the arrow on the upper margin is near the center of the scope trace Tek Al Tria d M Pos 5 a rns SAVE REL Saving Images Select Folder CHiw2 mw CHe 2 00vBy Ext X Trbmv 2d Jan T 22 47 lt 10Hz Figure 7 Cavity length increased by five turns of one lens tube 9 TeachSpin Fabry Perot Manual Before the next traces were made the other end mirror was turned out four turns making the cavity even longer Note the change in scale of the y axis for the FP signal It has changed from 20 to 200 mV per division Evidently as the cluster of modes coalesce the intensity in the peaks increases dramatically Here the highest peak has gone from about 85 to 360 mV Now you ought to check that you are not sweeping too fast through the Fabry Perot transmission peaks At a Gain of 10 MQ the PD has a 3dB bandwidth of about 5 kHz We might estimate a resolvable pulse width to be about one half the period or about 100 us In practice we observe the FP transmission peaks on the scope and watch the peak heights while changing the sweep speed As the sweep speed is reduced the peak height will increase Keep reducing the sweep speed until no further increase in peak height is observed Figure 9 shows a scan through two transmission peaks The tails have moved to the other side of the peaks indicating that the cavity is now too long You
65. 0 5 GHz Doppler width The method involves splitting the laser beam into a strong pump beam and a weaker probe beam arranged to cross each other at an angle of nearly 180 at a location occupied by rubidium atoms Now with milliWatt levels of optical power available the pump beam is intense enough to cause a non trivial depletion of the number of ground state atoms in the particular velocity class with which it s in resonance And the probe beam can sense this population depletion as a decrease in the amount of absorption that would ordinarily occur But that effect occurs only if the pump beam and the probe beam are interacting with the same sample of atoms and because of the Doppler effect that can only occur for atoms having v 0 By this saturated absorption effect it s possible to resolve below the Doppler limit and to see quantum transitions with a spectral width Af lt 0 01 GHz This is occurring at a laser frequency f 384 000 GHz and so we can form a figure of merit or quotient called the spectral resolving power finding f Af gt 4 x 107 Even at this superb resolution it s still not the laser which limits the frequency width Rather the natural width of the quantum transitions related to the finite lifetime of the upper states provides the next limit on resolution of Af 0 006 GHz But at this higher level of resolution there s yet more to be learned about atomic structure With the Doppler limit surpas
66. 009 Thinking about Saturated Absorption and Crossover Transitions Barbara Wolff Reichert Rev 2 0 11 09 Any discussion of saturated absorption spectroscopy must begin with a reprise of the source of the Doppler broadening of absorption features In absorption spectroscopy a beam of laser light which we will call a probe beam is sent through a gas sample in our case a mixture of Rb and Rb vapor into a photodiode detector The frequency of the light emitted by the diode laser is then modulated As the frequency of the laser probe beam sweeps through the frequency equivalent to the energy needed for a particular transition of the gas photons from the beam will be absorbed and the atoms excited to a higher energy state Of course this energy is quickly reradiated as the atoms return to the ground state The energy however is reradiated in all directions This three dimensional re radiation creates a dual phenomenon a line of fluorescence appears along the path of the photon beam and the intensity of light reaching the photodiode detector decreases significantly For the TeachSpin Saturated Absorption experiment the central frequency of the laser sweep is selected to stimulate a transition from the S15 to P355 energy state Were all the atoms at rest with respect to the beam a graph of light intensity reaching the detector vs the frequency of the laser would show a single sharp dip at the exact transition frequency fo The axes of a
67. 2mV oom 1000 800 600 400 200 0 200 400 600 800 1000 e 25 0kS s 244 Acqs T 2t A 1 74 V 1 3 A to coils nd polarizer 10 deg A s00mV Ch2 i 00mv M4 00ms Ch4 X 702mV 27 Jul 2001 Doo 800 600 400 200 0 200 400 600 800 1000 09 13 52 e 25 0kS s 28 Acqs T 3 2t T T A 1 74 V 1 3 Ato coils ov pos polarizer 10 deg 0 05 0 04 0 03 0 02 0 01 i H i 0 so0mv Ch2 i 00mv Ma b ms Ch4 X 702mV 27 jul 2001 1000 800 600 400 200 0 200 400 600 800 1000 09 14 09 Figure 4 Left Data showing light transmission as a function of laser frequency with 1 3 A going through the coils The polarizer angle was 0 top 10 degrees middle and 10 degress bottom Right A model of one absorption line indicated under conditions like those for the data whose only impact on the electric field is a global reversal of its direction should not alter the relative spacing of field lines in a CFLD Since the sign reversed version of Fig 6 must show uniform spacing of the outgoing field lines on the 4 charge equatorial clumping does not show the in variance under charge reversal that would be expected of a true field property Phillip M Rinard Delbert Brandley and Keith Pennebaker Plotting Field Intensity and Equipotential Lines Am J Phys 42 792 793 1974 While charge distributions lacking a monopole moment possess divergent field lines such as the 0 0 and 6 7 lines in the dipole such lines are few
68. 4 No 6 June 1996 e a 0 2 0 2 0 4 0 6 0 8 0 6 0 4 0 2 0 2 0 4 3 2 1 0 1 2 3 Detuning v v in units of natural width Av Difference n v n v in units of NA 8xDispersion n v 1 in units of NA 8r Fig 3 a Dispersion curves for the two circular polarizations of light in the Zeeman split model atomic system in the absence of Doppler broadening computed for the particular choice of magnetic field strength e 4a7m B Av 2 b The Faraday rotation angle computed from the curves in a showing the characteristic symmetric signal predicted for reso nant Faraday rotation Actual materials with electronic structure much more com plicated than that modelled here do in fact follow the Bec querel form of V quite closely except for a multiplicative correction factor the magneto optic constant y generally somewhat smaller than unity It is worth noting that the wavelength dependence of Faraday rotation is given by the dimensionless quantity dn d and that its scale is fixed by the combination of fundamental constants 293 34 rad T m 1 0084 arcmin Oe cm 24 2m c These results for small field B also make it clear why Faraday rotation can be so enormously enhanced near an atomic resonance First the index of refraction n departs maximally from unity near a resonance and second it does so with a dispersive shape going from maximum to mini mum in a frequency span of only the natu
69. 456 2 3911 47 070 44 630 42 340 40 170 38 130 36 190 34 370 32 660 31 030 29 500 28 060 4 1239 4 0848 4 0447 4 0034 3 9611 3 9175 3 8731 3 8279 3 7814 3 7342 3 6863 28 29 30 31 32 33 34 35 36 37 38 2 3375 2 2841 2 2315 2 1786 2 1268 2 0760 2 0250 1 9756 1 9269 1 8783 1 8308 8779 26 690 25 400 24 170 23 020 21 920 20 880 19 900 3 6372 3 5876 3 5367 3 4858 3 4336 3 3808 3 3278 39 40 41 42 43 44 45 5546 1 7837 1 7382 1 6922 1 6479 1 6044 1 5619 1 5203 18 970 18 090 17 260 16 470 15 710 15 000 14 330 13 680 3 2741 3 2200 3 1658 3 1111 3 0552 3 0000 2 9449 2 8885 46 47 1 4794 1 4393 1 4000 1 3618 1 3243 1 2878 1 2519 1 2170 4369 13 070 12 500 11 940 11 420 10 920 10 450 10 000 2 8327 2 7118 2 7211 2 6657 2 6099 2 5550 2 5000 1 1829 1 1497 1 1174 1 0858 3099 1 0552 1 0254 Table 1 Thermistor Resistance and Bridge Voltage versus Temperature Rev 2 0 12 09 LB 4 Laser Temperature Electronics Advanced Details The circuit is a modification of that described by C C Bradley et al Review of Scientific Instruments 61 2097 1990 The PID control parameters were determined from the Zeigler Nichols closed loop tuning method and then tweaked to give better performance These parameters give adequate performance but they are not guaranteed to be optimal especially if you operate your laser
70. B The Detectors Your apparatus is supplied with three photodiode detectors The detectors contain current to voltage converters The detector response is linear when the voltage output signal is between 0 and 11 0 Volts so you want to make sure you are no where near the 11 0 saturation voltage A switch on the back of the detector allows you to change the gain setting from 10 MO to 333 Q in ten steps The detectors have separate signal and power cables Three DETECTOR POWER plugs are on the front panel of the controller You can send the detector signal directly to an oscilloscope or to the DETECTOR MODULE of the Controller C The Absorption Cell Assembly The absorption cell assembly consists on an outer glass cylinder an insulation layer a heater assembly a cold finger a thermocouple to monitor the temperature and the gas filled Rb cell itself The cold finger is a small piece of metal that fits over a small protrusion on the side of the cell Because the metal is a good conductor and stays cooler than the cell any excess rubidium will condense in the protrusion rather than on the windows of the cell The heater is both powered by and monitored from the controller D The Magnetic Field Coils The magnetic field coils are a Helmholtz pair which produces a uniform field at the Rubidium cell They are used in experiments such as Resonant Faraday Rotation and Zeeman Splitting and must be powered by an external power supply The Absorption Cel
71. Connect a Photodiode Detector PD cable to the DETECTOR POWER output of the laser controller and connect the Photodiode Detector output BNC to Channel two 2 of the oscilloscope Set the Channel two 2 input coupling to DC the gain to 5 Volts div and the vertical position so that ground is in the middle of the oscilloscope display The signal from the Photodiode Detector is negative and saturates at about 11 0 volts Jf you are uncomfortable observing a negative going signal you can always use the invert function on your scope You can check that the piezo is actually moving by doing the following With the Ramp generator connected to the Piezo modulation input turn the AMPLITUDE of Ramp to zero change the ramp frequency to about 3 kHz And then increase the AMPLITUDE You should be able to hear the piezo vibrate WARNING Do not leave the piezo running at high frequency and amplitude for a long time It will cause heating and damage to the piezo Rev 2 0 11 09 2 Put the Photodiode Detector in place to intercept the laser beam coming through the Rb cell You can move the PD for alignment You will have to adjust the Gain on the back of the PD Make sure that the beam is hitting the sensor and bolt the photodetector down Operating note In the present configuration there is a very high intensity beam power per unit area going through the Rb cell This much power saturates the transition resulting in very little total abs
72. DG TEMP C Filter RDG FLTR 16 Control OUT1 CTRL PID Proportional Value OUT1 PROP 005 8 Reset Value OUT1 REST 0480 Seconds Rate Value OUT1 RATE 090 0 Seconds Cycle period OUT 1 CYCL 0001 Damping Value OUT1 DPNG 0005 We have chosen the PID values P Proportional I Integral reset D Derivative rate for reasonable temperature stability without the extra 1 2 hole foam inserts in place III F MAGNETIC FIELD COILS The Helmholtz magnetic field coils were designed to provide a field of about 10 mT at a current of three amperes 3 0 A The average radius of a coil is 3 44 87 4 mm There are 320 turns of 18 gauge copper wire on each coil 16 turns per layer and 20 layers The room temperature resistance of each coil is about four ohms 4 Q The terminal block on the side of the cell holder can be used to connect to the coils You will have to provide your own power supply to energize the coils For the Helmholtz configuration we estimate the field in Gauss from B Gauss 0 9 N turns per side I A R cm Rev 2 0 12 09 IV Optics Table 5 lists the optical components included in the complete instrument The thin film components Wratten neutral density filters linear polarizers and quarter wave plates can be damaged by the full power of the laser You should attenuate the beam before sending through one of these components STOCK MATERI FLA
73. E 5 EE E ig Ege t7 1 r xz 0 RE sO 1 Ez Wa E E E EE AE We can represent a polarizer using matrix notation in which the output fields after going w through the polarizer are Le le Lo oll i E FO Op ee Ey out io 0 1 Ey in for x and y polarizers If we use a y polarizer rotated by an angle 0 the matrix becomes cos sin 0 0 cos sin sinf cos 0 1 sin cos zs 0 60 24 the latter for small 0 Now we put all the pieces together We start with x polarized light and represent it in terms of two circular polarizations coe 1 Ab 1e Sd s When this light enters the cell the different circular polarizations propagate differently because of the Zeeman splitting Thus the field becomes E g i ecco L ewer re 2G Aw 6 1 E Agi 1 cepe exp t 2 iexp 74 iexp 7 5 and 6 B is the frequency shift from the Zeeman splitting Finally we hit this with the output polarizer and the final field is IMS L0 98 exp T exp T_ UU 0 1 iexp T4 iexp T Il Il where 2 1 i exp 74 exp 7 2 exp 7 exp 7 4 exp 774 exp 7 The final intensity is then the absolute square of this field 1K SW 25 UKs S 83 ACGS E T 21 T A 14 V o DR d zero B field polarizer O deg i s0 my Che 1 00mV IMADOM Chase 20
74. Faraday rotation is very small at large detuning and right near a resonance line since absorp tion in the vapor is very large there But because absorption drops off with detuning more rapidly than does the Faraday 734 Am J Phys Vol 64 No 6 June 1996 rotation signal it is possible for the cell to offer small ab sorption at two points on either side of the resonance where Faraday rotation is still as large as 90 The result is that the sandwich becomes nearly transparent to light in two spectral regions each only a few GHz wide this represents a pass band whose width is only a few parts per million of the optical frequency Filters like these have been proposed for systems involving laser communication with submerged submarines ACKNOWLEDGMENTS The development of this experiment was supported in part by National Science Foundation Grant No DUE 9255528 and thanks are also due to the participants in the diode laser workshop thereby supported for their comments on the experiment I also thank Hugh Robinson for helpful discussions about this paper and Leo Hollberg for the hos pitality that enabled me to write it APPENDIX The presence of Doppler broadening leads to the need to evaluate convolution integrals of the form d Av 2 or vg v 00400 C rey for absorption and dispersion signals respectively where g v9 is the normalized Gaussian function defined by 33 The further case of the Faraday rotation
75. I D 3 d Increase the laser current by 2 mA and search again If you still cannot find the retro reflection turn the TOP knob three turns in and search again Then turn the TOP knob out six turns this gives a net of three turns out from the starting position and search again I D 2 b Aligning the External Cavity Once you see the retro reflection adjust both the SIDE and TOP knobs so that the main beam and the retro reflection overlap You should notice an increase in the laser intensity when this happens You should also observe that when turning the TOP knob the main and retro beams move in opposite directions and when the SIDE knob is turned only the main beam moves Rev 2 0 12 09 I D 2 c Measuring the Threshold Current Threshold current measurements are used to set the lens position Again use the setup shown in Figure 9 Dim the room lights and reduce the laser current to just above threshold Connect a voltmeter to the laser current in the MONITORS section of the front panel Adjust the TOP and SIDE knobs to find the region of maximum laser intensity Reduce the current until it is again just above threshold Use the 5 64 Allen wrench as shown in Figure 2 of Initial Setup to gently change the knob positions A flicker in the laser spot indicates that the laser is passing through a series of modes You should be able to observe six or more vertical modes as you move the TOP knob and tens of modes as you move the SIDE knob Posit
76. ID The tube is threaded at each end 0 535 by 40 threads per inch These threads accept Thor Labs adjustable lens tubes model SM05V05 High reflectivity curved cavity mirrors have been placed into each lens tube and are held in place with a threaded retaining ring Both the lens tubes and the retaining rings have been shipped with the threads fully engaged and tightened You will find removable plastic caps covering the ends of the lens tubes When you first unpack your cavity remove the end caps and inspect the mirrors Make sure the retaining ring has not become loose during shipping CAUTION Do not scratch the mirrors with the retaining ring tool The lens tube should also be fully threaded in The end caps should be used to protect the mirrors any time the instrument is not in use You may want to keep them in place for the first part of the set up 3 TeachSpin Fabry Perot Manual Rev 2 0 11 09 Setting Up the Fabry Perot Cavity for the First Time To set up the cavity you will need to use the Diode Laser the rubidium absorption cell and two photodiode detectors along with the Fabry Perot system Figure 1 shows a convenient layout You are welcome to devise your own but alignment will be simplified if you put the Fabry Perot s input mirror close to the second steering mirror Before starting be sure that the lens tubes are fully threaded in This will mean that the cavity is set for its minimum length The oscilloscope traces inclu
77. INPUT to 1 0 fully CW Set the GAIN to 1 Connect a BNC Cable from the MONITOR connector above the gain triangle to Channel 1 on the scope 3 15 Rev 2 0 11 09 Change the BALANCE knob and observe the effect on the scope Position a second Photodiode Detector to intercept the beam that has been split off by the Beam Splitter Connect the power cable of the detector to one of the open ports Connect the BNC from Photodiode Detector 2 to the or left most DETECTOR INPUT Set the BALANCE knob above the INPUT to 1 0 fully CW and turn BALANCE knob above the INPUT to 0 Adjust the Gain on the back of Photodiode Detector 2 for a good 2 6 volts level signal on the scope and position the photodiode for a maximum signal Now increase the BALANCE knob above the INPUT to 1 0 and adjust the BALANCE to get a spectrum like the one is Figure 14 Tek Stop E oov MB 0oms A Ext 7 800mV Figure 14 Trace for Channel 1 only showing the combined signal from the detectors Subtracting the signals removes the effect of ramping the current The beams reaching both detectors are varying at the same rate and the BALANCE controls are used compensate for any difference in intensity The trace shows an excellent correspondence to the expected spectrum with all four Rb absorption dips on a flat background Note however that the subtraction technique does not immediately give an absolute measurement of absorption whi
78. If the laser frequency is constant then the fringe pattern goes through one cycle 1 cos every time the arm length changes by 4 2 Problem 3 If AL is fixed how much does the laser frequency have to change to send I through one brightness cycle For your known AL what is the fringe period in MHz From this you can convert your Page 11 measurement of AL into a calibration of the laser frequency scan Use the two oscilloscope traces to plot the interferometer fringes and the saturated absorption spectra at the same time as you scan the laser frequency Watch that the interferometer fringes are uniform as a function of PZT voltage if not the nonlinearities could compromise your calibration Zoom in on the hyperfine features you want to measure You will need to know which features belong to which lines so identify the features by comparing your spectra with the level diagrams in Figures 7 and 8 Print out some good spectra measure the spacings of the various features using a ruler and you can turn this all into a direct measurement of the hyperfine splittings Try to do this for both lines 87b and 85b in Figure 7 Note there are no tricks or complicated math in any of this You just have to understand what s going on and not lose any factors of two No fair adjusting the answer by factors of two until it agrees with the known splittings Lab Exercise 2 Measure and record the largest P3 2 hyperfine splittings for 55Rb and Rb in
79. LIFORNIA Scanning Spherical Mirror Interferometers For The Analysis of Laser Mode Structure Introduction Scanning spherical mirror interferometers have become common tools for the analysis of laser radi ation They are very high resolution spectrometers and can be used to provide information concerning laser mode structure that is difficult to obtain using any other instrument For a variety of practieal reasons scanning spherical mirror interferometers have been diffi eult to use Recently however it has been found that certain special types of these interferometers are comparatively easy to use these special types of interferometers are mode degenerate inter ferometers Of the mode degenerate interferome ters the most useful is the confocal interferometer first described in a somewhat different form than is now common by Connes The principal reason for the interest in using scanning spherical mirror interferometers to study laser radiation is of course that the light emitted by most ordinary gas lasers is not perfectly mono ehromatic The beam from a typical gas laser con tains several discrete optical frequencies separated from each other by frequency differences of radio frequency magnitude 109 10 Hz These dif ferent optical frequencies can be associated with different modes of oscillation of the laser It is common practice to distinguish two types of laser modes longitudinal modes
80. MHz Estimate the accuracy of your measurement knowing the various uncertainties you encountered along the Way III REFERENCES Cohen Tannoudji C Dupont Roc J and Grynberg G 1992 Atom Photon Interactions Wiley H nsch T W Schawlow A L and Series G W 1979 The Spectrum of Atomic Hydrogen Scientific American 240 94 March Milonni P and Eberly J 1988 Lasers Wiley Schmidt O Knaak K M Wynands R and Meschede D 1994 Cesium Saturation Spectroscopy Revisited How to Reverse Peaks and Observe Narrow Resonances Appl Phys D 59 167 Page 12 Appendix I The Optical Isolator Mi H YY INPUT FARADAY OUTPUT POLARIZER ROTATOR POLARIZER Figure 11 Schematic picture of an optical isolator Not shown is the large longitudinal magnetic field in the Faraday rotator produced by strong permanent magnets inside the device The optical isolator is a somewhat subtle device which uses the Faraday effect The Faraday effect is a rotation of the plane of polarization of a light beam in the presence of a strong magnetic field along the propagation axis You can get a feel for this effect by considering a simple classical picture An incoming light beam imposes an oscillating electric field on the electrons in the solid which causes the electrons to oscillate Normally the oscillating electrons re radiate the light in the same direction as the original beam which doesn t change the polarization
81. MP beam saturates the transition Since fewer particles are available to absorb probe photons the intensity of the probe beam reaching the detector is increased and the signal spikes gt B A 9 o o gt v a o E S A N S e Crossover Transition PUMP Beam Absorbs PUMP fA Absorbs probe E Probe Beam for DETECTOR Absorbs PUMP photons as fo Absorbs probe photons as fo Lowers PUMP to fo Promotes probe to fo Oscilloscope Trace Figure 3 PUMP Beam 4 of 4 When a transition can be made from the ground state to two upper levels adding the pump beam creates three spikes within the Doppler curve Increases in transmission occur as expected at the two actual absorption frequencies fo and fo2 The third spike called the crossover transition occurs exactly halfway between the two At this frequency an atom moving with the proper velocity in the v direction can either Doppler shift the probe beam photons down to fo or the pump beam photons up to foo Thus at this crossover frequency fi the atoms available for absorbing probe beam photons is reduced More probe beam photons pass through the vapor and the detected intensity rises Similar reasoning describes the fate of atoms moving at the proper velocity in the v direction When three possible transition frequencies fall within a Doppler curve as in our rubidium vapor experiment six spikes are produced
82. Rev 2 0 11 09 TEACH SPIN til Instruments Designed for Teaching Diode Laser Spectroscopy Spectroscopy and Much More Using Modern Optics DLS1 A USER S MANUAL A PRODUCT OF TEACHSPIN INC Designed in collaboration with Professor Kenneth Libbrecht of the California Institute of Technology TeachSpin Inc 2495 Main Street Suite 409 Buffalo NY 14214 2153 716 885 4701 or www teachspin com Rev 2 0 11 09 DIODE LASER SPECTROSCOPY Instructor Student Manual Table of Contents 1 Diode Laser Physics I Laser Basics 1 1 II Lasers with Grating Feedback A Introduction 1 4 B Laser Tuning 1 4 1 Medium Gain 2 Internal Cavity 1 6 3 Grating Feedback 1 7 4 External Cavity 1 8 III References 1 10 2 Saturated Absorption Spectroscopy I Background 2 1 IL Qualitative Picture 2 Level Atoms 2 1 III Qualitative Picture Multi Level Atoms 2 2 IV Quantitative Picture 2 Level Atoms 2 4 V Atomic Structure of Rubidium 2 7 VI References 2 9 3 Getting Started Initial Setup and First Explorations I Overview of the Instrument 3 1 A The Laser B The Detectors C The Absorption Cell Assembly D The Magnetic Field Coils E The Controller F TV and Camera G The Optics and Connectors IL Initial Setup What to do first A Unpacking and Setting up the Laser 3 2 B Setting up the Absorption Cell Assembly 3 3 C Starting up the Laser 3 4 D Aligning the Laser 3 4 E Setting up to Observe Rubidium Fluores
83. T amp 1 the finesse can be shown from the above to be approximately 5 nV R I R gm T The results so far describe an ideal cavity in which there is no absorption or other loss of light inside the cavity The peak transmission of such an ideal Fabry Perot cavity is unity as can be seen above Introducing small losses in the cavity leads to the expression Tae PELLE 1 Ra e where a is a loss parameter the fractional intensity loss from a single pass through the cavity is equal to E 1 o This gives a peak cavity transmission Ipeak T 1 amp PT ge lo T ep Te Page 2 and a finesse nav R 1 o R T T c amp It is sometimes useful to think of the Fabry Perot cavity as an interferometer and it is also useful to Dd think of it as an optical resonator If the input laser frequency is not near Vm the beam effectively just reflects off the first mirror surface which after all does have a high reflectivity If the input is equal to Vm however then light leaking out from inside the cavity destructively interferes with the reflected beam Right after turning on the input beam the power inside the cavity builds up until the light leaking out in the backward direction exactly cancels the reflected input beam and the beam leaking out in the forward direction just equals the input beam neglecting cavity losses Thus at Vm the total cavity transmission is unity and the light bouncing b
84. TNESS OPTICS SOURCE OTHER NUMBER AL INCH Mirrors protected Float Scratch Dig aluminum Thorkaps DROI Glass 5 60 40 Beam Splitter Edmunds Scratch Dig 50 50 NIR Optics Te BS 1A 60 40 Beam Splitter Red Scratch Dig 2 Wedge Optronics NER d M4 60 40 Beam Splitter Red Scratch Dig 1 Wedge Optronics SES ES MA 60 40 Beam Splitter Rolyn Scratch Dig 0 0 1 4 thick Optics 2991029 HIER 80 50 Neutral Density NEIOB Schott 15 trans Filter Glass mE NG4 14 780 nm Wratten Neutral Kodak EK141 0042 Gelatin 33 trans Density Filter s filter 96 ND 0 7 Q 780 nm Linear Polarizer American 98 0440 HN 32 42 trans Polarizer 3M 0968 0 0 03 780 nm American 98 0440 Quarter Wave Pate sed dnizee GMY 10644 Table 5 Optical components We have only noticed damage when using the laser at high current without the grating attached There we have damaged both linear polarizers and the Wratten neutral density filters You should be very careful using these components for this laser configuration But this is not the normal mode of operation When operating with the grating attached to the laser we have not noticed any damage but we do observe some rather strange behavior at higher powers See discussion in section IVC on page 5 30 Rev 2 0 12 09 IV A MIRRORS Economy mirrors from Thor Labs have a reflectivity of about 85 We have noticed no effects of the rather poor surface flatness of these
85. Vv 24 Jan 23 21 lt 10Hz 24 Jan O0 23 27 10Hz Figure 10 Near optimal cavity length Figure 11 Expanded view of single peak from Figure 10 Figure 11 shows an expanded view of one of the peaks in Figure 10 Traversing one free spectral range FSR occupies about 40 ms of time The full width at half maximum of the peak shown in Figure 10 is about 300 us giving a finesse slightly greater than 100 If you try and reproduce this data you will find that vibrations in the air and room will distort the line shape Now you are seeing markers equally spaced on the optical frequency scale and they can serve to calibrate the frequency scale as soon as you can assign a numerical value to the free spectral range If you could measure L well enough you could compute this FSR from the equation Af c 4nL but there is a better method It involves modulating your diode laser to put sidebands on its heretofore monochromatic signal The TeachSpin diode laser is equipped with a special electrical input in the form of an SMA connector right on the diode laser head at which a modulating current can be injected We have used an RF signal generator which delivers a maximum RF power of 0 7 Volts peak to peak into 50 ohms or about 0 dBm 1 mW of power into 50 ohms It may be possible to damage the diode if more RF power than this is applied The laser current may be modulated at frequencies from 100 kHz to over 150 MHz through the SMA connector on
86. ab sorption curve and intuition hints and computation con firms that its width will increase from the natural linewidth to very nearly the Doppler width The consequence is that the absorption at line center must decrease by about the same factor of 100 by which the linewidth increases Less intu itively obvious are the results for dispersion though clearly the convolution must smear out the width of the narrow dis persion feature by a similar large factor Numerical evalua D A Van Baak 728 0 02 0 015 0 01 0 005 Attenuation B v in units of B 0 01 0 005 0 005 0 01 Dispersion n v 1 in units of NA 8x o 0 015 3 3 2 1 0 1 2 Detuning v v in units of Doppler width Av Fig 4 Graphs of the absorption a and dispersion b signals computed for the model two level atomic system in the presence of Doppler broadening The curves were computed via 34 and the numerical methods of the Ap pendix the horizontal scale is in units of the Doppler width Av and the vertical scales are in the same units as those of Fig 2 The curves are computed assuming a Doppler width Avp of 511 MHz and a natural line width Av of 6 24 MHz tions confirm this with the broadened dispersion curve reaching its extrema just outside the frequencies at which the absorption curve reaches its half maxima Just as for the ab sorption curve so too for the dispersion this hundredfold increase in widt
87. absorption feature is small as one would expect For larger pump intensities the feature grows in height and width The width increases because at high laser intensities the effect of the pump laser saturates on resonance and continues to grow off resonance thus the width of the feature increases an effect known as power broadening Finally it should be noted that calculating the saturated absorption spectrum for real atoms which must include optical pumping many different atomic levels atomic motion in the vapor cell and the polarization of the laser beams is considerably more subtle A recent paper by Schmidt et al 1994 shows much detailed data and calculations for the case of cesium Problem 1 Show that To f dr vo v when the pump laser intensity is zero from the formula above Page 5 Saturated Absorption Spectrum of 2 Level Atom Probe Transmission 4000 2000 0 2000 4000 Probe Transmission 400 200 0 200 400 v vg MHz Figure 5 Calculated saturated absorption spectra for two level atoms for 7 I Isat 0 1 10 0 316 10 1 10 3 16 10 and 10 10 The two plots show the same spectra with the frequency axis at different scales Note the overall Doppler broadened absorption with the small saturated absorption feature at line center Hint the integral is simplified by noting that T amp Av Dopp Problem 2 The above calculations all assume that the pump laser ha
88. ack and forth in the cavity is 1 T times as intense as the input beam Problem 1 Derive the above expressions for E and E as a function of when e 0 Hint write down a series expression that describes the sums of all the transmitted and reflected beams Use reflected and transmitted amplitudes r and t where r R and t T Then sum the series Use the fact that if the reflected amplitude is r for light entering the cavity then it is r r for light reflecting from inside the cavity why in one case light is going from in air into glass in the other case light is going from glass into air Also derive the peak cavity transmission Ipeqx Io and finesse F in the limit T e lt R Plot the transmitted and reflected intensities Ijpan Ig and Ire fiect Ip of a cavity as a function of for R 0 9 0 95 0 99 and 0 The Optical Spectrum Analyzer If we can scan the cavity length for example by attaching one mirror to a piezo electric transducer PZT tube as shown in Figure 2 then we can make an interesting gadget called an optical spectrum analyzer Scanning the spacing L which equivalently scans the phase 6 you used in your calculations then scans the cavity resonant frequencies Vm If the laser beam contains frequencies in a range around some ro then by scanning the PZT one can record the laser spectrum as is shown in Figure 2 Note that there is some ambiguity in the spectrum a single laser frequency vo pro du
89. also easily satisfied since the fields need to be uniform only over the few millimeter transverse extent and the few centimeter length of the laser illuminated ru bidium vapor The data displayed below were obtained using two old short solenoid coils each of length 90 mm and effective diameter 112 mm arranged as an approximate Helmholtz pair The coils were put in parallel to match the capabilities of an available power supply and required 41 V at 1 3 A to produce the desired magnetic field The gap be tween the coils allowed a Hall effect Gaussmeter probe to be inserted from the side of the coil where it could measure the longitudinal field right next to the rubidium cell alterna tively for a coil system of simpler geometry the magnetic field could be computed from the measured coil dimensions and current The Faraday rotation experiment clearly requires that the laser light used be linearly polarized upon reaching the sample cell and that its rotated direction of linear polariza tion be analyzed subsequent to the cell The input polarization requirement could be satisfied in many ways but the simplest is merely to use the intrinsic polarization of the diode laser emission for a diode laser at rated power the nominal polarization purity of gt 100 1 is easily sufficient for the experiment described here Thus a linear polarizer suit able for 780 nm Ref 21 is only optional another luxury is a 780 nm half wave plate allowin
90. am see Figure 1 Focus the TV camera on the card Dim the room lights and turn the laser current to zero Now increase the current while watching the TV monitor You will see a light spot that becomes slightly brighter as you increase the current Your diode laser is below threshold it is not lasing but only acting as an LED As you continue to increase the current you will observe a sudden brightening of the beam spot and the appearance of a speckle pattern characteristic of lasing Adjust the current so that the laser is just above threshold You can measure the laser current with a voltmeter A diode current of 50 mA will give 5 0 Volt output on the LASER CURRENT in the MONITORS section You can compare your measured value with the threshold current recorded on your data sheet A lower threshold current represents better optical alignment Do not be concerned if your threshold current is slightly higher than that recorded on your data sheet You will align the cavity in the next few steps after which you can measure the threshold current again 3 5 Rev 2 0 11 09 Note Your laser was shipped with the laser aligned It many cases it will need little if any adjustment The following steps will allow you to check the alignment and optimize it if necessary 5 Look at the laser head itself You will see two knobs protected by the plastic cover The upper or top knob controls vertical alignment The lower or side knob provides a wavelength selec
91. ands of E SE AE TO anu E orders 2 and 3 are also visible Ret eres E AEE EE peser e ma 7i For this magic choice of PW REL modulation amplitude the original carrier frequency now has a E T AE EE Mound eder uU eae NE pan ae D001 0 1 1 TEKDOT3BMP vanishing amplitude CHDI M 1 00ms Et X 160y 25 Jan 07 0037 10Hz Tek J E Ready MPos2352ms SAYE REC Action Figure 12c Maximum Amplitude Maximum Amplitude trace shown using expanded time scale Su Two successive traces of the Fabry rU c ME DN pete Perot transmission over the 3 Meca AMET Folder spectrum of the laser when it is ee Tram ME CNNETE NER frequency modulated by a 5 MHz t do ox 5o i ATEROOT4 EMP wave form of maximum amplitude catenin ms C ERI 25 Jan 07 00 20 Hz Figure 12 Modulation of diode laser current at low medium and maximum amplitude and 5 Mhz frequency 12 TeachSpin Fabry Perot Manual Thus far you have seen the results of exciting the bow tie modes of the cavity which are spaced at Af c AL Figure 13 shows the scan for a well tuned cavity If your isolation between laser and cavity is good enough so that feedback is minimal you can try exciting the on axis modes A ray diagram for an on axis beam would show a round trip distance of 2L In that case the modes should occur at frequency spacing c 2L which is twice as big as what we have been seeing By tweaking your steering mirrors you may be able to find this on a
92. ant the laser intensity will decrease as the temperature is increased LB 1 Specifications Temperature Range O to 60 C Temperature Stability better than 0 05 C Control process Proportional Integral Derivative Adjustment Back Panel Potentiometer Thermo electric cooler 20W Q 2 5 A Sensor 10 kQ thermistor Modulation Input 12 kQ Input Impedance 5 V in 1 Volt Set Point Voltage Change The overall gain is the uppermost curve in figure 5 of section 1 Diode Laser Physics t This is a useful number if you wish to tune the laser to a new wavelength This estimate appears to be a severe restraint on the temperature In practice the temperature stability needed is less restrictive First the external cavity modes trump the temperature variations of the internal modes Secondly there is a natural time scale for changing the temperature of any object In an analogy to electronic circuits a time constant may be defined as the product of the thermal resistance and the heat capacity If we model the thermally connected parts as a cubic piece of aluminum this leads to the following expression The mass of the mirror mount cold plate and collimation tube assembly is 168 grams which gives a time constant of about 20 seconds Since we typically sweep through the absorptions in a time interval of about 0 1 sec the amount of temperature change possible is small For an optical cavity A 2L m where L is the cavity length and m i
93. arge must s ya be in order to have a transmission of 1 2 i e s s 2 initial final initia V ATOMIC STRUCTURE OF RUBIDIUM The ground state electronic configuration of rubidium consists of closed shells plus a single 5s valence electron This gives a spectrum which is similar to hydrogen see attached Scientific American article For the first excited state the 5s electron is moved up to 5p Rubidium has two naturally occurring isotopes Rb 72 percent abundance with nuclear spin quantum number J 5 2 and Rb 28 percent abundance with J 3 2 2841 L The different energy levels are labeled by term states with the notation where S is the spin quantum number L is the spectroscopic notation for the angular momentum quantum number i e S P D for orbital angular momentum quantum number L 0 1 2 and J L S is the total angular momentum quantum number For the ground state of rubidium S 1 2 since only a single electron contributes and L 0 giving J 1 2 and the ground state S y For the first excited state we have S 1 2 and L 1 giving J 1 2 or J 3 2 so there are two excited states P and P Spin orbit coupling lifts splits the otherwise degenerate P and P levels See any good quantum mechanics or atomic physics text for a discussion of spin orbit coupling Rev 2 0 11 09 The dominant term in the interaction between the nuclear spin and the electron gives ris
94. arrow in Figure 2 creating electron hole pairs that recombine in the active layer emitting light in the process The light is confined to a narrow channel in the chip 2 microns high 10 microns wide and about 400 microns long wavy line in Figure 2 The facets of the chip at the ends of the channel act as partially reflecting mirrors enclosing the laser cavity Near field pattern Perpendicular transverse mode Parallel transverse mode Figure 2 Schematic view of a laser diode chip Figure 3 shows a schematic picture of the actual semiconductor layer structure in a diode laser How all this really works the nitty gritty semiconductor technology is not something we will concern ourselves with in this discussion Since light generation in a diode laser results from the recombination of electron hole pairs injected into an active layer at the diode s n p junction the wavelength of the emitted light is approximately that of the band gap of the material The electron hole population inversion is restricted to a narrow strip in the active layer so the laser s optical gain is spatially localized Gain is the amount that an optical wave is amplified by stimulated emission as it passes through the laser cavity The diode heterostructure also serves as an optical waveguide the active layer has a higher index of refraction than its surroundings so light is confined to the channel by total internal refection The cleaved facets at
95. aser just to get a feeling for what the fringe pattern looks like Follow the set up in Figure 4 starting out without the negative lens and without the neutral density ND filter Make sure the beam goes through the centers of the rubidium cell windows where the optical quality is best In keeping with Page 6 what you found in Problem 1 above make sure the two arms of the interferometer are about the same length Check that the laser is tuned on resonance by blocking one arm of the interferometer and putting the ND filter back in You should then see a nice absorption spectrum on the photodiode when you scan the laser Adjust the mirrors so the two beams overlap on the second beamsplitter and then adjust the second beamsplitter so the two beams are collinear If the beams overlap well at the beamsplitter and the also overlap some distance downstream from the beamsplitter then you know they must overlap everywhere Iterate these steps so the two beams are overlapping and collinear as best you can At this point you should start to see fringes on the interfering beams Put in the negative lens to expand the beam before it hits the photodiode This makes it easier to see the fringe pattern and you can adjust the interferometer so that broad fringes are seen They should be broad enough so that the photodiode only samples a small part of a fringe 50 50 Rubidium Cell Photodiode Figure 4 Optical layout for the main part of the lab T
96. at temperatures far from room temperature 1 B 4 a Changing the PID Control Parameters To change the PID control parameters the top cover of the electronics box must be removed Because of the high voltage in the box we require that you turn off the AC power and unplug the electronics from the wall outlet before removing the top cover Four side screws hold the top cover in place When looked at from the front the temperature control board is located on the back left hand side Three 1 metal film resistors are used to set the control parameters These resistors are held in a series of terminal blocks see picture below Derivative Integral Gain y TT Figure 4 Picture of temperature control board showing terminal blocks There are two terminal blocks wired in series for each parameter The value is the sum of the resistances in each block This allows for fine tuning of the parameters In the Zeigler Nichols tuning method both the derivative and integral term need to be disabled The terminal blocks labeled Der Off and Int Off are used to enable or disable the derivative and integral control parameters respectively To turn a parameter off you must remove the wire from the terminal block AND cut the wire loop that is located just underneath the block To re enable these terms the wire loops must be reinstalled As shipped the wire in the block and the loop underneath it are redundant Both allow the parameter to be active
97. ator See appendix A for one technique of adjusting these components Figure 6 shows a made trace after the linear polarizer and quarter wave plate were inserted and adjusted to reduce feedback into the laser The horizontal scale has been expanded from Figure 5 The scan has been shifted so that the turning point of the piezo scan which is shown by the arrow on the upper margin is near the center of the trace In this section of the scan the grating first lengthens then shortens the wavelength of the laser You might notice that the long tails of cluster of modes stretch towards the long wavelength side of the spectrum This tells us that the cavity length is not at the confocal condition and needs to be lengthened A tail to the short wavelength part of the scan would indicate a cavity that needed to be shortened When you have determined whether the cavity is too long or too short change the length by tuning one of the adjustable lens tubes on either end of the cavity Watch the scope display as you do this Figure 7 shows the scan for our cavity with one adjuster rotated 5 turns You can put small pieces of masking tape on the lens tubes to keep track of how far you have turned them Tek MM Trig d M Pas B a rms SAVE REC Action Saving Images Select Falder Save i TEHRUDUS BIIP CHi 20 0m CHz42 00wBy Mi 5 ms Ext 1T mVv 24 Jan r 22 45 Hz Figure 6 Oscilloscope trace
98. be quite close to confocal The tolerance on the mirror spacing depends on the length of the interferom eter and its finesse For very short high finesse interferometers the mirror spacing should be set to within a few wavelengths In practice the ad justment of length is quite easy to make The mir ror spacing should be set so that it is approximately confocal By observing the mode structure of a la ser on an oscilloscope the final adjustment of the mirror spacing can then be made to maximize the P finesse of the interferometer Once the separation of the interferometer mirrors is set it needs no further adjustment The actual use of confocal interferometers is quite simple basically they need only be placed in a laser beam and adjusted so that the beam is re flected more or less back on itself With a relatively crude alignment fringes will be obtained To achieve the maximum finesse the angle should be adjusted fairly carefully to ensure that the inter ferometer axis is close to the axis of the incident beam To perform the fine angle adjustment it is convenient to mount the interferometer on an ad justable angle mirror mount It is usually desirable to put an optical isolator such as a circular polarizer in the beam between the laser and the interferometer even when the interferometer is illuminated off axis The reason for this is that there is usually a certain amount of back seatter from the interferometer m
99. beam splitters are perfect 50 50 beamsplitters the beams in the two paths have equal intensity so the photodiode output as a function of AL L3 L varies from zero destructive interference to the initial laser intensity Jo constructive interference as shown in the figure Page 3 Figure 3 Photodiode output vs kAL where k w c 27 A for a perfect Mach Zehnder interferometer with no rubidium cell at fixed laser frequency Next consider the effect of the rubidium cell on the propagation of a laser From Eqn 3 the total phase shift upon passing through the cell is e FnoRAz gikno Az Z eT FnoRAz gikAz p ik no 1 Az e 7 ei Az ib where Az is the length of the cell The factor e 4 in this expression is the free space propagation factor The e 7 factor comes from attenuation in the cell with 7 knokAz ki Nz Because we have a resonance line 7 depends on frequency and we can assume a Lorentzian line profile Toy Aw 72 where r9 is the absorption at line center The e factor is the additional phase shift from the refractive index of the rubidium atoms with 6 k ng 1 Az The atomic factors are related through 6 no 1 r amp 2 Awr which you should verify If we now put the rubidium cell in the interferometer the photodiode output will be given by I NE ibLo 4612 m X pies e 7eiFL2 e To 4 l e 77 2e7 7 cos kAL 6 4 Note that if the rubidium density is zero then 7 6 0 an
100. before connecting the controller box to AC power Figure 1 shows the pin out of the 9 pin connector and the protection diodes that are mounted inside the laser head Internal LD Photo Thermistor Piezo diode TEC Anode 1N5711 Cathode Piezo TEC Thermistor LD 3X Cathode 1N4148 GND Figure 1 9 pin Connector Pin out Rev 2 0 12 09 I B LASER TEMPERATURE Temperature has several effects on the laser The frequency of a bare diode laser changes with temperature for two reasons First the wavelength dependence of the overall gain changes with temperature As shown in Figure 6 of Section 1 this change is reflected in the large scale slope of the wavelength versus temperature graph 0 23 nm Cf Secondly the optical length of the bare diode increases with temperature This is shown in the small scale slope of the individual steps in Figure 6 From this slope 0 05 nm C 25 GHz C we can estimate that a temperature stability of 40 u Ct is necessary for the variation in the laser frequency to be less than 1MHz The temperature also changes the length of the external cavity formed by the grating From the linear expansion coefficient of aluminum Q 2 5 X 10 5 C 1 we can estimate a change in wavelength of 0 015 nm C 1 7 5 GHz C 1 Temperature also affects two other laser parameters First the threshold current increases with temperature Second if the current is kept const
101. bs 2 Probe Beam fo Probe Beam Frequency of Laser Detector Signal Oscilloscope Trace Figure 1 Doppler broadening occurs when the frequency of the laser is swept on either side of the true absorption frequency fo When the sweep frequency is below fo as fA probe photons are absorbed by gas particles moving towards the probe beam at a velocity which Doppler shifts f4 to fj When the sweep frequency is above fo probe photons are absorbed by particles moving away at velocities that see fg reduced to fy When the laser frequency is fo particles at rest or moving perpendicular to the beam absorb photons 3 of 4 Saturated Absorption DETECTOR PUMP Beam Absorbs probe fp or PUMP Probe Beam PUMP Beam Saturated by PUMP fo PUMP Beam Absorbs PUMP fa Absorbs probe Q Probe Beam Probe Beam Frequency of Laser gt Detector Signal Oscilloscope Trace Figure 2 At frequency f below true absorption frequency fo probe and pump photons are absorbed by particles moving towards the each beam These are completely different sets of particles so the probe signal is unchanged With the laser frequency at fg which is above fp photons are absorbed by particles moving away from each beam When however the laser frequency passes through fo particles at rest or moving perpendicular to the beams can absorb photons from either beam The PU
102. can convince yourself of this by increasing the cavity length further Rev 2 0 11 09 Tek alls Trig d Iv Pos 6 800ms SAVE REC Action Save Image File Format EMF About Saving Images Select Falder Save TEROOOG BMP Ext Tr amp mV lt 10H2 CHi 1 mw CHz4200vBy M S OOMS 24 Jan 0F 22 50 Figure 8 Cavity length increased by four turns at the other end of the cavity Tek MIN Tria d M Pos 354 4ms SAVE REC Action Saving Images Select Folder Save TEROOO8 EMF Ext diBmV x1 Hz Figure 9 Scan for a slow sweep through two transmission peaks Note that the tails are now to the short wavelength side indicating that the cavity is too long CHi 1 0mw CH2 2 00VBy M 5 ms a4 Jan r 23 13 For the next screen captures the cavity length was reduced by 1 4 turn This gives the near optimal cavity length See Figure 10 and 11 10 TeachSpin Fabry Perot Manual Rev 2 0 11 09 M Pos 354 4ms SAVE REC Tek Jl iB Stop M Pos 371 4ms SAVE REC Tek MIN Tria d Action Action bud UU Uu eee aE mom UT ZEE 3 2 3 2 3 Format 5 8 s Format EWF e E eA eU bu em BMP About About Saving Saving Images Images 2 TE A ien gered mariah Nie iler cheer m Folder qim amie ooo Lu Folder 1 3 TEKOOOS BMP z TEKOO10 BMP CHi 1 mwv CH2 2 00wEy MM 5 0 ms Ext 1TBm V CHi 2 mwv CHz 2400wBEy Mw 250us Ext r28m
103. carried out these detailed steps your laser will be tuned to the Rubidium resonance lines Once aligned it is unlikely that the laser will need any more than minimal tweaking A Unpacking and Setting Up the Laser 1 The room used for your diode laser should be able to be closed to other users first so that you can dim the room lights but most importantly so you can have absolute confidence that no stray laser beams can escape and potentially cause harm to anyone Rev 2 0 11 09 2 Unpack the various components from their shipping containers and place everything on a table with plenty of room to work 3 Place the Controller at one end of the optical breadboard we find it easier to put the controller and laser on the right side of the board the laser connection is behind the left end of the controller 4 Mount the laser on one end of the breadboard so that the beam will go across the board Before making placing the laser head on the board or making connections to it ground yourself to remove electrostatic voltages 5 Remove the protective plug from the laser head 9 pin D connector Connect the laser to the controller using the 9 pin D cable provided which plugs into the back of the controller 6 Make sure the laser power switch located on the left side of the controller on the front is in the off position Then plug in the laser controller power cord and turn on the main power switch located in the back near the power cord
104. ce Independent of the Angle of Incidence Re vue d Optique 35 37 1956 A L Bloom Properties of Laser Resonators Giving Uniphase Wave Fronts Spectra Physics Laser Techni cal Bulletin No 2 Mountain View California 1963 D R Herriott H Kogelnik and R Kompfner Off Axis Paths in Spherical Mirror Interferometers Appl Op ties 2 523 1964 d
105. ced in the SIDE knob The first order diffraction from the grating is directed back into the diode The zero order reflection from the grating is the light you observe leaving the laser The TOP knob rotates the grating about an axis that is parallel to the table top Turning the TOP knob changes the vertical angle of the light diffracted from the grating But to first order it does not change the wavelength of the light that is diffracted back into the laser The SIDE knob rotates the grating about an axis that is perpendicular to the table top Turning the SIDE knob does changes the wavelength of the light that is diffracted back into the diode E Setting up to Observe Rubidium Fluorescence 1 Remove the index card and position the Rubidium Absorption Cell Assembly so that the laser beam passes through the center of the cell You may use the IR viewing card to trace the path of the beam CCD Camera XE oye ND Filter Holder i L Xa US with Viewing Screen Beam Block Field Coils Figure 4 Setup for Observing Rubidium Florescence 2 Point the camera so it looks into the Rb cell from the Side Hole in the cell heater If you place the camera up on the base of the cell holder you can position the camera so that it abuts the glass holder surrounding the Rb cell It may also be helpful to dim the room lights since you will be looking for the fluorescence light emitted by the Rb atoms
106. cence 3 8 F Finding the Rb Fluorescence Initial Horizontal Adjustment 3 10 G Observing the Absorption Spectrum Using a Photodiode Detector 3 10 H Horizontal Modes Final Horizontal Adjustment 3 12 I Using Simultaneous Current and Piezo Modulation 3 14 J Using Two Photodiode Detectors 3 15 K All Finished L Shutting Down 3 17 III IV II III IV II III IV VI II Getting Started Continued Observing Saturated Absorption A The Optical Plan 3 18 B Some Basics 3 18 C Placing the Components 3 20 D Understanding the Functions of the Beams 3 21 Aligning a Michelson Interferometer 3 26 Appendix Making Beams Collinear 3 29 Experiments Section Saturated Absorption Spectroscopy Caltech Interferometric Measurement of Resonant Absorption and Refractive Caltech Index in Rb Resonant Light Propagation through an Atomic Vapor Caltech Resonant Faraday Rotation as a probe of atomic dispersion D Van Baak Apparatus Detailed Table of Contents Laser 5 1 Photodiode Detectors and Detector Electronics 5 23 Absorption Cell Assembly 5 26 Optics 5 30 CCD Camera and TV Monitor 5 32 Addendum Condensing Rubidium in the Tip 5 33 Appendix Brief Introduction to Diode Laser Spectroscopy Thinking About Saturated Absorption and Crossover Transitions Rev 2 0 11 09 Introduction to TeachSpin s Diode Laser Spectroscopy Diode Laser Spectroscopy was produced in collaboration wi
107. center of the viewing card is 4 inches above the tabletop Rev 2 0 11 09 2 When placing optics try to start with the beam centered in the optic This gives you maximum adjustment range before the beam walks off the end of the optic and you have to reposition the mount 3 When using the optical mounts to hold beam splitters observe that there are two possible configurations of the mount When looking at the mount from above the upper adjustment screw can be placed on the right or the left If placed on the wrong side the support for the upper adjustment screw will block the transmitted beam The upper screws are shown with a blackened edge in the figures below To change orientations you must remove the mount from the post and use the orthogonal mounting hole 4 Spend a bit of time planning your optical layout before you start Rev 2 0 11 09 C Placing the Components Now that you have completed the Initial Setup and have observed the Doppler broadened absorption spectrum of Rubidium you are ready to look for saturated absorption 1 Make sure you have two mounted mirrors a 10 90 and a 50 50 beamsplitter assembled 2 Reconfigure the apparatus you have been using into the layout shown in Figure 2 This is only part of the complete SAS setup We ll add the rest later BE SURE TO HAVE A BEAM BLOCK IN PLACE AS SHOWN Detector 2 Detector 1 to INPUT to INPUT Photo Photo diode diode Detector Detec
108. ces peaks in the spectrum analyzer output at vo jAV psg where j is any integer If a laser contains two closely spaced modes as in the example shown in Figure 2 then the output signal is obvious But if the laser modes are separated by more than Av psr then the output may be difficult to interpret In the lab you will scan the laser frequency while keeping the cavity length fixed but the resulting mea surements are basically the same as if you scanned the cavity length Laguerre Gaussian Modes The above analysis strictly holds only for the 1D plane wave case and real cavities must have mirrors of finite extent In this case it s best to thing of Fabry Perot cavities as full 3D optical resonators rather than simply a set of two mirrors By curving the mirrors the cavity supports a set of trapped normal modes of the electromagnetic field known as Laguerre Gaussian modes As long as the cavity has cylindrical symmetry the transverse mode patterns are described by a combination of a Page 3 PZT Input Output L Lo Laser V Photo Power Current Frequency V Figure 2 Using a Fabry Perot cavity as an optical spectrum analyzer Here the input laser power as a function of frequency P f is shown with a multi mode structure By scanning the cavity length with a piezoelectric PZT tube the laser s mode structure can be seen in the photodiode output as a function of PZT voltage I V Note the signal repeats with the period of the
109. corresponds to l 2 The confocal interferometer has even symmetric modes corresponding to m n even and odd symmetric modes corresponding to m n odd The even symmetric mode resonances fall exactly halfway between the odd symmetric mode resonances Thus the free spectral range of a confocal interferometer when it is illuminated simultaneously in several transverse modes is c 4d rather than c 2d In general the free spectral range of an l fold mode degenerate interferometer is given by c FSR pu 11 The transmittance of an I fold mode degenerate interferometer is given by l T R20 0 j 1 1 4R 9 2muld 1 R5 sin el 1 1 R 12 Note that if 1 the above equation reduces to the Airy formula 2 If the reflectance of the mir rors is close to unity we find for the transmittance of the interferometer near a resonant frequency sia a Ns ish te eet ic A 4rd V RS r 1 Gag e 13 The instrumental bandwidth is thus given by e u R Av oa 14 the resolving power by 2zvd GS TE 15 rae and the finesse by mT F Ta R 16 We thus see that the instrumental bandwidth and Q of a mode degenerate interferometer are the same as for a general spherical mirror interfer ometer or a Fabry Perot etalon but that the free spectral range finesse and peak transmission are reduced by a factor l We can also see why the con focal interferometer
110. cy vg can be transformed to results applicable to the actual Doppler distribution of atoms by a simple convolu tion For example the previously computed index of refrac tion n v vy a function of frequency v for a given line center vy changes to 4in2 g vo vA n v a vo dvg nti 34 Similar convolutions apply to the attenuation and the Faraday rotation signals v and A6 In the limit that the Doppler width Avp is negligible the distribution function g v turns into the delta function v vj and the convo lution reproduces the original results Alternatively in the limit that the laser frequency s detuning from resonance V voy is much larger than either the Doppler width or any Zeeman shift this delta function approximation is a good one thus the Becquerel result derived above remains valid for ordinary nonresonant Faraday rotation But for the ex perimental situation described in Sec III the case of interest is at the other extreme with the room temperature Doppler width exceeding the natural linewidth by a factor of about 100 This has dramatic consequences for the width and size of the absorption dispersion and Faraday rotation signals The Appendix discusses suitable numerical methods for per forming the convolution integrals but we go on here to present some of the results The results easiest to intuit are for absorption The convo lution defined by 34 preserves the total area under the
111. d we have the same result as before Note also that three terms in this equation are frequency dependent 7 6 and k However if AL is small then kAL changes very little as the laser frequency is scanned over a rubidium line so we can assume kAL is Page 4 essentially constant as a function of laser frequency see Problem 1 Problem 1 Consider the photodiode output from the interferometer without the rubidium cell Figure 3 shows the output at fixed laser frequency as a function of AL The maxima in this are referred to as fringes from their spatial structure which you will see in the lab when you set up the interferometer How small must AL be in order for the photodiode output to go through less than one fringe as the laser is scanned over the rubidium resonance line call it 5 GHz To get the best results you should try to set up your interferometer with AL less than this Problem 2 Compute the photodiode output as a function of laser frequency around the rubidium reso nance line Aw Jo for the set up shown in Figure 2 Assume the atoms in your cell are at rest for ease of calculation with some linewidth y so we can use the Lorentzian profile above for T w Make three dif ferent plots of I Aw Ip one for each of three different values of the line center optical depth To 0 4 2 and 20 Make your plots over the range 207 lt Aw lt 20y Plot six curves on each plot with values of kAL mod 27 equal to jx 5 with j
112. ded by the finesse of the interfer ometer Thus an interferometer having a finesse of 100 must have mirrors which are flat to 1 100 wavelength over the useful aperture If the aper ture of the interferometer is small enough the mirrors may indeed appear flat to within 1 100 wavelength However if the aperture is made small diffraction effects which limit the finesse of the interferometer become important The Airy formula given above neglects the effects of diffraction If the diameter of the inter ferometer mirrors is large compared to their sep aration diffraction is not important However if a small aperture is placed within the interferometer in an attempt to improve the effective figure of the mirrors diffraction effects at the edges of the aper ture cause a loss in the interferometer which is equivalent to a reduction in the reflectance of the mirrors This equivalent reduction in reflectance limits the finesse of the interferometer IH Spherical Mirror Interferometers The diffraction effects which are characteristic of Fabry Perot etalons can to a large extent be eliminated by using spherical mirrors in the inter ferometer The radii of curvature of the mirrors which for the sake of simplicity we assume to be equal must be greater than one half their separation The diffraction loss of a spherical mirror inter ferometer is orders of magnitude lower than that of a Fabry Perot int
113. ded in this manual were taken while a cavity was being set up for the first time Because the photodiodes PD put out a negative voltage both oscilloscope channels have been inverted The transmission through the Fabry Perot cavity FP is shown on Channel One Channel Two when displayed indicates the light intensity of a beam passing through a rubidium absorption cell This means that dips the trace on Channel Two show the rubidium D line s absorption signals Select area on the optical table for the cavity carefully The cavity should be placed away from other beams and located so that there can be two steering mirrors before the cavity At this point remove the vinyl end caps va Gres H Iris Photo diode Detector LJ X sI09 pial Glass ND Filter Q Q Ep S SS S WS i NS Figure1 This is a schematic of the setup used for aligning Fabry Perot cavity The linear polarizer and quarter wave plate which were placed between the two steering mirrors are not shown 4 TeachSpin Fabry Perot Manual Rev 2 0 11 09 FP Photodiode Iris Fabry Perot Cavity Second turning Mirror L2 x n x 1 Hn 1 4 Wave Plate Linear Polarizer One of Many Possible Configurations for Using the Fabry Perot Cavity This photograph shows only one possible arrangement of components for using TeachSpin s Fabry Perot Cavity We have shown a very compact version so that
114. derstand how these factors determine the laser output frequency The laser will tend to lase at the mode frequency with the greatest net gain i e stimulated emission minus optical losses see Yariv 1991 Once the laser begins to lase in this mode stimulated emission limits the number of electron hole pairs which are available for lasing in other modes and the result is a laser with a single mode i e single frequency output beam Note This does not always happen Our lasers will sometimes lase in two or more modes at the same time and sometimes the output Rev 2 0 11 09 frequency will vary rapidly and chaotically over a broad frequency range While these behavior patterns are interesting and the subject of some amount of research we will mainly try to find a place in parameter space where the laser operates in a single mode To determine the laser operating frequency assuming single mode operation we need to find the frequency with the highest net gain Figure 5 shows schematically the different contributions to the net gain These contributions are best explored individually e e g 8 Internal Cavit o y e Zo oq Grating Feedback ea Be Ht ML M External Cavity eo 670 6 670 8 671 671 2 671 4 Wavelength nm Figure 5 Schematic of the different contributions to the net optical gain of an arbitrary laser as a function of frequency The curves are displaced relative to one another for clarity 1 The medium gain
115. dis played in Fig 9 a for which the scope gain is the same as it was in Fig 8 b Each of the traces displays a set of four 733 Am J Phys Vol 64 No 6 June 1996 30 20 o 30 30 b 20 20 30 0 2 0 0 2 0 4 0 6 0 8 1 1 2 Relative incremental diode laser current Fig 9 a The experimental Faraday rotation signal for three values of magnetic field strength B 5 10 and 15 mT obtained at the same scale as the baseline data of Fig 8 b b Theoretical Faraday rotation signals expected for this experimental situation computed using the model de scribed in the text The theory uses the same horizontal and vertical scaling as in Fig 7 b and no adjustable parameters signals each arising at the location of one of the four zero field absorption features each of the four signals resembles the symmetric resonant Faraday rotation signals predicted by theory and depicted in Fig 5 Each of these traces was ob tained in one single sweep of total duration less than 2 ms so the Faraday rotation thus displayed is truly a real time phe nomenon in fact the inductive time constant of the magnetic field coils is the factor limiting the rate at which the Faraday effect display on the oscilloscope can be changed For purposes of more detailed comparison with the theory the theoretical prediction 40 was evaluated under the fol lowing assumptions The leading factor 5 repr
116. discussed in the Internet document sphere faq produced by Dave Rusin The document is located at http www math niu edu 80 rusin papers spheres sphere faq Uniform tilings are not achieved on golf balls or geodesic domes which either employ multiple tiling elements or contain defects at the north pole or at the equatorial weld line Reference 13 describes methods of obtaining nearly uniform distributions of an arbitrary number of points on the surface of a sphere SIf field line diagrams are seen as primarily serving visualization and peda gogic purposes rather than serving as a practical research design tool it may be time to reevaluate their pedagogic worth Tornkvist et al suggest that independent of any imperfections that may be present in CFLDS students often misinterpret these diagrams S Tornkvist A Petterson and G Transtromer Confusion by representation On students comprehen sion of the electric field concept Am J Phys 61 335 338 1993 Resonant Faraday rotation as a probe of atomic dispersion D A Van Baak Department of Physics Calvin College Grand Rapids Michigan 49546 Received 18 August 1995 accepted 4 December 1995 The Faraday effect the rotation of the plane of polarization of light as it propagates through a sample parallel to a static magnetic field is readily detected in room temperature rubidium vapor by a diode laser experiment near the D resonance line at 780 nm a
117. e 5 Calculated saturated absorption spectra for two level atoms for 7 7 1 0 1 10 0 316 10 1 10 3 16 10 and 10 10 The two plots show the same spectra with the frequency axis at different scales Note the overall Doppler broadened absorption with the small saturated absorption feature at line center Saturated Absorption Spectrum of 2 Level Atom Probe Transmission 400 200 0 200 400 v vg MHz Figure 6 Calculated saturated absorption spectra for two level atoms for 7 7 1 1 0 1 1 1 1 10 1 100 and 1 1000 Note at large laser intensities the saturated absorption feature is power broadened as the line saturates Finally it should be noted that calculating the saturated absorption spectrum for real atoms which must include optical pumping many different atomic levels atomic motion in the vapor cell and the polarization of the laser beams is considerably more subtle A recent paper by Schmidt et al 1994 shows much detailed data and calculations for the case of cesium Rev 2 0 11 09 Problem 1 Show that To dz vj v when the pump laser intensity is zero from the formula above Hint the integral is simplified by noting that T lt lt AV popp Problem 2 The above calculations all assume that the pump laser has the same intensity from one end of the cell to another This is okay for a first approximation but calculating what really happens is an interesti
118. e adjustment screws on the 50 50 BS mount to overlap the two beams at this position It is very likely that the strong pump beam will not be visible at position 2 initially You may have to loosen the screw that secures the post on the 50 50 BS and rotate it till you can find the beam If all else fails and you cannot get the beams to overlap easily you can temporarily move the Rb cell and magnet off to the side so that you can trace the pump beam path from the 50 50 BS Once the beams are overlapped at position 2 move back to position 1 and check the beams Again use the mirrors to overlap the beams here After a few iterations you should be able to get the pump beam and one of the probe beams overlapping in space and anti parallel in direction Now replace the glass ND filter and the Rb cell if you removed it into the beam path Look at the absorption signal on the oscilloscope Expand the scale so that you can observe the two large absorption features If your beams are close to being aligned you will start to see some sharp spikes within the broad absorptions See Figure 5 These spikes indicate that the ability of the rubidium atoms to absorb photons from the probe beam has been diminished more light from the probe beam is actually reaching the detector This is because atoms which in the past would have absorbed the probe beam photons are already in the excited state because they have absorbed photons from the pump beam Yo
119. e cavity and n is the index of refraction of the air inside the cavity When the frequency of a tunable laser is scanned in time a series of peaks in the transmitted light s intensity occur at C C C 2 1 j 1 1 2 f GD 4nL POS On 4nL 1 TeachSpin Fabry Perot Manual Rev 2 0 11 09 As the series in equation 1 2 indicates for any integer j the transmission maxima will be equally spaced in frequency The difference between adjacent maxima is defined as the free spectral range or FSR FSR Af 13 4nL For the TeachSpin cavity the adjusted length L will be near 20 cm which will give a free spectral range of about 0 38 GHz or 380 MHz The transmission maxima of course will not be perfect spikes The narrowness of a peak is described in terms of its full width in frequency units at half the peak height of the signal For a properly adjusted Fabry Perot cavity the width in frequency of the maxima peaks of will be much smaller than the spacing between the maxima Af The ratio Af f is called the finesse of the cavity and you should be able to achieve a finesse of over 100 To have an idea of the sensitivity of this instrument we can look at the three different frequency ranges involved Writing them all in MHz will make them easier to compare First there is the frequency equivalent of the particular light we are investigating For light of wavelength near 780 nm the optical frequency is ab
120. e mode inside the cav ity see Figure 1 you can see that the beams leaking out of the cavity diverge in both directions You can see this if you use a white card with a hole in it placed far from the cavity The reflected beam from the cavity will make a large spot on the card much larger than the incoming beam Thus the input beam is not well matched to the cavity modes To match the TEMoo mode the incoming beam should be converging You can achieve this by placing a 500mm focal length lens about 11 inches in front of the cavity Before aligning the cavity note that the size of the reflected beam is now about equal to the incoming laser size so the mode match is better than before Align the cavity with the lens in place and view the transmitted signal You should see fewer large modes Turn the sweep down to identify the different modes on the TV Find the TEMo9 mode and tweak the mirror alignment to maximize this mode while minimizing the others With some effort you can produce a transmitted signal that looks something like that shown in Figure 6 with dominant TEMo o peaks separated by Avrgr You cannot do much better than this even in theory for two reasons 1 the mode matching lens is actually not quite right to match to the cavity so you are bound to excite some other modes and 2 the incoming laser beam is itself not a perfect T EMoo mode expand the beam with a lens and you can see that it doesn t have a perfect Gaussian shape w
121. e of Saturated Absorption Spectroscopy Multi level Atoms If the atoms in the absorption cell had a single ground state and two excited states typically an electronic level split by the hyperfine interaction and the separation of the excited states was less than the Doppler width then one would see a spectrum like that shown in Figure 3 The peaks on the left and right are ordinary saturated absorption peaks at v and v the two resonance frequencies The middle peak at v4 v3 2 is called a cross over resonance If you think about it for a while you can see where the extra peak comes from It arises from atoms moving at velocities such that the pump is in resonance with one transition and the probe is in resonance with the other transition If you think about it a bit more you will see there are two velocity classes of atoms for which this is true atoms moving toward the pump laser and away from it 1 Probe Transmission 02 04 06 08 4000 2000 0 2000 4000 v vg MHz Figure 3 Saturated absorption spectrum for atoms with a single ground state and two closely spaced excited states 1 Probe Transmission 02 04 06 0 8 4000 2000 0 2000 4000 v vg MHz Figure 4 Saturated absorption spectrum for atoms with a single excited state that can decay into either of two closely spaced ground states Page 3 If the atoms in the vapor cell had a single excited state but two hyperfine ground states we call them b
122. e optical depth To The latter is proportional to the vapor density inside the cell Figure 5 shows calculated spectra at fixed laser intensity for different optical depths and Figure 6 shows spectra at fixed optical depth for different laser intensities In Figure 5 one sees mainly what happens when the vapor density is increased in the cell At low densities the probe absorption is slight with a Gaussian profile and the absorption increases as the vapor density increases At very high vapor densities the absorption profile gets deeper and broader It get broader simply because the absorption is so high near resonance that the probe is almost completely absorbed for greater vapor densities the probe gets nearly completely absorbed even at frequencies fairly far from resonance thus the width of the absorption profile appears broader The saturated absorption feature in Figure 5 does pretty much what you would expect The probe absorption is reduced on resonance due to the action of the pump laser At very high vapor densities the saturated absorption feature becomes smaller This is because while the pump laser reduces the absorption it doesn t eliminate it thus at high vapor densities the probe is nearly completely absorbed even with the pump laser The moral of this story is that the vapor density shouldn t be too low or high if you want to see some saturated absorption features In Figure 6 one sees that if the pump intensity is low the saturated
123. e peg 87 FST Tug Ld Select Pathe ks phat ERE RC a fe eh oe Me te Lh ia aa Folder 1 AEE ESP E S E E ri i ee About z i Save All CHisiooy CHE z D wBy j ms Ext 8 mW 23 Oct 04 n0 22 lt 10Hz Lower Trace Sawtooth ramp voltage which is creating a sweep of both the laser current and the grating angle This in turn creates the change in the laser frequency Falling sawtooth indicates increasing frequency Upper Trace Transmitted light received by the detector In the section of the trace shown frequency increases with time Diode Laser Spectroscopy David Van Baak July 2009 Optical Plan for Saturated Absorption Detectors Mirror Two E EEEL Reference 4 50 50 Splitter Pump Beam Rb Vapor Cell gt inside Helmholtz Coilse e annuun m nn nnn Mirror ba One Pump Beam Beam Splitter 1 0 5 wedge A schematic diagram of an optical layout suitable for performing diode laser pump probe experiments in rubidium vapor Transmitted Light vs Laser Frequency With Pump Beam On a db re a n e den a ibt re nnn eecbeccpeecpeeeteesdpeerpera Trace showing features that appear when pump beam is introduced In the section of the trace shown frequency increases with time For this trace only the grating angle is being changed The laser current is constant as indicated by the flat base line Diode Laser Spectroscopy David Van Baak July 2
124. e seen from Figure 6 this is not always possible with a free running laser With the addition of an external grating the laser can be made to operate at any wavelength within a reasonably broad range 3 The Grating Feedback Since a grating disperses light only light from a narrow wavelength band will be fed back into the laser for a fixed grating left right L R angle The grating up down U D angle should be set so that the light from the grating reflects back into the laser In this apparatus the grating is used in a Littrow configuration where the first order diffraction is sent back into the diode In this configuration the wavelength can be found from 2 d sin0 where d is Rev 2 0 11 09 the line spacing of the grating and 0 is the grating angle measured from the normal Assuming an ideal grating where the resolving power is limited only by diffraction the spectral width of the first order diffraction Av will be given approximately by v AvzN where v is frequency and N is the number of grating lines subtended by the laser beam see M ller 1988 or any general optics book for a discussion of grating properties For example with a 0 3 cm laser beam width we will find N 5400 and Av 70 GHz The position of this peak is determined by the grating L R angle 4 The external cavity This is similar to 2 above but with the external cavity one end of which is the grating and the other is the highly reflective back facet
125. e the new diode from its bag Put the new diode into the collimation tube Place the diode into the adapter Then drop the assembly into the collimation tube The diode adapter assembly should fit snugly into the tube without cocking Now thread the retaining ring into place Attach the socket and PCB to the diode and screw the strain relief body over the PCB and into the collimation tube As before keep the cable fixed with respect to the collimation tube Attach the cap to the back of the strain relief body Note The cap has a cutout to accept the bent cable Operating note Figure 13 shows the relationship between the bend in the cable the diode pin out the beam profile and the laser light electric field direction In the next section we will discuss how to orient the laser so that the long axis of the elliptical beam profile is horizontal In this orientation the grating provides the maximum resolution as the beam covers the largest number of lines in the grating Rev 2 0 12 09 1 D 4 b Setting the Laser Orientation and External Cavity Length Place the collimation tube assembly in the collimation tube holder and lightly tighten one of the setscrews The position of collimation tube within the holder determines the cavity length The major effect of the cavity length is to determine the external cavity mode spacing See diode laser physics section It is found that a short cavity works best Position the tube so that there is a 2 to 3 m
126. e to the magnetic hyperfine splitting this is described in many quantum mechanics textbooks The form of the interaction term in the atomic Hamiltonian is H J eI which results in an energy splitting AE rr n ra n 7G D where F I J is the total angular momentum quantum number including nuclear spin and C is the hyperfine structure constant Figures 7 and 8 show the lower S and P energy levels for Rb and Rb including the hyperfine splitting F 4 F 3 SP 3 3 2 1 0 2 1 8 1 0 e 0 9 87a 5 85a n lt a d rt 87b a 3 F 2 o 5S F 3 1 2 R 2 os 85b F 1 85 Rb S7Rb MET 2 0 2 4 Detuning GHz Figure 7 Left Level diagrams for the D2 lines of the two stable rubidium isotopes Right Typical absorption spectrum for a rubidium vapor cell with the different lines shown P mh T a F 35 N NL 4 E s d 0 287 GHz S Y I Y i M i H F 2 i 0 157 GHz 1 5P35 Fs E ie Petco 1 OoOo Miwa 1 l Pe eee esi 7 780 2np i 780 2 nm 384 000GHz 384 000 GHz E 14 1 57 eV 1 57 e i F 3 m 3 to 3 5845 F 2 m 2to 2 9912 3 036 GHz 6 835 GHz F 2 m 2to42 F 1 1 to 1 m 1 t0 85 7 Rb 72 87 Rb 28 Figure 8 More rubidium level diagrams showing the hyperfine splittings of the ground and excited states Rev 2 0 11 09 VI REFERENCES Cohen Tannoudji C Duponi Roc J and Grynberg G 1992 Atom Photon Interactons Wiley H nsch T W Schawlow A L
127. eam diameter and divergence of the incoming laser beam must be matched to the beam diameter and divergence of the TEM mode of the interferometer If the above conditions are not fulfilled the inter ferometer will not work properly The most serious defect of general spherical mirror interferometers is that if they are not properly mode matched to the incoming laser beam they will have spurious transmission fringes These fringes are caused by the excitation of high order transverse modes of the interferometer which generally resonate at different frequencies than the TEM mode The above requirements make the general spher ical mirror interferometer rather difficult to use Fortunately by using special forms of spherical mirror interferometers these requirements can be considerably relaxed These special forms of spher ical mirror interferometers are called mode degenerate interferometers IV Mode Degenerate Interferometers For practical applications mode degenerate in terferometers are more useful devices than are general spherical mirror interferometers The fun damental reason for this is that mode degenerate interferometers do not need to be mode matched to the incident laser beam This fact permits consid erable simplification in the experimental use of mode degenerate interferometers Specifically 1 Since the transverse modes of the laser do not need to be matched to the transverse modes of the int
128. ect match to calculation but the results should provide a reasonable demonstration of the Kramers Kronig relations Take several spectra at high 7 at different phase angles In particular take spectra at kAL 0 and kAL m III REFERENCES Page 8 Jackson J D 1975 Classical Electrodynamics 2nd Edition Marion J B and Heald M A 1980 Classical Electromagnetic Radiation 2nd Edition Reif F 1965 Fundamentals of Statistical and Thermal Physics Page 9 Resonant Light Propagation through an Atomic Vapor The Macaluso Corbino Effect KENNETH G LIBBRECHT Norman Bridge Laboratory of Physics California Institute of Technology 264 33 Pasadena CA 91125 1 The Experiment This experiment is extremely easy to set up as is apparent from the optical layout shown in Figure 1 Note it would take just a few seconds to switch from a saturated absorption experiment to this one polarizer photodiode Figure 1 Basic optical layout The large ND filter makes sure one is in the unsaturated regime The light coming out of the laser is linearly polarized so only one polarizer is needed Figure 2 shows the light transmitted through the cell as a function of frequency when the B field is not present and the polarizer is at some random angle Rotating the polarizer only changes the overall scale of the figure Nothing here but simple resonant absorption Figure 4 shows the light transmitted with 1 3 amps going
129. ed Intensities Adjust the cavity length to its confocal value and align the input beam to maximize the height of the transmitted peaks Tweak the length and alignment with some care to produce sharp symmetrical peaks with the highest possible amplitude When that looks good insert a pick off mirror somewhere in the beam and send it to the second photodiode Use the mir ror to maximize the photodiode signal on the oscilloscope so the beam is centered on the photodetector and measure the output voltage and note the photodiode gain It works well to use the measure fea ture on the oscilloscope to measure the average output voltage With care you could convert this voltage to milliwatts of laser power but you will be taking power ratios so you don t need this conversion Without changing the cavity alignment set up the second lens and photodiode as shown in Figure 7 Again make sure the beam is centered on the photodetector and measure the output signal The value should be about 2596 of what you measured previously because the beam intensity was diminished twice by the 50 50 beamsplitter If you don t get within a few percent of that value something is wrong probably the alignment Next send the first photodiode signal directly into the oscilloscope along with the second Note that the dips in reflected light correspond to the peaks in transmitted light as you would expect Measure the peak widths and make sure they are greater than 20 u
130. embly is out of the glass cylinder remove the remaining piece of the cold finger This is the aluminum piece that contacts the rubidium cell at the tip You may need a pair of tweezers to pull this piece out of the foam Now push the Rb cell and foam support piece out of the aluminum heater This completes the removal IILB 3 Installation Installation is the reverse process of removal Put the cell into the foam support piece It is easy to tear the foam so be gentle The small hole in the support piece is for the tip and the larger hole is for viewing Slide the cell and foam support into the aluminum heater The large hole in the aluminum heater is for the cold finger and the smaller hole is for the viewing window Note there is a little area of aluminum heater exposed around the viewing window this is to keep the viewing window hot and prevent Rb metal condensation Place the aluminum cold finger in the foam support piece so that it covers the cell tip You should notice that the cold finger pieces have been machined to fit the curve of the cell Slide the assembly into the glass cylinder When the assembly is half way in insert the spring and brass part of the cold finger Adjust the cell and foam pieces so that the cell is centered in the heater and also centered in the viewing window Place the thermocouple sensor next to the cell just under the foam support near the cold finger We suggest that you keep the viewing window and cold fing
131. ended variation with laser frequency allows a theoretical model to include laser power variation Of course D A Van Baak 731 140 120 100 80 60 40 20 b 120 100 80 60 40 20 0 2 0 0 2 0 4 0 6 0 8 1 12 Relative incremental diode laser current Fig 7 a Intensity of linearly polarized light transmitted though a cell of rubidium vapor as a function of relative incremental current in the diode laser light source The central value of diode laser current has been empiri cally selected to give a central optical frequency near 384 200 GHz and the width of the sweep has been selected to give a scan of about 10 GHz in optical frequency Optical frequency decreases to the right cell length L 51 mm temperature 298 K magnetic field zero b Theory for this transmission signal computed using the model described in the text The horizontal scale and the size and slope of the baseline have been adjusted to match the data but the shapes and sizes of the absorption dips are calcu lated from not fit to the model the more interesting content of the data of Fig 7 is the set of narrow absorption features displayed this is a high resolution view of the Rb D line The scan was taken at low enough intensity 0 4 mW in a spot about 3X6 mm to avoid the saturation of the absorption features the scan du ration was under 2 ms The very first conclusion to be drawn is that rubidium is not as
132. er horizontal Viewing window on one Figure 18 Insertion of Cold side and cold finger on other finger into Cell Assembly Rev 2 0 12 09 II C THERMOCOUPLE POSITION AND TEMPERATURE There is a significant thermal gradient across the cell of about 10 C at a set point of 50 C The thermal gradient is mostly vertical with the bottom cooler and the top hotter The density of rubidium in the cell is determined by the temperature of the pool of excess rubidium that condenses in the tip near the cold finger If you need to have a reasonably accurate measure of the rubidium density you should check that the thermocouple is placed close to the cold finger For most experiments the exact temperature is not important We have included some foam inserts that may be placed in the foam end caps for higher temperature operation III D CONDENSATION OF RB ON THE CELL WINDOWS Rubidium metal condensed on the cell windows creates a silver mirror like layer on the inside of the cell This reflects part of the laser beam and can lead to confusing results Because there is a vertical temperature gradient across the cell the first condensation will probably be on the lower portion of the windows The heater assembly has been designed to keep any excess Rb metal in the cell condensed in a hidden tip rather than the end windows To accomplish this equal areas of the aluminum heater must be exposed at each end of the assembly See Figure 16 on page 5 25 If
133. er result 11 we can deduce for the index of refraction n v of the sample the curve us NX Vg V RU ET ee Or v FA a7 which shows a dispersive dependence on frequency with positive values occurring below the resonant frequency and a peak departure of index n from unity occurring at frequen cies v7 vy Av 2 of size i NMj 1 NM T n Imax 35037 Ay 16g mau 18 This tightly related behavior of absorption and dispersion has distinct implications for an experiment seeking to detect atomic dispersion for example if a sample of length L is dense enough to attenuate at line center the fields to e or the transmitted power to e 13 5 then it has B uL 1 so Xo isi 19 n zT lax which is very small indeed for plausible sample lengths If one tries to detect this deviation of refractive index from unity by interferometric means then the phase shift relative to vacuum that will accumulate in a one way trip through this sample is Aet iL Ae _ 27 Xo NE di XM SO m 4L 5 ra ian 20 This phase shift is only 8 of the 2a radians required to produce a single interferometric fringe and it would have to be detected in the face of the deep absorption accompanying it Conventional detection of atomic dispersion is carried out much farther from line center using samples of much greater optical thickness and relying on the fact that dispersion drops off with detuning less rapidly than does absorption We will see
134. erent values of m and n define the differ ent tranverse modes of the interferometer Note that to any specific transverse mode there corre spond a number of longitudinal modes The frequency separation of any two interfer ometer resonances defines the free spectral range of the interferometer In order for the free spec tral range of the interferometer to be large enough to be useful it is necessary to restrict the excitation of the interferometer to a single transverse mode The various longitudinal modes corresponding to that transverse mode then determine the free spec tral range to be c 2d as is the case for the Fabry Perot etalon In practice the only transverse mode of the interferometer which is convenient to excite is the lowest order TEM mode The requirement that a general spherical mirror interferometer be excited in a single transverse mode causes considerable complication in practical applications of the device In order to match the laser beam into the TEM mode of the interfer ometer the laser itself must operate in the TEM mode In addition the interferometer must be care fully aligned so that its axis corresponds to the propagation axis of the incoming laser beam When such alignment is accomplished light reflected from the interferometer travels back into the laser and perturbs the modes of the laser It is thus nec essary to use an optical isolator between the laser and the interferometer Finally the b
135. erferometer and is usually small enough to be negligible In addition the sur face figure on the mirrors of a spherical mirror interferometer is considerably less critical than the figure on the mirrors of a Fabry Perot interferom eter The reason for this comparatively large figure tolerance is that only a small area typically 1 mm of the spherical mirror interferometer mir rors is useful Thus mirrors which are good to within 1 10 wavelength over their entire area may contain small areas having a figure of better than 1 100 wavelength The salient characteristic of a general spherical mirror interferometer is that it must be illumi nated with a narrow diffraction limited beam to work properly In laser terminology it must be mode matched to the laser which is to be ana lyzed The various modes of a spherical mirror cavity resonate at frequencies given by w or a amn cos 3 8 where c is the velocity of light d is the separation of the mirrors R is the radius of curvature of the mirrors q is an integer denoting the longitudinal mode number and m and n are integers denoting the transverse mode numbers A spherical mirror interferometer will have a high transmission for frequencies which satisfy the resonance condition 8 The resonance fre quencies corresponding to different values of q define the different longitudinal modes of the inter ferometer The resonance frequencies correspond ing to diff
136. erferometer it is not necessary that the laser operate in a single transverse mode 2 There are no spurious resonances in mode degenerate interferometers 3 Since mode matching is not required the in terferometer need not be accurately located on the axis of the incident laser beam this reduces the re quired alignment tolerance of the interferometer 4 When the axis of the interferometer does not coincide with the axis of the incident laser beam the light reflected by the interferometer does not travel back into the laser and perturb the laser os cillation It is thus usually desirable to use the interferometer with off axis illumination A mode degenerate interferometer is a spherical l mirror interferometer whose transverse modes are degenerate in frequency The operation of such in terferometers can be understood by considering that if the radii of curvature and separation of the mirrors of a spherical mirror interferometer sat isfy the equation aq where l is an integer then the resonance equation 8 can be written as w pq lla ltm n a0 Since increasing the sum m n by l and de creasing q by one leaves the resonant frequency of the interferometer unchanged it follows that the interferometer will have l sets of degenerate transverse modes These sets of modes will be equally separated in frequency The best known mode degenerate interferometer is the confocal interferometer which
137. erstand the structure of atoms and molecules but also to define standards in metrology For example the second is defined from atomic clocks using the 9192631770 Hz exact by definition hyperfine transition frequency in atomic cesium and the meter is indirectly defined from the wavelength of lasers locked to atomic reference lines Furthermore precision spectroscopy of atomic hydrogen and positronium is currently being pursued as a means of more accurately testing quantum electrodynamics QED which so far is in agreement with fundamental measurements to a high level of precision theory and experiment agree to better than a part in 10 An excellent article describing precision spectroscopy of atomic hydrogen the simplest atom is attached H nsch et al 1979 Although it is a bit old the article contains many ideas and techniques in precision spectroscopy that continue to be used and refined to this day photodiode mer f N probe vapor cell beam Figure 1 The basic saturated absorption spectroscopy set up Qualitative Picture of Saturated Absorption Spectroscopy 2 Level Atoms Saturated absorp tion spectroscopy is one simple and frequently used technique for measuring narrow line atomic spectral features limited only by the natural linewidth T of the transition for the rubidium D lines I zz 6 MHz from an atomic vapor with large Doppler broadening of Av Dopp 1 GHz To see how saturated absorp tion spectroscopy wor
138. es Three detector power plugs are on the front panel The signal is on the coax cable with BNC connector The polarity of the signal is negative If you plug the signal into an oscilloscope the signal will be from 0 to 11 0 Volts The detector voltage saturates at about 11 volts You should adjust the gain of the detector so that you are not near the saturation voltage Gain High Frequency 3dB Noise 10 MQ 5 8 kHz 1 57 uV Hz 3 3 MQ 10 3 kHz 0 90 uV Hz 1 0 MQ 20 kHz 0 42 uV Hz 330 kQ 28 kHz 0 20 uV Hz 100 kQ 54 kHz 91 nV Hz 33 KQ 88 kHz 48 nV Hz 10 KQ 165 kHz 24 nV Hz 3 3 KQ 260 kHz 16nV Hz 1 0 KQ 480 kHz 13 nV Hz 3300 720 kHz 13 nV Hz Table 3 Photodiode Detector Parameters Measured in 3 Hz to 44 kHz frequency range At high light intensities the response of the photodiodes becomes non linear A doubling of the light intensity gives an output voltage that is less than double This occurs at an output current of about 0 5 mA If you wish to use the photodiode as a power meter you should make sure that the light current is below this value If it is not place a ND filter in front of the photodiode Students will need to calibrate the Neutral Density filters using the photodiode detectors at low laser light levels The current to voltage converter gain has units of ohms li Vout Rean from which the input power can found using photodiode resp
139. es it See Figure 20 This tuning method requires either the fast or slow axis to be aligned vertically RETARDANCE nim TOM DITE 10 an 40 ANGLE OF TILT IN AIR DEGREES Figure 20 Tilt Tuning of Quarter Wave Plate IV F ASSEMBLY AND CARE OF OPTICAL COMPONENTS Loading optical elements into mirror mounts You will have to place the various optical components into the mirror mounts It is best to do this without touching the components with your fingers If you must touch the components wear protective gloves and touch the components only at the edges Rev 2 0 12 09 V TV Monitor and CCD Camera V A THE TV MONITOR The TV monitor was shipped with its wall mounted AC to DC power supply in the box The TV requires 12 V DC at 850 mA The CCD camera power supply 12 V DC at 250 mA plugs into the red plug on the cable attached to the back of the camera The yellow plug on the same cable is the video output which plugs into the back of the TV monitor We have included an extension video cable for the camera and there may be an adapter plug attached to the extension cable to make the cable compatible with the video input on the back of the TV VB Camera focus V B CAMERA FOCUS The CCD camera focus may be adjusted by turning the lens on the front of the camera You may have to loosen a small setscrew to do this The camera has an automatic gain control so that it adjusts to low and high light levels To get a nice image on t
140. es on both sides of the 50 ohm resistor and 47 uH inductor We included two sets of protection diodes to provide maximum electrostatic protection 50 0 Ferrite bead From Current SMA Control Connector Figure 6 Schematic High Frequency Modulation Circuit Also shown are two sets of protection diodes The three diodes in series are 1N4148 s and the diodes used to prevent reverse voltages are 1N5711 s Rev 2 0 12 09 I D LASER OPTICS AND DIODE Figure 7 is a diagram of the Laser Head as viewed from above The diagram includes the diode collimating lens grating PZT stack ball tipped setscrew that provides contact between the mirror mount and grating holder and the 6 32 socket head cap screws that fix the grating holder to the mirror mount The basic design is from Arnold et al Review of Scientific Instruments 69 1236 1998 The only major change is the use of a flexure mount to hold the diffraction grating The diode is held in a Thor Labs Collimation tube LT230P B which also holds the aspheric collimation lens C230TM B f 4 5 mm 0 45 na The holographic diffraction grating is from Edmunds Optics R43 775 and has 1800 lines mm The actuators used for adjusting the grating and mirror mount have 100 threads per inch From the grating equation A 2dsin0 and dimensions given above one can calculate the wavelength tuning rate of the actuators to be about 5 2 nm per turn Diode Laser PARRER RAA LARAARA AN i
141. es or those of AAPT or ALPhA They can then be shared both with people using this TeachSpin instrument and with other members of the advanced laboratory community who may have built similar experiments on their own We wish you and your students challenging exciting and satisfying adventures exploring Diode Laser Spectroscopy DIODE LASER SPECTROSCOPY LASER PHYSICS Rev 2 0 11 09 Diode Laser Physics I LASER BASICS Beginning in the mid 1960 s before the development of semiconductor diode lasers physicists mostly used tunable dye lasers in pioneering atomic physics experiments needing tunable laser light Dye lasers use a chemical dye as the active medium i e the material which produces the laser emission A population inversion in the dye is created typically with a fixed frequency pump laser An individual dye will lase over a limited wavelength range and different dyes are available to make tunable lasers at essentially all visible and near infrared wavelengths Unfortunately dye lasers are large cumbersome instruments that are both very expensive to purchase 100 000 00 and expensive to operate and maintain Some of the solid state lasers used as dye laser replacements such as the popular Ti sapphire crystal titanium doped sapphire work better than dyes and other techniques using non linear crystals exist to generate tunable laser light Yariv 1991 However while these may be less difficult to use than d
142. escribe later how the linear polarizer and quarter wave plate may be set up as a poor man s optical isolator Other techniques that can reduce the feedback are putting an attenuating filter in the beam path and keeping the optical path length between the laser and Fabry Perot cavity as long as possible The distance helps because the beam reflecting from the FP is diverging due to the curvature of the mirrors Figure 2 The upper trace shows a normal absorption signal The trace below is the same signal in the presence of optical feedback from the Fabry Perot cavity to the diode laser We now need to place the FP cavity in the beam such that the beam goes approximately down the center of the cavity This is not a simple task because the highly reflecting mirrors mean that only a very small fraction of the light will pass through the cavity The mirrors are specified to be 99 5 reflective and we will make a power measurement to put an upper limit on this number You can use the iris as an alignment aid 6 TeachSpin Fabry Perot Manual Rev 2 0 11 09 Place the FP in its approximate position Place the iris at a location on the table so that it will be just after the FP Now remove the FP and position the iris so that the beam goes through the center Reduce the iris size and use the IR viewing card or a photodiode detector PD to help in correct positioning Even if you don t use the PD to help center the iris it s a good idea to p
143. esenting the characteristic variation in intensity that accompanies a diode laser s tuning was taken from the pure absorption data above the attenuation constants 8 and G_ were taken from Doppler broadened and Zeeman shifted versions of 15 and the Faraday rotation angle A0 was taken from the Doppler broadened version of 21 This was done for four features assumed to be located at the positions of the four zero field absorption phenomena and assumed to arise from species of the number densities given in Table I Again the quantities B B and A0 in 40 are linear in number density N so they can be summed over the assumed four species to give values applicable to the whole sample then evaluating the exponential and sine functions in 40 gives a result compa rable to the data The results are shown in Fig 9 b which displays a set of theoretical simulations of the actual experi D A Van Baak 733 ment There are no new parameters adjusted in computing the Faraday signal since the scaling of Fig 7 suffices to fix all the necessary quantities The agreement of the two halves of Fig 9 illustrates that a simple model of atomic dispersion is indeed sufficient for a detailed description of resonant Far aday rotation there is surprisingly good agreement in the details of the vertical scale of the signals and some disagree ment in the details of the broadening and saturation of the Faraday rotation signals with increasing magne
144. ew York 1985 3rd ed Chap 5 this result omits the counter rotating term so it is valid any where near resonance but not at dc 12A M van der Spek J J L Mulders and L W G Steenhuysen Vapor pressure of rubidium between 250 and 298 K determined by combined fluorescence and absorption measurements J Opt Soc Am B 5 1478 1483 1988 BH Becquerel On an explanation applicable to the phenomena of Faraday and Zeeman C R Acad Sci 125 679 1897 Jan Evetts Ed Concise Encyclopedia of Magnetic amp Superconducting Materials Pergamon New York 1992 article on Magnetooptics Robert W Schmieder Allen Lurio W Happer and A Khadjavi Level crossing measurement of lifetime and hfs constants of the P states of the stable alkali atoms Phys Rev A 2 1216 1228 1970 16John R Brandenberger Lasers and Modern Optics in Undergraduate Physics Lawrence University Appleton WI 1989 pp 33 58 Up A Van Baak Temperature servomechanisms using thermoelectric modules Am J Phys 60 803 815 1992 18 ens LP 04 by Universe Kogaku Glen Cove NY Cell supplied by Opthos Inc Rockville MD Coils Heath 440 694 from the Berkeley Physics course INote that the polarizing efficiency of conventional Polaroid sheets is very low at these wavelengths ZH Adams D Reinert P Kalkert and W Urban A differential detection scheme for Faraday rotation spectroscopy wi
145. fined by two irises Rev 2 0 11 09 eS a ee am ee ee ee E ROM g od o 2 p El o US 2 sl gt a oe a o o no D gt c P e SS ES 7 yoyew 0 eur 5 yoyew 0 eur amp Oo eee z S gt IN 3 30 Rev 2 0 11 09 EXPERIMENTS SECTION for DIODE LASER SPECTROSCOPY Experiments I III were written for the Advanced Physics Laboratory of the California Institute of Technology Pdf versions of these documents can be found on the Caltech advanced lab website Experiment IV can be found in an article written for the American Journal of Physics by Professor David Van Baak of Calvin College who is also a TeachSpin collaborating physicist I Saturated Absorption Spectroscopy Caltech II Interferometric Measurement of Resonant Absorption and Refractive Index in Rubidium Caltech III Resonant Light Propagation through an Atomic Vapor The Maculuso Corbino Effect Caltech IV Resonant Faraday rotation as a probe of atomic dispersion D A Van Baak Am J Phys Vol 64 No 6 June 1996 Ph 76 ADVANCED PHYSICS LABORATORY ATOMIC AND OPTICAL PHYSICS Saturated Absorption Spectroscopy I BACKGROUND One of the most important scientific applications of lasers is in the area of precision atomic and molecular spectroscopy Spectroscopy is used not only to better und
146. for them to give up that energy except by radiative decay they emit in about 25 ns on average a photon of light in reverting to the ground state These photons emerge in directions random with respect to the incident laser beam in fact a whole thread of atoms inside the cell lying in the volume of the laser beam glows as it emits into all directions this resonance fluorescence You can t see it by eye only because your eyeball s sensitivity is so poor at these wavelengths But simple solid state CCD cameras have full sensitivity in the near infrared so a monitor s display of the camera s view of the cell will image this fluorescence for you in real time One of the instructional pleasures of the diode laser system is that the correlation of absorption and fluorescence can be seen in real time all that s needed is a slow scan in frequency over the resonance region which will show that it s when and only when the transmitted power diminishes that the atoms are fluorescing Diode Laser Spectroscopy David Van Baak July 2009 But the next thing that appears in such scans slow or fast is that there are as a function of frequency four occurrences of absorption and fluorescence not just one This can be attributed to two causes 1 There are two isotopes in natural rubidium Rb 85 and Rb 87 and they have separate transitions frequencies 2 Each isotope s atoms have two ground states separated in energy by the tiny hyperfine
147. g the input polarization to be rotated as desired The requirement of detecting the rotation of polarization is a bit more complicated If the light emerging from the sample cell were purely linearly polarized then its direction of polarization could be found at any one wavelength by searching for extinction with a rotatable linear polarizer used as analyzer But there are two objections to this classical technique first in the presence of differential absorption the output light is in general elliptically polarized as 4 shows so that exact extinction cannot be achieved and second this technique does not lend itself to an automated procedure giving a real time display of polarization rotation as a func tion of laser frequency So for this application we have in stead built a simple polarimeter based on a polarizing beamsplitter cube and two photodiodes arranged as shown in Fig 6 For input light parallel to the axis shown and lying in the wavelength range of the device the beamsplitter ap proximates very nearly the intended function of transmitting all of the input light of one linear polarization and deflecting through a right angle all of the input light of the orthogonal linear polarization In practice the laser beam used is of D A Van Baak 730 detector 2 detector 1 am rotation angle Fig 6 The polarization analyzer used to gather the Faraday rotation data of this paper composed of a polarizing
148. ge circuit leads to the following relation between thermistor resistance RT and voltage VT VT 2 5 0 RT 10 000 RT Values of thermistor resistance and voltage for temperatures from 10 to 60 C are listed in Table 1 on the following page The set point voltage is adjusted using the ten turn potentiometer located on the back panel The set point may also be controlled remotely with the temperature modulation input on the back panel The set point voltage is the difference between the voltage set by the potentiometer and the modulation voltage Set Point Monitor 10k Q PID Circuit Instrument Amplifier Temperature Monitor Figure 3 Laser Temperature Control Electronics The voltage modulation circuit is not shown in Figure 3 Modulation input voltage is attenuated by one fifth so a five volt change in the modulation voltage leads to a minus one volt change in the set point voltage In the MONITORS section of the front panel the LASER DIODE TEMPERATURE and SET POINT voltages may both be measured Two LEDs mounted on the front panel indicate when the laser head is above or below the set point temperature Rev 2 0 12 09 Thermistor Resistance and Bridge Voltage as a Function of Temperature Temperature Resistance Voltage Temperature Resistance Voltage Ohms Volts C Ohms Volts 55 330 52 440 49 690 4 2347 4 1992 4 1623 25 26 27 10 000 9574 2 5000 2 4
149. get back into the laser and corrupt the scan If this is a problem adding more attenuators after the glass neutral density filter will help Rev 2 0 11 09 V Appendix Making Beams Collinear Two points define a line iterative procedure to align a laser beam to a line in space The pictures are only for aligning in one dimension The process is shown in the Figures 1 4 below The objective is to get the laser beam the narrow line to be collinear to the line in space represented by the darker dashed line The angles have been exaggerated to make it easier to see what is going on 1 With the viewing card near to mirror M2 adjust angle of mirror M1 until the laser beam is intersecting with the desired line in space See Diagrams and 2 2 Now move the viewing card to a distance far away from M2 as shown in Diagram 3 3 Adjust the angle of mirror M2 so that laser beam again intersects the line in space You will notice that this makes the alignment at the first position near M2 off a bit 4 Now move the viewing card back to position shown in Diagram 1 and repeat You will probably have to repeat the process several times to get the beam where you want it That s iterative for you The closer the viewing card is to M2 the faster this procedure converges You might ask where the line in space that you are trying to match comes from It could be another laser beam or perhaps a desired beam path de
150. gin to look like Figure 5 We can now see some structure in the FP transmission signal Each peak represents the excitation by the laser of a different resonant mode of the FP cavity The transmission maxima occur in repetitions of a cluster of modes Successive clusters are spaced by the cavity s free spectral range and differ in the longitudinal mode number of the cavity mode Within each cluster is a collection of modes which occur because you are exciting various transverse modes of the cavity Tek MIM Trig d M Pas 43 20ms SAWEFREC Action Save Image Lu fe ee ee ur uu ui le i i t Format LUEIUEE Da Pa BIETER UE Saving Images 2 vibra rain pinitiret Pikes id NONE EE nS Gee eem Falder r i Save TEKOOO2 BMP CHi iiim CH2 e1 00vBy M 10 0rms Ext 20 uv 24 Jan 07 04 37 10Hz Figure 5 Same signal as Figure 4 but steering mirrors have been tweaked for maximum signal 8 TeachSpin Fabry Perot Manual Rev 2 0 11 09 In Figure 5 we can see that these transverse modes are occurring at distinct frequencies This is because the cavity length is not set to the confocal condition where all the transverse modes become degenerate and occur at the same frequency When tweaking the steering mirrors you may notice that there is still some light feeding back into the laser Now is a good time to use the linear polarizer and quarter wave plate to Tu construct a poor man s optical isol
151. ground states are given by P P 1 2P5 and gus s 2 1 s 46 T where s I Isat and 6 v vo vov c Isat is called the saturation intensity for obvious reasons if you consider the above formula for P gt with 6 0 P saturates P gt 1 2 as I Isat oo The value of Page 4 Isat is given by Isat 207 hc 3A3 For the case of rubidium T 6 MHz giving Isat 2 mW cm The underlying physics in points 1 and 2 should be recognizable to you Point 3 results from the competition between spontaneous and stimulated emission To see roughly how this comes about write the population rate equations as Pi DP ol P P5 P TP al P Pz where the first term is from spontaneous emission with I equal to the excited state lifetime and the second term is from stimulated emission with a a normalization constant Note that the stimulated emission is proportional to the intensity J In the steady state P P 0 giving aIr 1 42oI T The term aZ T corresponds to the s 2 term above note Isat is proportional to D A more complete 2 derivation of the result with all the normalization constants is given in Milonni and Eberly 1988 and in Cohen Tannoudji et al 1992 but this gives you the basic idea Assuming a fixed vapor temperature atomic mass etc the saturated absorption spectrum is determined by two adjustable external parameters the pump intensity pump and the on resonanc
152. h is accompanied by a decrease in height by a similar factor The results are shown in Fig 4 which re semble the unbroadened curves of Fig 2 in character but which are smaller in vertical scale Remarkably enough the dispersion per unit absorption is scarcely affected by Dop pler broadening in fact for a Doppler broadened sample of density sufficient to give the same absorption at line center the dispersion at its extrema is actually some 23 larger than in the unbroadened case Since the Faraday rotation signal is related to the differ ence between two dispersion signals the same results apply to it The large increase in horizontal scale implies that the magnetic field required to maximize the line center Faraday rotation will be increased by a similar factor giving the re quirement kB A vp 2 for the case of interest Av5 500 MHz so that a field of about 18 mT 180 Gauss is required The previous results for Faraday rotation per unit absorption still apply with the Doppler related correction noted above a sample giving e transmission at zero field line center is predicted to display maximum Faraday rotation of 0 5 rad xX 1 23 35 Finally Fig 5 gives some computed results for Faraday rotation as a function of laser frequency for some different 729 Am J Phys Vol 64 No 6 June 1996 Magnetic field e 4xm B 1 2 4v Faraday rotation angle A0 v in units of NA 7L 8i 3 3 2 1 0 1 2 Detu
153. he ND filter should usually be removed when aligning the beams Point the TV camera at the photodiode when looking at fringes You should also note that by gently pressing on the breadboard one can move the fringe pattern ef fectively changing AL above With the photodiode sampling the interfering beams and the laser off resonance wiggle one of the mirrors with your finger gently while watching the photodiode output on the oscilloscope You should see a time dependent fringe pattern that looks something like a that shown in Figure 3 Measure the fringe contrast Imax Imin Imax You can adjust the interferometer while wig gling the mirror to get high contrast fringes on the oscilloscope You may find it necessary to play with the alignment a bit to get a good fringe contrast For best results the contrast should be better than 0 8 Page 7 since your theory assumed a constrast of unity When you get good fringes capture the photodiode output while wiggling the mirror on the digital scope and put a hard copy in your notebook a m a theory for tau0 25 phase 0 500MV M 00ms A Ext X S00mV I 4 800 13Sep 2002 10 01 59 Figure 5 A comparison of a measured spectrum left with a calculated spectrum right The plot shows I Aw Ig versus Aw y The calculation assumed 7 25 at line center and kAL 0 The measured spectrum is for the 85b line but the adjacent 87b line complicates the right
154. he TV monitor it is often necessary to adjust either or both the background room light and laser intensity Use the neutral density filters to adjust the laser intensity This is particularly true if you are trying to image the laser beam profile or when you are looking for fringes while lining up an interferometer Rev 2 0 12 09 VI Addendum VI A CONDENSING RUBIDIUM IN THE TIP When operating the cell at elevated temperatures above the normal 40 50 C it is possible that excess rubidium may move out of the cooled tip and condense on the windows The following procedure may be used to evaporate the Rb off the windows and condense it back in to the tip 1 Place the foam inserts into the open ends of the cell heater as shown in the figure below The smaller foam plug was only included in Diode Laser s with serial numbers DL154 and greater If you have an earlier model Diode Laser just use a piece of foam or insulation to block the opening in the cell heater 2 Increase the cell temperature set point to about 120 C The exact value is not important See section A8 5 and A8 6 for details on cell temperature controller 3 Let the cell heat up and stay hot for about 1 hour You can remove the foam plugs quickly and check to see if all the Rb has moved off the windows 4 After the Rb has been evaporated off the windows return the cell temperature set point to its usual operating point 40 50 C Leave the foa
155. he beam by about 45 degrees using the Faraday effect and the beam exits through the second polarizer which is set at 45 degrees A beam coming back toward the Page 10 laser sees all this in reverse the beam polarization gets rotated in the crystal so that the polarization is 90 degrees with respect to the vertical polarizer and the beam is not transmitted These devices are also sometimes called optical diodes since light only passes through them in one direction We use an optical isolator here to keep stray light generated downstream note the pump beam goes backward after it passes though the cell from getting back to the diode laser where is can adversely affect the frequency stability Note the 10 90 beamsplitter puts most of the laser power into the probe beam The irises are an alignment guide if you have both the pump and probe beams going through small irises then you can be assured that the beams overlap in the rubidium cell If you block the pump beam you should get a spectrum that looks pretty much the same as you had in the previous section Lab Exercise 1 Observe and record the best spectra you can for whatever rubidium lines you can see especially the two strongest lines 87b and 85b in Figure 7 Get some nice spectra and put hard copies into your notebook Note but don t bother recording that the saturated absorption features go away if you block the pump beam as expected Week 2 Measuring the Hyperfine Splitti
156. he direction indicated on the polarizer Figure 14a Laser Beam with Figure 14b Laser Beam with Figure 14c Laser Beam with laser current below threshold laser current just above laser current well above Only incoherent LED light is threshold laser light and LED threshold An ND filter has been visible light visible placed between laser and viewing screen only laser light is visible There exists a magic cavity length for which as the angle of the grating is changed both the wavelength diffracted by the grating and the wavelength of an external cavity mode determined by the cavity length change at the same rate with angle This distance can be determined from the diffraction angle and distance from the grating pivot point to the center of the beam spot on the grating For the TeachSpin laser head this distance is about 0 58 inches 14 7mm This would Seem to promise extremely long mode hop free scans Unfortunately the presence of internal cavity modes in the diode itself destroys the potential of long scans See Diode Laser Physics Section A diode with an antireflection AR coating on its output facet would have no internal cavity modes and should show these long scans The cost of AR coating a diode 2 000 00 has precluded any investigations by TeachSpin We would be interested in hearing from anyone who has access to or has tried diodes with an AR coating Rev 2 0 12 09 I D 4 c Adjustment of Lens Position Opt
157. he isolator works because when light is specularly reflected from a surface there is a change in the momentum vector but not the angular momentum Thus a light beam that is right hand circularly polarized RHCP when approaching a mirror is left hand circularly polarized LHCP after a 180 degree reflection from the mirror See Figure 1 below When the reflected light passes through the 1 4 wave plate in the reverse direction the beam again becomes polarized Because of the change in handedness the plane of polarization of the returning light is at a 90 angle to the Linear Polarizer and so its passage is blocked We have optically isolated the source of the incoming light In the case of a laser this is extremely important because light re entering a laser cavity significantly disturbs its performance polarization P ert axis incoming light Linear Polarizer linearly polarized photons 1 4 Wave Plate RHCP Reflectin photons e Figure 1 Schematic showing the change in the direction of circular polarization at reflection and the resulting change in linear polarization which prevents the light from passing back through the Linear Polarizer The 1 4 wave plates that come with your diode laser are not specified to be exactly a quarter wavelength for 780 nm light Fortunately it is possible to tune the optical thickness retardation of the wave plate by tilting the wave plate about either its fast or its s
158. he magnetic field and which preserves the selection rules of Am 1 for the fields described by E But such exact calculations are not particularly illumi nating and for the purposes of this paper we will instead adapt reality to the model by the following prescription We will treat not only the two isotopes but also the two ground state hyperfine populations of each isotope as sepa rate noninteracting populations we will ignore the upper state hyperfine structure entirely and we will assume that the transitions out of the ground state obeying the Amp 1 selection rules follow a simple Zeeman shift given by 13 In other words we will treat the data as if rubidium were a mixture of four distinguishable kinds of the model atoms treated in the theory section above the expected relative populations of the four species are given in Table I With this heavy handed approximation we can readily predict the expected size of the absorption signals using the number densities of Table I for each of the four notional species of rubidium we can use 15 to evaluate the absorp tion exponents 2A v L for the four species present and then subject these to Doppler broadening by the methods of the Table I Statistical weights and number densities for the four species of rubidium giving rise to the four absorption features in Fig 7 The features are labeled by the convention of Ref 26 and are given in order of decreasing opt
159. here are two velocity classes of atoms for which this is true atoms moving toward the pump laser and away from it If the atoms in the vapor cell had a single excited state but two hyperfine ground states we call them both ground states because neither can decay via an allowed transition and the separation of the ground states was less than the Doppler width then one might see a spectrum like in Figure 4 The extra cross over dip results from a phenomenon called optical pumping which occurs because atoms in the excited state can decay into either of the two stable ground states Thus if atoms are initially in ground state g1 and one shines in a laser that excites 21 e atoms will get excited from gl e over and over again until they once spontaneously decay to g2 where they will stay The state g2 is called a dark state in this case because atoms in g2 are not affected by the laser We see that a laser exciting g1 e will eventually optically pump all the atoms into g2 To see how optical pumping produces the extra crossover dip remember that only the pump laser can optically pump the probe laser is by definition too weak Also remember the atoms in the cell are not in steady state When they hit the walls they bounce off about equally distributed in both ground states and the optical pumping only 1 amp mc 2 o m Bo eo go o a amp oo 4000 2000 0 2000 4000 v vg MHz Fig
160. hich defines the optical depth t is proportional a c to the atomic vapor density and the path length E S As a result the probe spectrum is essentially a B M simple Gaussian profile E The lower plot in Figure 2 shows the spectrum P S with the pump beam A spike appears right at the y A atomic resonance frequency The reason this spike appears is as follows If the laser frequency is 4000 2000 0 2000 4000 Vo Av then the probe beam is absorbed only by 0 i iig v vg MHz atoms moving with longitudinal velocity v cAV vg moving toward the probe beam 1 These atoms see the probe beam blue shifted into resonance other atoms are not in resonance with the probe beam and so they do not contribute to the probe absorption Because the pump beam is in the opposite direction these same atoms see the pump beam red shifted further from resonance so they are unaffected by the pump beam Thus for laser frequencies v V the probe absorption is the Probe Transmission 02 0 4 06 0 8 0 same with or without the pump beam However if vy 2vg then atoms with zero velocity v 0 4000 2000 0 2000 4000 i v vy MHz contribute to the probe absorption Fig 2 Absorption spectra for 2 level atoms both These v 0 atoms also see an on resonance without upper and with lower the pump beam pump beam which is strong enough to keep a significant fraction of the atoms in the excited state
161. hich means it contains other modes Page 9 at some level Print out a trace showing your best TEMoo modes The Confocal Cavity The next task is to set up the confocal Fabry Perot cavity as shown in Fig ure 7 and to look at some of its properties Unlike the previous cavity the confocal cavity is insensitive to the precise alignment and mode matching of the input beam because the different transverse modes are degenerate in frequency see the discussion in Section I above Nevertheless you still have to align things reasonably well using the same procedures described above Observe the Mode Structure of the Cavity Align the input beam and adjust the cavity length until the transmitted signal shows a series of sharp peaks much different than with the non confocal cavity Tweak the cavity length so the peaks are narrow and symmetrical which should maximize the transmitted peak intensity Once that looks good change the cavity length by a large amount say 10 turns of the mounting tube and observed the transmitted spectrum As the cavity length is changed away from the confocal length the transverse modes are no longer degenerate At first you see the peaks broaden and become asymmetrical Then as you change the length more you can see individual mode peaks show up Change the input beam alignment to see the different modes change in amplitude Print out a few spectra with different cavity lengths Measure the Transmitted and Reflect
162. hip between wave number k and frequency w for any monochromatic plane wave propagating through the material ll 1 z 1 x 8 In the limit of low density we will see that x is so small even near resonance that we can adequately write ke X slt 9 L w 5 then the usual decomposition of y into real and imaginary parts x x tix 10 gives the results r X 2 T n 1 gt and H 11 Thus the macroscopic propagation constants n and f have been related to the real and imaginary parts of the micro scopic susceptibility respectively The third part of the derivation is to assume a model for the medium and to compute its electric susceptibility The D A Van Baak 725 1 0 1 Z COMPONENT OF ANGULAR MOMENTUM Fig 1 The model atomic system used in this paper to compute absorption dispersion and Faraday rotation in a dilute vapor The ground state is non degenerate and the excited state has three magnetic sublevels here shown as slightly split by an external magnetic field simplest model system is a gas of independent atoms of number density N with each atom having a nondegenerate ground state and an excited state forming a Zeeman triplet as shown in Fig 1 This is exemplified by a 1S P tran sition of an atom with no nuclear spin or hyperfine structure such an atom shows the normal Zeeman effect and in the presence of a magnetic field B Bz the upper state sublevels split as s
163. hown in Fig 1 with m 1 states undergoing en ergy shift AE ugB 12 where ug efi 2m is the Bohr magneton Then transitions from the unshifted ground state to the m 1 excited states will occur at Bohr frequencies AE B e Vo 7 vot E yt voc For the electric fields introduced in 1 the electric dipole selection rules allow the fields E to induce only the reso nant upward transitions with Am 1 respectively Thus each circular polarization will separately interact with its own two level system and so each polarization will propa gate with its own index of refraction and attenuation con stant as was assumed above These numbers in turn will be those arising from the susceptibility of a generic two level atomic system which is given as a function of optical fre quency v by NX 1 x 1 e dw INVE Tg B 13 14 where c v vo is the Bohr frequency of the transition Av 277 is its natural linewidth full width at half maximum in ordinary frequency and 7 is the spontaneous decay lifetime of the upper state Then from the result 11 above we can write the attenu ation constant for the electric field as ONY Av 2 T B v 16727 v vo Av 2 15 which shows the conventional Lorentzian line shape It gives peak absorption at line center where v vg and A Ag c V here 8 reaches the value 726 Am J Phys Vol 64 No 6 June 1996 Bows Temer Ay dm so Again from the earli
164. i est solution is to buy and test multiple diodes and find one which does not mode hop past the desired frequency In any given mode these lasers exhibit typical tuning rates of about 120 GHZ K as their case temperature is varied and 2 GHz mA as their injection current is varied In order to vary and then stabilize the laser diode temperature we have used two stage thermoelectric servomechanisms although single stage systems would likely suffice in this application In order to perform real time scanning of the laser frequency we vary the diode laser current about its average value of order 60 mA by a sawtooth modulation of audio frequency and peak to peak amplitude of about 5 mA this gives in addition to a characteristic but undesired modulation of the optical power output a sawtooth scan of optical frequency over a range of about 10 GHz This is sufficient to scan over the rubidium resonance line s hyperfine structure pattern Fi nally since the light emerging from the diode laser is strongly divergent we use an optimized lens mounted just in front of it to produce a collimated beam of transverse dimensions about 2X5 mm Such a lens can easily be ad justed to produce a beam with a divergence negligible over a meter s flight path the elliptical cross section and residual astigmatism common to most diode laser beams do not present a problem in this experiment However the large optical intensity of order 5 mW in just a fe
165. ical frequency Isotope Isotopic Statistical Overall Number Feature and F value abundance weight weight density iv 8Rb F 1 0 2785 3 8 0 1044 0 26 x 10 6 iii Rb F 2 0 7215 5 12 0 3006 0 75x10 ii 85Rb F 3 0 7215 7A2 0 4209 1 05x10 6 i 8Rb F 2 0 2785 5 8 0 1741 0 44x 1015 732 Am J Phys Vol 64 No 6 June 1996 M HH L s Statistical weight is computed from 2F 1 2 2 1 where 2F 1 is the number of degenerate magnetic sublevels in a ground state hyperfine level of a given F value and 2 2 1 is the total number of ground state sublevels Number densities in m are computed assuming rubidium temperature T 25 C 298 K and overall ru bidium number density 2 5X 10 6 m from Ref 12 D A Van Baak 732 NE ee 20 20 60 30 b 20 20 30 d 0 2 0 0 2 0 4 0 6 0 8 1 t2 Relative incremental diode laser current Fig 8 a The signals obtained from the two photodetectors of the polar ization analyzer of Fig 6 under conditions of polarizer angle 45 zero magnetic field and one signal electronically inverted b The sum of the two signals of a further expanded vertically by a factor of 2 this is the signal representing zero Faraday rotation Appendix Summing these and using the B 0 A0 0 version of 37 above then gives a theoretical model for the ab
166. ically sample the 4 dimensional alignment space defined by the four adjustments of M1 and M2 Your TA can show you how Once you have the transmitted beam down to a single sharp spot place the photodiode to intercept the beam and place the TV camera to view the shape of the beam With the sweep on you should see a forest of peaks on the transmitted signal Each peak corresponds to a single cavity mode you are exciting with the laser Each TEM mode has a slightly different frequency so each gives a separate peak In addition the spectrum repeats with a period of Av pgr If you tweak the alignment of the incoming beam slightly you will see the peaks all change height This is because you excite different modes with different alignments With the sweep off you can examine the shapes of the different modes using the TV camera Move the piezo DC offset adjust to select different modes Compare with Figure 3 above Print out an oscillo scope trace showing a typical scan and tape it into your notebook Page 8 TEMO0 mode i TEMOO mode other modes Cavity transmission Figure 6 The cavity transmission with fairly good mode matching Note the dominant TEMg 9 modes separated by Av psr The peaks heights are very sensitive to alignment and even to vibration Mode Matching Now you should try to excite just the TEMoo mode of the cavity which means you have to mode match the incoming beam to the cavity mode If you think about th
167. ies atomic absorption Faraday s own account of his discovery is available in a reprint edition discussions of it in biographical and bibliographical contexts are also available The enhance ment of the Faraday effect near resonance lines in atomic vapors was discovered in 1898 by Macaluso and Corbino and has been applied in modern times to create narrow band optical filters Two earlier papers in this Journal describe Faraday rotation experiments in bulk matter this effect has also become the basis of optical isolators The deriva tion worked out in this paper has been guided by that of Preston and Dietz who however are motivated by experi ments on nonresonant rotation in bulk matter Section II of this paper gives a quantum mechanical treat ment of Faraday rotation in a dilute vapor of a model atomic system Section III discusses the instrumental requirements for diode laser spectroscopy of rubidium vapor in general and the added requirements for Faraday rotation experiments in particular Section IV presents and discusses typical ex perimental results and Sec V presents conclusions and ap plications II THEORY We divide this derivation of Faraday rotation into four parts The first step is to consider the propagation of linearly polarized light through a medium resolving it into two op positely directed circularly polarized fields which are as sumed to propagate independently The second step is to relate the
168. iffraction grating holder a Removing the grating Components b Installing the grating V CCD Camera and TV Monitor 5 32 c Setting the beam height A The TV Monitor d Contacting the PZT stack B Camera Focus 4 Collimation tube a Replacing the diode VI Addendum 5 33 b Setting laser orientation and A Condensing Rubidium in the Tip cavity length c Adjusting the lens position Rev 2 0 12 09 I Laser LA 9 PIN CABLE AND CONNECTOR The 9 pin cable provides electrical connections between the laser head and electronics box A pin out of the connector is shown in Figure 1 Your Laser diode head was shipped with a protective plug on the 9 pin connector on the laser head When you are ready to use the laser diode remove the protective plug and attach the 9 pin cable Do not discard the protective shipping plug It can be used to protect the laser whenever the cable to the controller is removed For both operational and safety reasons it is important to keep the 9 pin electrical cable connected between the laser head and Laser Diode Controller box whenever possible There is protection circuitry inside the laser head but large electrostatic voltages may still damage the laser diode Ground yourself before removing the plug and attaching the cable When the instrument is turned on there is also the possibility that high voltage is present on the cable a maximum of 100 Volts that drives the piezo stack Always connect the 9 pin cable
169. ight reaching the detector As the laser frequency sweeps through fo however atoms with a v 0 can absorb photons from either of the beams The stronger pump beam saturates the transition leaving far fewer atoms to interact with the probe beam As a result the intensity of the probe beam light reaching the detector increases significantly creating the sharp spike shown in the lower section of Figure 2 But what happens if there are two or more closely spaced transitions transitions so close that the oscilloscope signal appears as single wide Doppler dip As Figure 3 indicates for a case of two closely spaced transitions fo and fo the oscilloscope trace will show not two but three spikes within the Doppler curve While two spikes are at the expected frequencies the frequency of the third spike is exactly halfway between the two actual transition frequencies At this halfway frequency fi two groups of particles have velocities which allow them to absorb photons from either beam Because of their motion atoms with velocity v 1 see the frequency of pump beam photons as elevated to fo while the probe beam photons appear to have a frequency of fo For atoms of velocity V 12 the opposite effect occurs For both sets of atoms the absorption of probe beam photons decreases creating a spike in the Doppler curve 2 of 4 Doppler Broadened Signal Vz Absorbs probe fg T Probe Beam fa Absor
170. illimeter gap between the collimation tube and diffraction grating Do not let the collimation tube touch the grating You need to leave space for the grating to move If not already connected attach the 9 pin cable to the laser head and turn on the AC power to the Laser Diode Controller The angular orientation of the laser within the collimation tube holder can be determined either by measurement of the polarization direction or observation of the beam profile Figure 9 showed the setup to observe the beam profile as well as the retro reflection Figure 14 shows several images of the beam profile In image 15c the glass Neutral Density filter has been placed in the beam path so that the LED light from the diode does not interfere with imaging of the laser light Turn on the Laser Power and increase the current till the laser is above threshold Loosen the setscrew and rotate the collimation tube within the holder until the long axis of the beam imaged on the video screen is horizontal Figure 14c You might also notice that two streaky features above and below the image that are from the LED light Making these streaky lines vertical also sets the correct orientation To measure the polarization direction of the beam place a linear polarizer available only with the complete optics package after the glass ND filter and turn the polarizer until a minimum intensity image is observed on the video monitor The electric field is polarized 90 degrees to t
171. imal alignment of the diode laser involves adjustment of the lens position within the collimation tube We have found that proper lens position is crucial for obtaining long mode hop free scans of the laser When installing a new diode we have found that you have to adjust the lens position about half of the time For some of the new diodes the old lens position will work just fine To determine whether the lens position needs to be adjusted we observe the laser behavior as we scan with the piezo only no current scan through the rubidium absorption features If after careful external cavity alignment you can sweep through the first three absorption features 87b 85b and 85a See the diagram in Initial Setup section 27 then the lens position is fine If on the other hand you find that you cannot make a nice long sweep the lens position may need adjustment Operating note During the following procedures you will be turning the laser current on and off while you adjust the lens position To adjust the position you will be looking almost directly into the output of the laser We strongly urge you to exercise extreme caution and use proper laser safety Keep your laser safety goggles on and always check that the laser current is set to zero and that the laser power has been turned off before you check the lens position LD 4 c 1 Coarse Lens Adjustment If you are installing a new diode into a collimation tube that has been previously used you ma
172. in Figure 10 shows both the primary and retro reflected beams The intensity of the retro reflected beam is only 2 3 that of the main beam You will have to set the laser current a few milliamps above threshold to see the retro reflection As discussed in Initial Setup of Chapter 3 Section II D 5 the TOP knob is used to change the vertical position of the beam and the SIDE knob is used to change the horizontal position See Figure 2 of Initial Setup on Chapter 3 page 6 Use the TOP knob to set the beam height at 4 0 If the grating has been removed refer to Section I D 3 b and c Installation of the grating and setting the beam height Dim the room lights The retro reflected beam may appear above or below and to the right or left of the main beam spot Be sure to position the viewing card with the main beam spot in the center e 7 0 Buisness Card in Card Holder Figure 9 Setup for Viewing Beam Profile and Figure 10 Laser Beam Image Retro reflection Misaligned external cavity both main beam and retro reflection are visible Turn the SIDE knob until you see the weak retro reflection on the monitor You may have to make several turns of the SIDE knob in both directions Reposition the viewing screen to keep the main beam centered on the screen If you cannot find the retro reflection make sure that the laser is above threshold Section I C 3 or
173. inal output power 3 mW and wavelength 780 nm the further facts that their output is of very narrow spectral width of order 20 to 50 MHz and also tunable by changing the diode temperature or injection current make them wonderfully useful spectroscopic sources The happy coincidence of their nominal wavelength with the strongest resonance line in the rubidium spectrum and the extremely convenient vapor pressure of rubidium at room temperature make diode laser experiments in rubidium vapor extraordinarily simple and straightforward Even once exotic phenomena like Doppler free spectroscopy via saturated absorption can easily be per formed on a benchtop in real time The instrumental requirements for diode laser spectro scopy of rubidium in general can be divided into four cat egories laser source rubidium cell optical detectors and ancillary electronics For the laser source in such experiments we have used consumer market laser diodes such as the Mitsubishi MLA102 and Sharp LTO22MC devices Although nominally of 780 nm output wavelength in fact these devices can be D A Van Baak 729 discontinuously temperature tuned at average rate about 0 25 nm K or 1000 GHz K so that diodes of various nominal wavelength can be tuned to near the desired 780 nm wavelength The nuisance is that these diode lasers exhibit mode hops such that any given device has probability below 50 of being tunable to a target wavelength the eas
174. ion both knobs so that the laser is near the center of these mode patterns Position the TOP knob so that you are at a mode maximum and reduce the current till you can just see the diode start to lase We will define this as the threshold current This procedure is a little subjective but as long as you are consistent it will work fine LD 3 Diffraction Grating Holder The grating holder may be removed either to study aspects of the diode laser without the external cavity or to adjust the position of the collimating lens I D 3 a Grating Removal Set the Laser Current to zero and turn off the Laser Power Set the Piezo dc offset to zero and disconnect any cables from the Piezo modulation input Loosen the ball tipped setscrew that contacts the piezo stack See Figure 7 Remove the two 6 32 socket head cap screws that hold the grating holder to the mirror mount It will be necessary to hold the mirror mount with one hand as you loosen the 6 32 screws Remove the grating holder and set it aside Be careful not to touch the front face of the grating LD 3 b Installing the Grating Place the grating holder on the mirror mount insert and tighten the two 6 32 socket head cap screws You will have to hold the movable end of the mirror mount while doing this There is a certain amount of play in the angular position of the grating holder This play allows for the beam height to be set to 4 0 See below For the initial installation pres
175. irrors Al though the specular reflection from the interfer ometer mirrors does not retro reflect into the laser the back seatter can in some cases perturb the modes of the laser VI Applications of Scanning Spherical Mirror Interferometers As stated in the introduction scanning spherical mirror interferometers are useful for studying the general mode structure of gas lasers In this sec tion we consider two specific applications The first applieation of scanning spherical mir ror interferometers that we consider is their use in adjusting a laser so that it operates in a single transverse mode The conventional method for making such an adjustment consists of visually ob serving the intensity distribution in the output beam of the laser while adjusting the mirrors When the output beam has an apparently Gaussian intensity distribution the laser is assumed to be oscillating in the TEM transverse mode The above method for adjusting a laser is some what unreliable often lasers which appear to be operating in a single transverse mode actually are oscillating simultaneously in two transverse modes This double oscillation can be detected easily using a scanning mode degenerate spherical mirror interferometer Figure 4 shows the mode spectra obtained when a typical helium neon laser is oper ating in a two transverse modes and b a sin gle transverse mode 9 a Q FY EET
176. is the relative population of the excited state P P 1 ue dn e mv 2T qv is the Boltzmann distribution for v along the beam axis and DI 2z v vg Vovie T 4 F v v is the normalized Lorentzian absorption profile of an atom with natural linewidth I including the Doppler shift Putting this together we have the differential contribution to the optical depth for laser frequency v and atomic velocity v V s dt V V P P F v v e mv DAT qv C The overall normalization comes in with the zt factor which is the optical depth at the center of resonance line i e T dt V9 v with no pump laser the integral is over all velocity classes 3 The populations of the excited and ground states are given by P P 1 2P and s 2 145 4482 22 where s 1 1 and V Vo Vo v c I is called the saturation intensity for obvious sat reasons if you consider the above formula for P with 0 P saturates P 1 2 as IlI o sat Rev 2 0 11 09 The value of 7 is given by I 20 hcT132 For the case of rubidium I 6 MHz giving Z 2 mW cm The underlying physics in points 1 and 2 should be recognizable to you Point 3 results from the competition between spontaneous and stimulated emission To see roughly how this comes about write the population rate equations as B TP amp I P P P 2 TP al P P where the first term is from spo
177. ished III REFERENCES Camparo J C 1985 The Diode Laser in Atomic Physics Cont Phys 26 443 Moller K D 1988 Optics University Science Books Wieman C E and Hollberg L 1991 Using Diode Lasers for Atomic Physics Rev Sci Instrum 62 1 Yariv A 1991 Optical Electronics 4th edition Holt Rinehart and Winston DIODE LASER SPECTROSCOPY SPECTROSCOPY Rev 2 0 11 09 Diode Laser Spectroscopy I BACKGROUND One of the most important scientific applications of lasers is in the area of precision atomic and molecular spectroscopy Spectroscopy is used not only to better understand the structure of atoms and molecules but also to define standards in metrology For example the second is defined from atomic clocks using the 9192631770 Hz exact by definition hyperfine transition frequency in atomic cesium and the meter is indirectly defined from the wavelength of lasers locked to atomic reference lines Furthermore precision spectroscopy of atomic hydrogen and positronium is currently being pursued as a means of more accurately testing quantum electrodynamics QED which so far is in agreement with fundamental measurements to a high level of precision theory and experiment agree to better than a part in 108 An excellent article describing precision spectroscopy of atomic hydrogen the simplest atom is H nsch et al 1979 details are in References Although it is a bit old the article contains many ideas
178. its of natural width Av Fig 2 Graphs of the absorption a and dispersion b signals computed for the model two level atomic system in the absence of Doppler broadening The curves arise from Eqs 15 and 17 respectively the horizontal scale is in units of the natural linewidth Av and the vertical scales are in units natural to the problem n n vo V HY 35x75 yp YF A D Vo V E vo v Av 2 21 Figure 3 shows the general character of the Faraday rotation signal deduced from this result its frequency dependence arises from the difference of two offset dispersion signals so that the A v signal has a symmetric form centered at the unshifted line center v The analytic form of the Faraday rotation signal is thus a bit complicated but two special cases are worth extracting The first is applicable whenever the magnetic field and thus the Zeeman shift is small enough it makes use of the general result f x e9 f x e 2e f x O e 22 which using 17 allows 21 to be written to lowest order in B as 1 e dn e dn A VBL with Ve onde OBI dv Q3 Thus the Faraday rotation A60 is predicted to be proportional to the strength of the magnetic field and the sample length with a proportionality factor V called the Verdet constant and V is predicted to have a frequency dependence v dn dv or dn dA in agreement with the Becquerel formula 727 Am J Phys Vol 6
179. ity well below the saturation value Tune the laser so you can see all four of the rubidium transitions although probably not all in a single sweep Check how much background light is getting into the photodiode by blocking the laser beam You may need to turn out the lights and shield the photodetector to keep the stray light down Remember that zero volts on the photodiode may not mean zero light All amplifiers have offsets so you may need to compensate for the photodiode reading at zero light When you observe the photodiode signal on the scope you will probably notice that Iout wo Lin changes with laser settings in particular with the laser current This is because the laser doesn t always run in a single mode When it runs multi mode some light is not resonant with the atoms and thus is not absorbed This is a serious problem that limits how accurately you can measure 54 wo I You can get pretty good results if you do the following set the high voltage so the transition you want to observe is centered in the sweep and then adjust the laser current to minimize Iout wo Tin If you think the laser is scanning okay and giving you accurate measurements then start making measurements of Iguz wo Lin on the middle 85a line as a function of temperature Measure Iou wo Iout nonresonant Iin and Iaa4 4 at each temperature You can take J54 nonresonant to be an eyeball average of the intensity on either side of the line Don t move the cell
180. k in this lab is to look at the light transmitted through a simple cavity using the set up shown in Figure 5 Use the ramp generator in the laser controller to scan the laser frequency ask your TA how and monitor the photodiode output on the oscilloscope In order to get any light through the cavity you need to align the incoming laser beam so that 1 the beam hits the center of the first mirror and 2 the beam is pointed down the cavity axis The mirrors M1 and M2 provide the necessary adjustments to align the incident beam and note that the different degrees of freedom are nicely decoupled M1 mostly changes the laser position at the cavity and M2 mostly changes the angle of the entering beam Page 7 12 inches 50 50 beamsplitter Photodiode Short Cavity N TV camera w o lens gt Figure 5 Optics set up to view the light transmitted through the short cavity First adjust M1 so the beam is centered on the cavity and then adjust M2 so the backreflected beam coincides with the incident beam Use a white card with a hole in it to see the position of the backreflected beam Iterate as necessary When this looks good place a white card behind the cavity to view the transmitted beam It will be faint but you should be able to see a pair of bright spots or perhaps a bright ring on the card To bring the transmitted beam to a single spot you will probably need to walk the input beam which is a way to systemat
181. ks consider the experimental set up shown in Figure 1 Two lasers are sent through an atomic vapor cell from opposite directions one the probe beam is very weak while the other the pump beam is strong Both beams are derived from the same laser and therefore have the same fre quency As the laser frequency is scanned the probe beam intensity is measured by a photodetector If one had 2 level atoms in the vapor cell one might record spectra like those shown in Figure 2 The upper plot gives the probe beam absorption without the pump beam Here one sees simple Doppler Page 1 1 ao o a o 2 Bo go m a ro o a amp o 4000 2000 0 2000 4000 v vg MHz amp dc o u o a o ES i lt E e o amp o 4000 2000 0 2000 4000 v vo MHz Figure 2 Probe absorption spectra for 2 level atoms both without upper and with lower the pump beam broadened absorption in our case the Doppler width is much larger than the natural linewidth Av Dopp gt gt T and the optical depth of the vapor is fairly small r v lt 1 the transmitted fraction of the probe is e 7 which defines the optical depth 7 is proportional to the atomic vapor density and the path length so the probe spectrum is essentially a simple Gaussian profile The lower plot in Figure 2 shows the spectrum with the pump beam showing an additional spike right at the atomic resonance frequency The reason this spike appears is a
182. l Assembly in mounted at the center even when they are not in use E The Controller While almost all functions of the apparatus are controlled by the modules on the front on the Laser Diode Controller the potentiometer used to set the laser temperature is on the back to prevent accidental changes The laser temperature determines the lasing frequency and will be set at the factory The temperature should be touched only if for some reason a check of the Laser Temperature Set Point indicates it has been altered or the diode itself is changed Rev 2 0 11 09 The Modules starting from the right DETECTOR LOW PASS DC LEVEL This module provides power for three detectors and offers two detector inputs and a series of Monitor options You can look at either detector or a combined signal PIEZO CONTROLLER This controls the piezo modulation which determines the way the angle of the grating is changed and thus the change or sweep of the laser frequency It includes a monitor output RAMP GENERATOR This provides a bipolar variable amplitude and frequency triangle wave which can be used via the RAMP OUTPUT connection to modulate either or both the piezo stack and the laser current The resulting changes in the grating angle and current produce the variation or sweep of the laser frequency The RAMP GENERATOR module can supply a wide range of frequencies and amplitudes The SYNC OUTPUT connection for the oscilloscope is located in thi
183. l the Temperature Set point recorded on the data sheet shipped with your laser If it does not adjust the 10 turn potentiometer on the back of the chassis to obtain the correct set point b Make sure the LASER TEMPERATURE INDICATOR lights are both off If either of these is on then the laser temperature has not yet reached its set point temperature With a voltmeter connected to the LASER DIODE TEMPERATURE pin jacks you may monitor the laser temperature 2 PUT ON SAFETY GOGGLES Your laser typically runs with an output optical power of 10 30 mW all concentrated into a narrow intense beam Staring directly at the Sun sends about mW into your eyes and this is already enough to cause permanent eye damage To make matters worse the laser light has a wavelength close to 780 nm which is nearly invisible Practice proper laser safety anyone that is in the room and can see the laser should wear safety goggles when the laser is on 3 Set the laser CURRENT potentiometer fully counterclockwise low current then turn the LASER POWER switch on D Aligning the Laser 1 Locate the IR viewing card The sensitive area of the IR card is a dull orange color This contains a polymer that absorbs UV light from the ambient lights in the room especially fluorescent lights The polymer molecules are then excited into a metastable state and incident IR light from the laser can induce a transition that emits visible light Note the IR card will not w
184. lace it on the table now and center the PD on the beam Keep the PD reasonably close to the iris and cavity You will be making small changes in the position of the beam through the cavity you don t want the beam to move off of the active area of the PD as you do this Now place the FP back in the beam path Use the iris to center the downstream section of the FP on the beam and use the IR viewing card to position the upstream input mirror of the FP centered on the beam path Open up the iris so that the hole is at its largest opening and monitor the PD voltage on an oscilloscope as the diode is swept through the Rb absorption Set the gain of the PD near its maximum value 1 to 10 Mohm You should see an ugly signal on the scope See Figure 3 below note the evidence in the Rb absorption signal of feedback from the FP to the diode laser Tek MIN Trig d M Pas 43 20ms SAVESREC 2 rrirrdaggrd raga daga dd da dd Select lal ChB todd 45 4 Folder 1 Rind ER LONE Mal Gah USA KEAT UU URSI Save TEROOULD BIP CHi 200v CHz31400vBy Mi 10 0ms Ext 2L uv 24 Jan 04 33 TUHz Figure 3 First view of F P with no attenuation or isolator in beam path Upper Trace is Rb detector Lower trace shows transmission through F P cavity Gain in FP PD detector is 3 3M ohm Gain Rb absorption detector is 10k ohm Now place the glass neutral density filter in front of the laser Adjust the photodiode and
185. ld be 100 Part of the reason is losses inside the cavity as described in the discussion in Section I but that s only a small part Calculate about how great the losses would have to be to produce a 5 transmitted intensity assuming a mirror transmission of 1 The actual mirror losses are probably less than 0 1 per bounce unless the mirrors are very dirty which they shouldn t be The main reason for the low transmitted intensity is that the mode degeneracy is not perfect If you change the cavity length or input beam alignment only slightly you can see the peak height drop quickly Since the input beam is not mode matched to the cavity the transmitted intensity of any given mode is fairly low And if the modes are not perfectly degenerate they don t overlap well resulting in a low peak intensity With a non confocal cavity and a well mode matched beam it is possible to achieve a peak trans mitted intensity close to 100 However for simply looking at the frequency structure of a laser i e with an optical spectrum analyzer the confocal cavity is quite convenient to use even with its lower transmit ted intensity Page 11 FM Spectroscopy Next you should observe the FM spectra you calculated in the prelab exercises using the confocal Fabry Perot cavity as an optical spectrum analyzer With the transmitted signal show ing nice sharp peaks reduce the sweep to zoom in on a single peak Then take the RF function generator turn
186. le the digital method does Operating note You should always be wary that zero light on a photodiode may not correspond to zero voltage output You can check this by simply blocking the beam and noting the voltage K z Rev 2 0 11 09 All Finished At this point the initial alignment is complete and you are ready to move on to the more sophisticated spectroscopy experiments You may need to realign the grating feedback from time to time following the above procedures If not disturbed however the alignment will likely be stable for months Shutting Down If you are not using the laser for a few hours for some reason you can you can leave the controller on Then the diode laser and the Rb cell will stay at their operating temperatures and be ready to go when you need it BUT TURN THE LASER CURRENT OFF You should turn the laser current down and the laser power switch off whenever you leave the lab This is a safety precaution plus it will prolong the life of your laser With use the diode laser will eventually burn out and need to be replaced so leave the laser itself off when not in use It s okay to leave the ramp generator and piezo controller on and running at whatever setting you wish for examples the settings determined above You can also leave the Rb cell temperature at whatever setting you wish Then these will be set up when you want to use the laser just turn on the laser power switch and turn up the current Af
187. low axis Rotation about the slow axis causes an increase in the retardation and about the fast axis causes a decrease In practice one does not know which axis is the fast or slow or whether the retardation needs to be increased or decreased Happily the optimal setting of the wave plate can be found empirically 14 TeachSpin Fabry Perot Manual fast Set up the isolator near the source of the unwanted reflection Position the 1 4 wave plate so that its 0 mark is at the top making one of its axes vertical Orient the linear polarizer so that its polarization axis is at 45 degrees with respect to the vertical It is best to NOT have any mirrors between the isolator and reflection optics because the mirror will cause a change in the polarization state of circularly polarized light You may observe that I slow did not follow this advice in the set up shown in axis the photograph on page 5 of the manual The reason for this was that I wanted to keep the second 1 4 Wave Plate steering mirror close to the input of the F P cavity Figure 2 Diagram of 1 4 wave plate 4 for ease of alignment showing reference axes Alignment of the isolator involves two separate rotations first rotation of the wave plate in its own plane in the 360 degree mount that is provided and secondly rotation of the wave plate about the vertical axis using the optical mount that holds the wave plate to the table The diagnostic you will use for alignment will
188. ltage is applied This preloads the piezo stack If you find it difficult to tell when the setscrew has made contact you can turn on the laser power and current and use the viewing screen and CCD camera to look at the beam spot as you tighten the ball tipped setscrew When the beam spot starts to move the setscrew is in contact with the piezo stack LD 4 Collimation Tube Figure 12 shows an exploded view of the collimation tube and associated parts The aspheric lens threads into the front side of the collimation tube The split aluminum adapter and diode laser slide into the backside of the collimation tube The black plastic retaining ring threads into the backside of the collimation tube and holds the diode in place The printed circuit board PCB and 5 6 mm socket plug into the back of the diode The strain relief body slides over the PCB and threads into the backside of the collimation tube Three screws hold the strain relief cap onto the strain relief body Strain Black Palstic lit Alum Relief Cap Retaining Ring poni LT230 B Aspheric Strain Relief Body Plug in Collimation Tube Lens PCB 7 PL 2 56 Socket Head Screws 5 6mm Socket Thread Figure 12 Exploded View of Collimation Tube The aluminum adapter and retaining ring are for use with 5 6 mm diode lasers Included with your laser is a different retaining ring that can be used with 9 mm diodes if you
189. m plugs in place as the cell cools This is critical The windows must be kept warm to assure that the Rb will now condense in the tip 5 Once the cell cools the plugs may be removed and the cell heater returned to normal operation If you are doing high temperature experiments it is always advisable to put the plugs into the open ends of the cell before turning off the power to the heater This will prevent Rb from condensing onto the end windows as the cell cools Figure 21 Cell assembly showing placement of foam plugs DIODE LASER SPECTROSCOPY APPENDIX CONCEPTUAL INTRODUCTION to DIODE LASER SPECTROSCOPY THINKING ABOUT SATURATED ABSORPTION and CROSSOVER TRANSITIONS A Brief Introduction to Diode Laser Spectroscopy The ideal spectroscopic experiment would involve illuminating a free and unperturbed atomic system with perfectly monochromatic light and then seeing what happens to the light and to the atom as a function of the frequency of the light And nowadays it s feasible for undergraduates to get hands on experience of this very scenario in a tabletop real time experiment The nearly ideal monochromatic light comes most conveniently from solid state diode lasers mass produced for the needs of the optical data storage industry The first technology to be commercialized using aluminum gallium arsenide AlGaAs semiconductors led to the establishment of the near infrared 785 nm standard for CD readout Such laser diodes a
190. macroscopic index of refraction and the attenua tion of the two circular polarization components in a me dium to the microscopic susceptibility of the atoms in the sample The third step introduces the simplest quantum mechanical system for which the susceptibility can be com puted and extracts the results for Faraday rotation Finally this section takes up the effects of Doppler broadening on the signals computed from the model The first step of the theory resembles Fresnel s method for understanding optical rotation in chiral media in which an incident linearly polarized field is decomposed into two op positely directed circularly polarized fields of equal ampli tude the fundamental assumption is that each circularly po larized field propagates independently but differently through the medium Here we will suppose that each of the two circular polarizations has its own index of refraction and attenuation coefficient and work out the results for propaga tion We introduce the two circularly polarized fields propa gating in the z direction real parts understood E z t Eo xtiy exp i kz ct 1 and write the incident field as the superposition E 0 t E 0 0 E 0 7 2E X exp i k0 ct 2 which is clearly a linearly polarized field with polarization along x Now we assume that the fields E propagate with indices of refraction n and attenuation constants B respec tively Then the wave number k is given
191. mirrors they have focal lengths of 10 cm Therefore when properly adjusted the mirrors are 20 cm apart Part of your task will be to find the confocal condition experimentally 2 TeachSpin Fabry Perot Manual Rev 2 0 11 09 The ray diagram for a confocal cavity is quite simple any ray leaving either mirror at any paraxial angle and reaching the other mirror will return to its original point of departure after two round trips for a total distance traveled that s very near 4 L If the incident light reaches the ee x cavity parallel to but laterally displaced from the E common axis of the mirrors then the rays inside the cavity follow a bow tie pattern Emerging from the far end of the cavity are two transmitted rays either of which will show the transmission maxima you ll be studying From the mirror at the input end of the cavity there is also an immediate reflection from the cavity which can be used in advanced applications of a Fabry Perot interferometer At non resonant frequencies almost all of the light is reflected At resonant frequencies this immediate reflection reaches a minimum Unpacking the Instrument TeachSpin s Fabry Perot Cavity comes with an iris for aligning the beam and a brass spanner wrench which can be used to remove the retaining ring if you wish to change or replace the mirrors The Fabry Perot Cavity itself consists of an aluminum tube with a 0 5
192. must be tuned to about a part in 10 Start with the simple set up shown in Figure 8 The ND filter can be removed when aligning the laser beam Once you have the beam going about where you want it sweep the high voltage going to the grating PZT with a triangle wave so that the voltage varies from about 0 to 100 volts Use the HV 100 to monitor the high voltage on the oscilloscope Sweeping this voltage sweeps the grating position using a small piezo electric actuator made from lead zirconate titanate hence PZT While the high voltage is scanning you should then also change the laser injection current up and down by hand The current makes large changes in the laser frequency while the PZT makes small changes see the laser primer for details The plan is that with all this sweeping the laser will sweep over the rubidium lines and you will see some fluorescence inside the vapor cell This will appear as a bright line inside the cell don t be confused Page 9 by scattering off the windows of the cell If you cannot see the atoms flashing at all ask your TA for help The laser may need some realignment or you may just not be doing something right Once you see fluorescence compare the photodiode output to the rubidium spectrum shown in Figure 7 Usually you can only get the laser to scan over part of this spectrum without mode hopping see the laser primer Record your best spectrum using the digital oscilloscope and print it out At this poi
193. n oscilloscope trace of photodiode detector voltage vs time would be proportional to received light intensity vs frequency and so would have the same shape Because however atoms are in motion atoms with a component of velocity toward the laser beam which we shall call v a will see the photons with a frequency fA which is actually an amount Af below the transition frequency as having a frequency fo These atoms will therefore absorb photons from the beam In the same fashion atoms moving away from the laser beam at speed vzg will see photons of frequency fg an equal amount above fo as being at the transition frequency As a result of this phenomenon the oscilloscope trace we see is a wide smooth curve a Doppler broadening rather than a sharp dip Figure 1 offers a way to visualize this Doppler process In the upper section of the Figure the vertical axis of the graph indicates the magnitude of a particle s velocity in the direction of the laser beam The horizontal axis is the frequency of the laser The plotted line shows the velocity that a particle atom must have in order to absorb the laser photons at that particular laser frequency within the sweep The lower section represents an oscilloscope trace of the detector signal vs time as the frequency of the laser is swept from below to above the fo transition frequency of our imaginary gas The vertical axis thus indicates the amount of laser light reaching the detec
194. n tested Rev 2 0 12 09 I C 2 Current Electronics The ten turn potentiometer of the CURRENT module is used to adjust DC laser current One turn of the dial will change the current by about 10 mA The BNC plug labeled modulation input is used for external modulation of the current The attenuator dial is linked to the current modulation input With a maximum modulation frequency of 1 MHz and with the attenuator turned to 1 full on the input provides a modulation of 2 mA Volt The current itself can be measured using the BNC labeled laser current which is in the MONITORS section of the front panel The conversion factor is 1 Volt 10 mA I C 2 a Diode Protection Currents injected in the wrong direction or in excess amounts can render your diode inoperable The laser head is shipped with a protective shorting plug This must be removed before attaching the 9 pin cable Protective diodes are present in the laser head Refer to Figure 6 for details When the laser is on the three over voltage diodes will conduct slightly about 10 of the current from the electronics box will flow through these protection diodes Current to the diode laser is shunted to ground when the front panel laser power toggle switch is in the off position There is also a slow start circuit in the current controller that applies power to the electronics slowly after the AC power is switched on I C 2 b Current Limit Diodes are specified by the maximum optical power
195. nd a probe beam passing through the same sample to measure Faraday rotation Such an experimental arrangement would represent the use of the method of polarization spectroscopy in the presence of a magnetic field With the limitation of Doppler broadening removed the next obstacle to spectroscopic resolution would be the intrinsic linewidth of free running laser diodes This limit could in turn be surpassed through the use of extended cavity diode laser systems of very narrow spectral widths this would leave the natural linewidth of rubidium transitions as the limit on spectroscopic resolution There are other experimental arrangements that could be tried much higher rubidium densities are easily accessible at moderately elevated temperatures A larger departure would be investigation of the Voigt effect the study of polarization rotation using a magnetic field transverse rather than paral lel to the direction of light propagation i It is also worth remarking on a fascinating technological application of the Faraday effect for producing optical filters of extremely narrow bandwidth but high peak transmission and wide field of view The simplest of such filters is a sandwich with a rather high density vapor cell between a pair of crossed linear polarizers Such a filter would be opaque at all wavelengths in the absence of a magnetic field in the presence of a suitable field it is still opaque far from a resonance line since the
196. nd the theoretical treatment of this effect provides an unusually clear insight into the relation between absorption and dispersion in the interaction of light with matter 1996 American Association of Physics Teachers I INTRODUCTION Impelled by a belief in the unity of the forces of nature Michael Faraday sought and in 1845 provided the first phe nomenological evidence for a connection between light and magnetism when he discovered the effect that still bears his name He found that plane polarized light propagating through matter parallel to a static magnetic field underwent a systematic rotation of its plane of polarization The effect though unambiguous is typically not large with rotation per unit distance per unit field of order 10 rad m T 40 03 arcmin cm Oe in ordinary glass samples in the midvisible this Verdet constant is itself a function of wavelength typically growing dramatically toward the blue end of the visible spectrum Not until the atomic electron hypothesis toward the end of the 19th century was it possible to provide a more detailed model for Faraday rotation Becquerel pre dicted a Verdet constant related to the dispersion dn dX of the material A modern picture of Faraday rotation emerges from the quantum mechanical response of an atom to a mag netic field in this picture the atomic absorption and disper 724 Am J Phys 64 6 June 1996 sion are both affected by the field and in this sense
197. ng Now finish the set up in Figure 10 by adding the interferometer Turn off the laser frequency scanning while setting up the interferometer so the fringes are stable Make the arm difference as long as you can If you want you can add another mirror to the long arm to bounce it across the table The longer the long arm the better your measurement will be Recombine the beams on the beamsplitter and send one of the output beams through a strong lens so that the beam is expanded quite a bit Align the overlap of the beams in position as well as angle until you see nice fringes on the expanded beam Align the overlap so the fringes spacing is very large Place the photodiode such that it only intercepts the light from one fringe of the interferometer If you now scan the laser frequency you should observe temporal fringes on the photodiode output The fringe spacing can be computed from the arm length difference which you should measure When a beam travels a distance L it picks up a phase y 27L A so the electric field becomes E Eget et When the beam is split in the interferometer the two parts send down the two arms and then recombined the electric field is E Earm Earm2 Bye Lia 4 guum where L and L are the two arm lengths The additional factor of two comes from the fact that the beam goes down the arm and back again Squaring this to get the intensity we have isra fA 4 gian I e where AL Li La
198. ng problem Consider a simple laser beam the pump shining through a vapor cell If the laser intensity is weak and the atoms are all pretty much in the ground state then the laser intensity changes according to the equation d dx od where av depends on the laser frequency but not on position inside the cell In this case ot is a called the absorption length This equation has the solution x Imre where J is the initial laser intensity The transmission through the cell e where L is the length of the cell is what we called e above Your job in this problem is to work out what happens when the input laser beam is not weak and thus we cannot assume that the atoms are all in the ground state In this case amp a v x which makes the differential equation somewhat more interesting Assume the laser is on resonance for simplicity Then the attenuation coefficient at any position x is proportional to P P which in turn is proportional to 1 1 s Thus we have Q Vg x al 1 s x In the weak beam limit 7 this reduces to our previous expression so a To L sat Write down an expression which relates the saturation parameter of the laser as it exits the cell S ina the saturation parameter at the cell entrance s and the weak limit optical depth T Check your expression by noting in the limit of finite T and small s you gets fina Sinitiale initial If To 100 how l
199. ng the TV camera Keep track of where this knob started and DO NOT TURN THE KNOB MORE THAN ONE HALF TURN You may find it useful to use the 5 64 Allen wrench placed in the back of the knob as a position indicator It is also easier to make small adjustments of the knob by using the long arm of the Allen wrench as a lever You should see the laser spot change in intensity as the TOP knob is turned If you rotate the TOP knob very slowly you will notice that the bright region actually changes from bright to dim These are modes of the laser You should be able to distinguish six to ten of these modes with fewer modes when the current is just above threshold You are seeing different longitudinal modes in the external cavity defined by the grating and back facet of the diode As you turn the top knob you are not only changing the grating angle but also the external cavity length You have changed the cavity length by one half wave length when you move from one bright peak to the next You will need to have to set the current just above threshold to see this clearly This may involve a few iterations of setting the TOP knob to give an intensity maximum and then adjusting the laser current Figure 3 at the right shows an oscilloscope trace of the intensity of the laser as the TOP knob is adjusted It will give you an idea of how the brightness of the spots you are seeing is varying It is hard to tell the middle ones apart For best alignment
200. ning v v in units of Doppler width Av Fig 5 Faraday rotation angles computed for the model problem of this paper in the presence of Doppler broadening for three values of magnetic field strength B e 4am B Avp 6 Avp 3 and Avy 2 values of magnetic field Each curve is symmetric around the zero field line center and each has long tails of sign opposite to that of the central peak Since these long tails describe the ordinary off resonant Faraday rotation and since Faraday found that the direction of off resonant rotation is the same as that of the conventional current in the solenoid produc ing the field we deduce that resonant Faraday rotation should have a direction opposite to that of the current pro ducing the field this prediction is readily checked experi mentally Since the Faraday rotation signal is the difference of two antisymmetric dispersion signals the Faraday rotation signals also share their property of having zero net area un der their graphs Thus broadband light cannot be used to display the phenomenon of resonant Faraday rotation the light interacting with the atoms needs to have a spectral dis tribution no wider than the Doppler width of the transition III APPARATUS It is the availability of low power but tunable diode lasers that makes this resonant Faraday rotation experiment fea sible in the undergraduate laboratory The diode lasers pro duced by the millions for compact disc players have nom
201. ns the laser frequency see the Diode Laser Physics section of this manual for more on how this works RE DETECTOR MONITOR RAMP GENERATOR PIEZO CONTROLLER FREQUENCY RANGE DC OFFSET 5 6 4 7 1 1 100 mE o1 T s 9 goi ok Mire 24 Frequency Multiplier COARSE Hz 100V Full Scale 0 0 0 1 0 5 AMPLITUDE OFFSET ATTENUATOR OUTPUT OFFSET MODULATION MONITOR BALANCE QNO DETECTOR INPUTS To Oscilloscope Chan 1 To Oscilloscope Trigger Figure 5 Modules showing connections for setting the frequency sweep F l m Rev 2 0 11 09 Actually Finding the Rb Fluorescence Initial Horizontal Adjustment Set the laser current to the value listed on your data sheet You will need to connect a voltmeter to the LASER CURRENT MONITOR to accurately set the current If the horizontal grating position has not been changed much during shipping or because of accidental adjustment then you will see a flashing streak of light within the cell on the TV monitor This is rubidium fluorescence Atoms of Rb in the cell absorb laser light at the atomic resonance frequency and re emitting it in all directions f you do not see any fluorescence do not despair You only need to make a slight adjustment of the SIDE knob Put the 5 64 allen wrench hex key in the back of the SIDE knob and use it as a rotation marker Remember the starting position of the wrench you could even draw a little picture in your lab b
202. nside the semiconductor Cavities are often made from two curved mirrors as shown in Figure 1 In this lab you will investigate some cavity properties and you will see how a cavity can be used as an optical spectrum analyzer to measure the spectral content of a laser In this capacity you will use the cavity to observe radio frequency RF sidebands on the laser output A basic Fabry Perot cavity consists of two reflectors separated by a fixed distance L as is shown in Figure 1 curved reflectors are typically used because such a configuration can trap light in a stable mode Two flat mirrors can also make a cavity of sorts but it is not stable the light walks off perpendicular to the cavity axis An excellent detailed discussion of the properties of Fabry Perot cavities is given by Yariv 1991 and you may want to look through Chapter 4 of this text to better understand the details of cavity physics Another useful although somewhat dated reference is attached as an appendix at the end of this hand out Much of the physics of optical cavities can be understood by considering the flat mirror case which reduces the problem to 1D Physically this case can be realized if the flat mirrors have effectively infinite extent and the input light can be approximated by a perfect plane wave For two identical mirrors each with reflectivity R and transmission T R T 1 the amplitude of the transmitted and reflected electric field amplitudes
203. nsisting of a rubidium vapor cell in one arm of a Mach Zehnder interferometer The Mach Zehnder interferometer is related to the Michelson interferometer with which you are probably familiar The input laser light is first split by a beamsplitter we will assume both beamsplitters in the interferometer are perfect lossless 50 50 beamsplitters and the two beams travel down different paths through the interferometer They are recombined at the second beamsplitter and the light intensity in one direction is measured with a photodetector The intensity seen at the photodiode is sensitive to the relative phases of the two beams as they interfere at the second beamsplitter Your first job before attempting the experiment is to model the expected signal seen at the photodiode in Figure 2 as the laser frequency is scanned through the rubidium resonance line If we consider the interferometer in Figure 2 without the rubidium cell it is straightforward to calculate the photodiode signal As the two beams propagate through the separate arms of the interferometer each picks up a phase shift as it travels given in Eqn 3 Without the rubidium cell no 1 neglecting the contribution from Nair and amp 0 giving simple free space propagation e The output power hitting the photodiode comes from the combination of the two beams at the second beamsplitter and is given by I ja 4 eikLe 1 cos kAL 2 2 which is plotted in Figure 3 Since the
204. nt the laser is tuned to the rubidium lines Before proceeding with the rest of the experiment move the ND filter from its location in Figure 9 to a new position right in front of the photodiode If you look closely you ll see the absorption lines are still there but much weaker How come There are two reasons First optical pumping is faster with more laser power so the atoms are more quickly pumped to the dark state That makes the absorption less Second the atoms become saturated with the high power just like you calculated above That also reduces the absorption 10 90 Beamsplitter R T Photodiode 50 50 Beamsplitter 10 90 Beamsplitter ___ Y Photodiode 50 50 Beamsplitter Figure 10 Recommended set up to record rubidium saturated absorption spectra and for measuring the hyperfine splittings Week 1 Getting a Saturated Absorption Spectrum The suggested set up for observing saturated absorption spectra is shown in Figure 10 Since the laser is on resonance from the last section leave it alone while you change the set up Ignore the interferometer part for now that comes in after you ve gotten some spectra The optical isolator is a device that contains a two polarizers a special crystal and strong permanent magnets see Appendix I The first polarizer is aligned with the polarization of the input laser vertical and simply transmits the beam The crystal in the magnetic field rotates the polarization of t
205. nt Noise lt 50 nAnys 3 Hz 20 kHz bandwidth Modulation Front Panel Gain 2 mA Volt Maximum Amplitude 11 mA Frequency DC to 1 MHz RF on Laser Head Gain 20 mA Volt Frequency 100 kHz to 100 MHZ Current Monitor Gain 100 mV mA 10 mA 1 0 V Current Limit 50 100 mA set at 80 mA ESD protection Schotty diode reverse voltage Three switching diodes 1N4148 over voltage Some fraction of the light remains LED like at least for currents just above threshold where both types of light can be seen t Changing the current can be thought of a means of rapidly changing the diode temperature for times longer than 1 us The current also changes the carrier density in the diode which changes the index of refraction This effect is smaller than the thermal effects and predominates only at time scales shorter than 1 us This shortest response time is set by the relaxation oscillation frequency We measured the current noise with the Teachspin Signal Processor Lock in Amplifier SPLIA configured in the amplitude detection mode by detecting the voltage noise across a 100 resistor in series with the diode Unfortunately most of the noise measured was not current noise but voltage noise from the Lock in Pre Amplifier about 10 nV Hz A more sensitive front end would be needed to get an accurate measure of the noise Most likely higher modulation frequencies are possible This is highest frequency for which the laser has bee
206. ntaneous emission with I equal to the excited state lifetime and the second term is from stimulated emission with amp a normalization constant Note that the stimulated emission is proportional to the intensity 7 In the steady state P P 0 giving ar 2 142aVT The term o T corresponds to the s 2 term above note 7 is proportional to I A more complete derivation of the result with all the normalization constants is given in Milonni and Eberly 1988 and in Cohen Tannoudji et al 1992 but this gives you the basic idea Assuming a fixed vapor temperature atomic mass etc the saturated absorption spectrum is determined by two adjustable external parameters the pump intensity I and the on pump resonance optical depth t The latter is proportional to the vapor density inside the cell Figure 5 shows calculated spectra at fixed laser intensity for different optical depths and Figure 6 shows spectra at fixed optical depth for different laser intensities In Figure 5 one sees mainly what happens when the vapor density is increased in the cell At low densities the probe absorption is slight with a Gaussian profile and the absorption increases as the vapor density increases At very high vapor densities the absorption profile gets deeper and broader It get broader simply because the absorption is so high near resonance that the probe is almost completely absorbed for greater vapor densities the probe gets nearly c
207. ode eO and as the grating continues to move the laser will jump into mode e 1 As the angle is decreased further the laser will reach the point shown in graph c and the laser will hop to mode e 2 Finally in graph d the maximum of the grating feedback frequency is about half way between internal modes IntO and Intl As the angle continues to decrease the laser will make a relatively larger mode hop and lase in external mode e3 under internal mode Intl You should notice that during this change in angle the laser has swept through the same small frequency range under IntO several times After these changes the laser moved to a new frequency defined by Intl with a rather large gap of frequencies in between To be able to cover the entire frequency range we need to be able to change the position of the internal Rev 2 0 11 09 modes This is done by changing the laser current To tune the laser to the correct wavelength for the rubidium transitions both the correct grating angle and laser current must be found The procedure for doing this is discussed in the next section The next section will also describe a clever trick in which both the grating angle and laser current are swept simultaneously at rates such that both the internal mode IntO and the maximum of the external modes e0 change in frequency together resulting in long 20 GHz mode hop free scans An understanding of the Figures 8 and 9 should help you visualize how this is accompl
208. ode junction forms a small Fabry Perot etalon or optical cavity and like all optical cavities it has a normal mode structure This translates to an effective frequency dependent net gain function which is periodic in frequency as shown in Figure 5 see Yariv 1991 or M ller 1988 for a discussion of optical cavities The period is called the free spectral range and is given by AVrsr c 2Ln where c is the speed of light n is the index of refraction n 3 6 in the semiconductor and L is the cavity length For this particular laser we have AVrsr 60 GHz AA 0 122 nm The internal cavity gain function will shift in frequency with changes in the diode temperature at roughly 0 05 nm C this is measured from the small scale slope the individual steps in Figure 6 Unfortunately the temperature of the laser head can not be changed very quickly The thermal time constant of the laser head can be estimated to be on the order of 10 seconds The internal cavity modes will also change with the diode current See Figure 7 Estimated from the mass 170grams heat capacity and thermal conductivity assuimng the laser head is a solid cube of aluminum with the TEC on one face and the diode and temperature sensor at the center 1 6 Rev 2 0 11 09 780 2 780 0 779 8 779 6 779 4 779 2 Wavelength nm 779 0 0 122 nm FSR 778 8 T222 5C 20 30 40 50 60 70 80 90 100 110 Injection Current mA Figure 7 Free
209. oelectric spacer the separation of the mirrors can be varied by a few wavelengths In practice a sawtooth or sinusoidal waveform is usually applied to the piezoelectric spacer to scan the separation of the interferometer mirrors For a confocal inter ferometer a change in separation of the mirrors of one fourth wavelength scans the interferometer through one free spectral range An aperture is placed outside the entrance mir ror to limit the diameter of the incident beam The upper limit on the aperture size can be determined using equation 18 If the beam entering the in terferometer is collimated no further apertures are required However if the interferometer is used with non collimated beams it is also neces sary to use an aperture on the exit of the interfer ometer to eliminate the reduction in finesse caused by spherical aberration in the mirrors The use of this second aperture will reduce the peak transmis sion of the interferometer and it is generally more desirable to focus the incoming beam properly rather than use a second aperture The light transmitted by the interferometer is detected by a photecell or photomultiplier and the output signal of the photedetector is recorded on an oscilloscope as a function of the voltage applied to the piezoelectric spacer The oscilloscope thus dis plays a signal which is equivalent to the laser mode intensity vs optical frequency It is important that the mirror separation
210. of the light it does change the phase however which is the cause of the material index of refraction With the application of a strong longitudinal magnetic field you can see that the Lorentz force e v x B will shift the motion of the electrons and rotate their plane of oscillation As the electrons re radiate this tends to rotate the polarization of the light beam Obviously a hand wavy argument but it gives you the right idea The optical isolator uses the Faraday effect to rotate the polarization angle of the input beam by 45 degrees and the output beam exits through a 45 degree polarizer see Figure 12 Note that the diode laser s beam is polarized in our case along the vertical axis If one reflects the beam back into the optical isolator the polarization experiences another 45 degree rotation in the same direction as the first and the beam is then extinguished by the input polarizer You can see that the rotations have the correct sense using the classical picture Thus the overall effect is that of an optical diode light can go through in one direction but not in the reverse direction The Faraday effect is typically very weak so the optical isolator uses a special crystal which exhibits an anomalously large Faraday effect and a very strong longitudinal magnetic field produced by state of the art permanent magnets Optical isolators have gotten much smaller over the last couple of decades as magnet technology has improved The
211. ogy while the other terms at frequencies wo nQ form sidebands around the carrier The sideband amplitudes are given by J4 which rapidly becomes small for n gt 3 Note that the total power in the beam is given by E E Eg J 8 2 I B Eo n l which is independent of 8 as it must be for pure frequency modulation Often one wishes to add two small sidebands around the carrier for which one wants 8 lt lt 1 and the sideband power is then given by J1 8 8 4 Evaluating the above sum and convolving with a Lorentzian laser cavity spectrum gives an output power I w J B L w wo Ja B L w wo nQ L w wo nQ n 1 where L w wo is a normalized Lorentzian function centered at wo Problem 2 Evaluate and plot the above optical spectrum as you might expect to see it using your Fabry Perot optical spectrum analyzer remember that a photodiode measures optical power not electric field amplitude Plot versus frequency v w 2 which is what a frequency meter reads Assume a Lorentzian laser cavity linewidth of Av 10 MHz Plot three curve with 1 0 27 120 MHz 6 0 5 2 0 2x 30 MHz 6 1 5 and 3 0 27 1 MHz 6 20 Note for the last plot you will have to eval uate the sum up to fairly high n at least to n gt f For 6 gt 1 note that the spectrum looks much like what you would expect for slowly scanning the laser frequency from wo BQ to wo BQ II LABORATORY EXERCISES Your first tas
212. oller The configuration of the controller has been done by TeachSpin Unless the controller has been accidentally reset you should not need to change the configuration The Instrument Configuration list at the end of this section includes only those items that have been changed by TeachSpin The value in parenthesis is the main menu heading under which the changed settings are located All other values are the factory default See page 62 of the Controller Manual for details and additional explanations Rev 2 0 12 09 To change the Proportional Reset or Rate values enter the Instrument Configuration mode by pressing the MENU key until CNFG is displayed and then press ENTER Using the MENU key scroll through the various options until OUTI Output 1 is displayed then press ENTER Again scroll through the options with the MENU key until the CTRL option is displayed and ENTER Use MENU to set the CTRL to PID and ENTER Now that you are in the Configuration mode use MENU to scroll until PROP REST or RATE is displayed Press ENTER then use the UP and DOWN arrow keys to change the value of the selected parameter Press ENTER again to save and store the value Once all changes have been made use the Menu key to return to RUN mode Please refer to section 3 page 15 of the controller manual for a complete description Instrument Configuration List for Temperature Controller Set Point 1 SP1 50 0 Input Type INPT ICs Temperature Unit R
213. ompletely absorbed even at frequencies fairly far from resonance thus the width of the absorption profile appears broader The saturated absorption feature in Figure 5 does pretty much what you would expect The probe absorption is reduced on resonance due to the action of the pump laser At very high vapor densities the saturated absorption feature becomes smaller This is because while the pump laser reduces the absorption it doesn t eliminate it thus at high vapor densities the probe is nearly completely absorbed even with the pump laser The moral of this story is that the vapor density shouldn t be too low or high if you want to see some saturated absorption features Rev 2 0 11 09 In Figure 6 one sees that if the pump intensity is low the saturated absorption feature is small as one would expect For larger pump intensities the feature grows in height and width The width increases because at high laser intensities the effect of the pump laser saturates on resonance and continues to grow off resonance thus the width of the feature increases an effect known as power broadening Saturated Absorption Spectrum of 2 Level Atom 0 8 T p eit a o a 3 e f i E f et v Of A o amp oq e zi 1 L 2a L 4000 2000 0 2000 4000 v vg MHz X T T T T T i T P Ita a A LLL 7 n fo amp co a v e a 2 a N eo e 200 0 200 400 v vg MHz Figur
214. on Rev 2 0 12 09 LE PIEZO STACK The piezo stack is an NEC Tokin model AE0203D04 which has a nominal displacement of 3 um at 100V The piezo stack is polarized and voltage of only one polarity should be used The stack is sandwiched between two metal plates A setscrew contacts the bottom metal plate from the side and holds the stack in the movable portion of the mirror mount See Figure 7 A ball tipped setscrew in the grating holder contacts the piezo stack When voltage is applied to the piezo stack the ball tipped setscrew transmits the motion of the stack to the holder and grating changing the grating position Both the distance from the grating to the laser the cavity length and the angle of the grating are changed by the expansion and contraction of the piezo stack LE 1 Electronics Voltage is applied to the piezo stack through the 9 pin cable The PIEZO CONTROLLER module in the electronics box adjusts the voltage applied to the stack Piezo Displacement 3 0 um 1 5 um 100 Volts Piezo Maximum Voltage 150 volts Piezo Frequency Response DC to 1 kHz DC OFFSET COARSE Ten turn Oto 100 Volts FINE Single Turn 0 to 2 Volts MODULATION INPUT 1 V input 5 V across piezo stack Input Impedance 10 KQ ATTENUATOR Reduces MOD Input MONITOR OUTPUT 1 10th of voltage across stack OUTPUT OFFSET Changes DC level of monitor voltage 0 to 5V does not change piezo stack voltage The voltage applied to
215. onsivity 0 6 Amps watt 5 23 Rev 2 0 12 09 II B DETECTOR LOW Pass DC LEVEL ELECTRONICS Detector electronics on the front panel allow for conditioning of the signals The BALANCE controls are two input attenuating potentiometers that can be adjusted to balance two signals from the photodiode detectors The internal instrument amplifier can be used to take the difference of the two signals with a GAIN from 1 to 100 Table 4 lists the gain and high frequency 3dB point Gain 3dB Freq Hz 1 1 3 M 2 1 0M 5 780 k 10 650 k 20 470 k 50 220 k 100 110k Table 4 High Frequency Response Figure 16 Detector Power Pin out looking of Detector versus Gain into connector on front panel The LOW PASS filter and DC LEVEL controls are provided for side locking the laser to a spectral feature The single pole low pass filter has switch selectable time constant from 10 us to 0 1 seconds The DC LEVEL has a ten turn potentiometer that provides a DC offset from minus five volts to plus five volts For positive offset voltages the voltage may be read off the dial directly For voltages less that zero the voltage is found by subtracting ten from the number displayed on the dial 9 0 dial 1 0V 7 2 dial 2 8V There is a final DC gain stage of 1 to 30 after the DC level adjustment There are monitor outputs after the first difference and gain stage and after the low pass filter These can be used to record
216. ook While you observe the TV screen looking for the fluorescence flash slowly rotate the SIDE knob first one way and then the other You should not need to rotate it more than one half turn in either direction If still no fluorescence is observed then return the SIDE knob to the starting position and adjust the current in 3mA increments about 1 3 of a turn both above and below the Laser current recorded on you data sheet At each new current setting rotate the SIDE knob again so that you don t lose your position always return the knob to its starting position before changing the laser current If you do NOT see any fluorescence first repeat the above steps again doing them with care You might have someone else go through the steps as well It s easy to miss some detail and thus not observe fluorescence In particular check the laser temperature the vertical alignment and make sure you are sweeping the piezo If you still see no florescence then you can try making bigger excursions in the grating angle with the side knob plus and minus one whole turn It may be that the Cavity became grossly misaligned during shipping refer to section A4 2 in the appendix for details on aligning the external cavity Once you see the florescence flash move the SIDE knob so that the florescence is always visible Now adjust the laser current to make the florescence as bright as possible Observing the Absorption Spectrum Using a Photodiode Detector
217. orders of magnitude larger than that seen in bulk matter The maximum value of Faraday rotation at kB Av 2 in 25 arises from the particular circumstance depicted in Fig 3 a where the dispersion curves for n and n_ are split apart by the Zeeman effect until the maximum of one lies immediately above the minimum of the other this maxi mizes the difference n 7 and thus the Faraday rotation The maximum value of the rotation angle is given by NAL 2 NML A Oma AV Bm 27 If we again suppose that the sample density and length have been chosen so as to attenuate transmitted light by factor e at resonance when the magnetic field is off then the rela tion Bra 1 again applies and from 16 the maximum Faraday rotation obtainable with this sample is NML 4m 1 A Omax Eno 8a 2 radian 28 Once again the intimate relationship between absorption and dispersion has imposed a maximum on the signal obtainable with a sample of a given optical thickness and once again the observable signal is limited to one half radian But this Faraday rotation of 0 5 rad is vastly easier to detect experi mentally than the 0 5 rad of phase shift derived in 20 above First no interferometric setup is required to obtain the Faraday rotation signal but rather the mere one way trans mission of linearly polarized light through a sample second the signal to be extracted is not the phase shift of a fringe pattern but the much more concre
218. ork well if the room lights are off for an extended period The IR card allows you to see actually locate the laser beam even when you are wearing your protective goggles since the goggles do not block the visible light emitted by the polymer 2 Hold the IR card at the laser output the hole in the plastic cover of the laser while you turn up the laser CURRENT knob You will need to turn the knob 3 4 turns before the beam becomes detectable on the card Rev 2 0 11 09 3 Set up the TV and Assemble the TV camera a Put the TV monitor near the controller and set it up to display camera image b Connect the power cable of the camera to the 12V power supply provided and connect the camera output cable to the TV monitor You should see an image on the monitor c Place the TV camera mounted on an optical post into a post holder Then the camera can conveniently be placed on the optical table with the laser and other optical components amp i eS Buisness Card in Card Holder Figure 1 External Cavity Alignment Operating note The camera lens can be focused over a broad range of working distances from infinity to as close as a few centimeters The focus is adjusted by turning the lens Do NOT shine the laser beam directly into the TV camera for this may damage the CCD sensor 4 Place a business card in the Neutral Density Filter holder and locate it so that it intercepts the laser be
219. orption of the beam 3 Attenuate the Signal Reaching the Detector a Assemble the glass neutral density filter in a fixed mirror holder and place it in a post holder Please refer to the Optics section in the Apparatus Chapter of the manual if you are unfamiliar with putting optical components into mounts b Place the attenuator between the laser and the Rb cell not between the cell and photodiode Adjust the PD Gain so you can observe something on the scope showing that light is hitting the PD For the best performance you want the PD Gain to be as high as possible without saturating the PD This keeps the noise from the PD at a minimum The PD gain changes in 1 3 10 steps a signal level of 2 to 6 volts is reasonable Block the beam with your hand to convince yourself that the PD is detecting the transmitted laser light You should see a scope signal that looks something like this Tek EE Trig d M Pos 40 00ms SAVE REC Action Select Folder About Save All CHT 200V CH2 100v M 10 0m Ext Z 512mV 26 Oct 04 22 01 lt 10H2 Figure 6 Upper trace Channel 1 shows piezo monitor signal Lower trace channel 2 shows Detector output Note that signal is negative going so absorption features appear as spikes Rev 2 0 11 09 4 Interpreting the Oscilloscope Signals a The upper trace shown in Figure 6 is the piezo monitor which shows the voltage on the piezoelectric stack as a function of time The lower trace
220. oshitaka Tukubo and Manabu Yamamoto Resonant Voigt effect spectrum of the rubidium D transition J Opt Soc Am B 11 409 414 1994 Yat Ching Chan and Jerry A Gelbwachs A Fraunhofer Wavelength Magnetooptic Atomic Filter at 422 7 nm IEEE J Quant Elec 29 2379 2384 1993 William J Thompson Numerous neat algorithms for the Voigt profile function Comput Phys 7 627 631 1993 Milton Abramowitz and Irene K Stegun Handbook of Mathematical Functions NBS Washington DC 1964 7 1 3 Reference 34 7 4 13 and 14 THE SAME OLD STUFF YEAR AFTER YEAR Instead of teaching the same old stuff year after year the teacher will constantly enrich his knowledge keep his teaching alive and dynamic and prevent his mind from falling into the disease of authority and age which is paralysis There is no other solution Life is a process of constant change No one can teach a subject in the same way two years running Even if he uses the same books and teaches the same facts and conclusions the second year he will have blurred a few outlines by repetition cut a few corners because of age The alternatives are only these to allow your teaching to petrify by neglect or constantly to refresh it by transfusions of new vitality and interest from your own reading The choice is not too difficult if it is clearly seen One of the few consolations of age is that while the body becomes weaker the mind can gro
221. osition shown in Figure 3 Upper You should see two beams on the card one from each mirror With the card holder close to the 50 50 BS adjust mirror 2 to make the two beams over lap Then move the card holder to a position far from the 50 50 BS a few feet 1 2 meter or so Again you should see two beams now adjust mirror 1 to make the beams overlap Go back to the near position and repeat In a few iterations you should start to see some fringes appear in the overlapped area of the two beams You will not see any fringes if the laser is scanning its wavelength so turn off the wavelength scan during this part of the operation Set the Ramp Generator attenuator to zero Once you see some fringes you can still repeat the above steps a few more times If done correctly the fringe spacing should become larger as the alignment approaches optimum Gently pushing on one of the mirror mounts should cause the fringe pattern to change Now put a photodiode in the beam and restart the laser scan You should be able to see some nice periodic modulations of signal from the photodiode I find that a contrast ratio of 10 is about the best I can do minimum intensity is 10 of maximum intensity Other tips Remove the glass Neutral density filter from the laser beam when doing the alignment This will help make the beams easier to see You will have to replace the filter when you want to make scans Feed back from the interferometer can
222. oth ground states because neither can decay via an allowed transition and the separation of the ground states was less than the Doppler width then one might see a spectrum like in Figure 4 The extra cross over dip results from a phenomenon called optical pumping which occurs because atoms in the excited state can decay into either of the two stable ground states Thus if atoms are initially in ground state g1 and one shines in a laser that excites g1 e atoms will get excited from gl e over and over again until they once spontaneously decay to g2 where they will stay The state g2 is called a dark state in this case because atoms in g2 are not affected by the laser We see that a laser exciting gl e will eventually optically pump all the atoms into g2 To see how optical pumping produces the extra crossover dip remember that only the pump laser can optically pump the probe laser is by definition too weak Also remember the atoms in the cell are not in steady state When they hit the walls they bounce off about equally distributed in both ground states and the optical pumping only operates for a short period of time as the atoms travel through the laser beams If you think about it a while you can see there are two velocity classes of atoms that are responsible for the dip For one velocity class the pump laser excites g1 e which tends to pump atoms into g2 Then the probe laser which excites g2 e for these a
223. out 384 000 GHz or 384 x 10 MHz We have calculated that Af the free spectral range of our cavity is about 380 MHz This means that as we sweep the laser frequency whenever the frequency of the transmitted light changes by one part in a million you ll get another transmission maximum Now let s look at the transmission peaks themselves Since the finesse of our cavity is around 100 having a FSR Af of 380 MHz means that the frequency width of the peak itself of will be on the order of 4 MHz Since f is measured half way up the peak we can easily see changes 1 4 as great Thus a Fabry Perot interferometer can be sensitive to frequency changes on the order of 1 MHz out of an optical frequency of 400 million MHz The optical cavity of a Fabry Perot interferometer is created by the pair of high reflectivity concave mirrors mounted at the two ends The TeachSpin mirrors have a power reflection coefficient of R gt 0 995 or 99 5 The experiment must adjust the distance between the mirrors so that the focal points of the two mirrors coincide in space at the center of the cavity in other words the mirrors must be arranged to be confocal When properly aligned these mirrors define a cavity mode that is stable against the otherwise inevitable transverse spreading of a beam that bounces back and forth between the mirrors for hundreds of round trips The mirrors used in the TeachSpin cavity have radii of curvature 20 cm so as concave
224. ower broadened as the line saturates 1 1 s Thus we have a vo x oo 1 s x In the weak beam limit I amp Isat this reduces to our previous expression so To L Write down an expression which relates the saturation parameter of the laser as it exits the cell sfinqi the saturation parameter at the cell entrance s 4 and the weak limit optical depth rog Check your expression by noting in the limit of finite T and small s you get Sfinal Sinitiale 7 If To 100 how large must sinitiqg be in order to have a transmission of 1 2 i e Sfinal Sinitial 2 Atomic Structure of Rubidium The ground state electronic configuration of rubidium consists of closed shells plus a single 5s valence electron This gives a spectrum which is similar to hydrogen see attached Scientific American article For the first excited state the 5s electron is moved up to 5p Rubidium has two stable isotopes Rb 72 percent abundance with nuclear spin quantum number J 5 2 and Rb 28 percent abundance with I 3 2 The different energy levels are labeled by term states with the notation 5 HE where S is the spin quantum number L is the spectroscopic notation for the angular momentum quantum number i e S P D for orbital angular momentum quantum number L 0 1 2 and J L S is the total angular momentum quantum number For the ground state of rubidium S 1 2 since only a single electron contributes and
225. ral linewidth Thus a quotient like An Av has near resonance the largest pos sible numerator and a very small denominator In terms of the graph of Fig 3 a ordinary nonresonant Faraday rotation depends on a tiny difference between two refractive indices each of which is separately very close to one but resonant Faraday rotation involves the difference of two refractive indices each of which is near its maximum possible depar ture from unity and whose departures from unity are of op posite sign D A Van Baak 727 This enhancement of Faraday rotation at a resonance mo tivates the examination of a second special case of 21 namely the Faraday rotation at the center of the zero field atomic resonance at y vg The result is Aie ut NAL 7 kB 7 32727 BJE AV en where k e Azm 13 996 GHz T this function grows lin early with B for KB Av 2 reaches a maximum at kB Av 2 and then decreases gradually The initial linear depen dence of Faraday rotation on B allows the extraction of an at resonance Verdet constant of 1 d A0 QNM k Nr e L dB _ 3207 Av2 4m me 26 which for values of experimental interest like N 2 5x10 m A420 78X10 m e m 1 76xX10 C kg and 7 25 5X10 s Ref 15 yields the enormous value of V 5 4X10 rad T m Thus despite a gas density some 12 orders of magnitude smaller than that of typical solids the resonant Faraday effect yields a computed Verdet constant about 5
226. re physically small and need only a DC power supply to produce useful 10 mW level optical output But astute physicists realized that the output wavelength could be varied by changing the laser s temperature and further fine tuned by changing the DC current operating the laser Thus was born a wonderfully convenient spectroscopic light source To what atomic system might it be applied Photons of wavelength 785 nm each convey an energy of only 1 58 eV insufficient to excite most atoms from their ground states even to their lowest excited states The exceptions are alkali metals particularly rubidium Rb and cesium Cs In fact rubidium s lowest excited states are split by the spin orbit interaction into states accessible from the ground state by photons of wavelengths 780 and 795 nm Now these alkali metals are fiercely reactive to air or water but compatible with glass which brings up another convenience A simple glass cell evacuated and permanently sealed with a bit of the solid metal inside creates a great environment for spectroscopy Light can get in and out through the glass and for temperatures in the range 20 50 C the metal will co exist with its own vapor in the form of a gas of freely flying atoms of just the range of densities convenient for spectroscopic experiments Now it s time to imagine such an experiment what will happen when 785 nm light shines into such a cell Answer nothing at all the light flies right
227. rent monitor resistor and then across the diode laser Different diode lasers will have different forward biased voltage drops and hence the ultimate current limit will change slightly for different diodes Turn off the power to the laser controller and unplug the AC power line from the wall Turn the electronics box over and remove the four screws that hold the bottom cover of the electronics box in place and remove the cover The current limit trim pot potentiometer is located on the front panel circuit board underneath the cell heater controller Figure 5 shows a picture of the current control circuit board with the location of the supply voltage potentiometer and test point indicated Turning the trim pot counter clockwise when viewed as shown in Figure 5 will increase the supply voltage and current limit One turn of the trim pot will increase the voltage by about 0 2 V and the current by about four milli amperes 4 mA Rev 2 0 12 09 I C 3 b High Frequency Modulation Figure 6 shows a schematic of the high frequency modulation circuit connected to the SMA connector on the laser head A 0 033 uF capacitor is used to AC couple the RF into the diode The RF is sent into the laser diode through the 50 ohm resistor The resistor also acts as a 50 ohm impedance match for the RF The connections are made on a small circuit board inside the laser head base right above the 9 pin connector Also shown in the figure are the two sets of protection diod
228. s an integer It is interesting that the change in wavelength with temperature depends only on the material and wavelength and not on the cavity length AA a Rev 2 0 12 09 I B 2 Laser Head Figure 2 shows the Laser Head without the insulation between the cold plate and heat sink The Thermo electric cooler TEC is visible between these two aluminum pieces The thermistor located close to the diode laser in the collimation tube holder is also shown Four stainless steel screws secure the TEC between the cold plate and heat sink These screws pass through nylon shoulder washers inside the heat sink which provide electrical and additional thermal isolation between the cold plate and heat sink Note stainless steel is a poor thermal conductor A 1 4 20 brass screw passes through the cold plate and mirror mount and threads into the collimation tube holder This screw and the large aluminum contact area thermally link the cold plate with the diode laser On the other side of the laser head not visible in the picture copper braid is used to thermally link the cold plate to the grating holder and the movable portion of the mirror mount Optical Thermo electric Cooler Heatsink Figure 2 Picture of Laser Head I B 2 a Plexiglas Cover A Plexiglas cover over the laser provides isolation from air currents There are two holes in the cover to allow the laser beam to exit both with and without the diffraction grating in place
229. s follows If the laser frequency is Vo Av then the probe beam is absorbed only by atoms moving with longitudinal velocity v cAv vo moving toward the probe beam These atoms see the probe beam blueshifted into resonance other atoms are not in resonance with the probe beam and so they do not contribute to the probe absorption These same atoms see the pump beam red shifted further from resonance since the pump beam is in the opposite direction so they are unaffected by the pump beam Thus for laser frequencies v vo the probe absorption is the same with or without the pump beam However if v vo then atoms with v 0 contribute to the probe absorption These v 0 atoms also see an on resonance pump beam which is strong enough to keep a significant fraction of the atoms in the excited state where they do not absorb the probe beam in fact they increase the probe beam intensity via stimulated emission Thus at v vo the probe absorption is less than it was without the pump beam If the pump beam had infinite intensity half of the atoms would Page 2 be in the excited state at any given time and there would be identically zero probe absorption One would say these atoms were completely saturated by the pump beam hence the name saturated absorption spectroscopy The advantage of this form of spectroscopy should be obvious one can measure sharp Doppler free features in a Doppler broadened vapor Qualitative Pictur
230. s module CELL TEMPERATURE The cell temperature is both set and monitored through keys on the LED display It has been configured by TeachSpin In case it is accidentally reset see the Apparatus section for detailed help CURRENT The current module controls the current to the laser It houses a modulation input so that the current can be ramped along with the piezo stack and an attenuator to control the degree of modulation MONITORS This set of connectors and indicators located on the lower part of the cell temperature panel provides a place to monitor as a voltage the set point temperature of the laser as well as the actual temperature and current The indicator lights indicate the temperature of the laser in reference to the set point F TV and Camera The TV and camera will be used to observe both the light coming from the laser and the Rb fluorescence in the vapor cell While invisible to our eyes the 780 nm light can be detected by the camera and seen on the TV G The Optics and Connectors Your Diode Laser Spectroscopy system comes with a whole collection of bases supports mirrors polarizers neutral density filters and beam splitters which can be combined in a wide variety of ways to do a wide range of experiments that is limited only by your imagination II Initial Setup What to do first This may take one or two hours These instructions will help you set up and align your laser for the first time When you have
231. s the grating holder from the side so that the holder makes contact with both 6 32 screws as you tighten the screws See picture in Figure 11 This will approximately set the correct beam height Figure 11 Initial installation of the Grating Grating holder is pressed against screws as screws are tightened This procedure is the same as outlined in Chapter 3 Section II D Aligning the Laser The one difference is that you will now also adjust the SIDE knob 5 15 Rev 2 0 12 09 I D 3 c Setting the Beam Height After the initial installation of the grating holder turn on the laser and align the external cavity See Section I D 2 b Place the viewing screen or IR viewing card at the far end of the optical table from the laser in a position to view the beam Loosen the two 6 32 socket head cap screws and tilt the grating holder to set the beam height at four inches 4 above the optical table as seen on the viewing card Retighten the 6 32 socket head cap screws Align the external cavity once again and confirm that you have the correct beam height I D 3 d Contacting Piezo Stack with Ball Tipped Setscrew Once the beam height has been set turn the ball tipped setscrew until it makes contact with the piezo stack Once the ball tipped setscrew just makes contact the screw should be tightened an additional one quarter turn DO NOT tighten it more than one quarter turn as this could lead to damage to the piezo stack when the high vo
232. s the higher frequency mode or the lower frequency mode Both situations will give the same radio frequency output signal With direct optical frequency spectroscopy this ambiguity does not occur the output signal gives complete infor mation regarding the spectrum Radio frequency measurements are most useful when it is only necessary to detect the presence or absence of certain modes in a laser beam In general direct optical frequency measurements are easier to interpret and easier to perform Il The Fabry Perot Interferometer Scanning spherical mirror interferometers be long to the general class of multiple beam inter ferometers The most common multiple beam interferometer is the Fabry Perot etalon which consists of two plane mirrors which are placed par allel to one another separated by a distance d The resonance condition for such an interferometer is that the spacing between the mirrors be equal to an integral number of half wavelengths of the in cident light If the interferometer is illuminated at normal incidence with a collimated beam of fre quency v the resonance condition is mc Yo od 1 where m is an integer and c is the velocity of light More generally it can be shown that the trans mittance of the etalon is given by the famous Airy formula I 1 1 2 where I is the intensity of the beam incident on the interferometer I is the intensity of the beam emerging from the interferometer R i
233. s the reflec tance of the mirrors T is the transmittance of the mirrors and A is the dissipative loss of the mirrors For high reflectance mirrors typical of modern Fabry Perot etalons the transmission fringes are extremely sharp Under these conditions the transmittance of the Fabry Perot etalon will be negligible unless the sine term is nearly zero We may thus use the approximations sin 0 zz 0 and R zz 1 to write the Airy formula as OG eS ie ev C 8 This formula is illustrated graphically in Figure 1 We see that near a transmission fringe the trans mittance of a Fabry Perot etalon is a Lorentzian function of frequency having a full width at half maximum of c 1 R Av a 5 4 The quantity Av is called the instrumental band width of the etalon INSTRUMENTAL TRANSMISSION Tr in o o E 05 04 03 02 01 O Ol 02 03 04 05 d os FREQUENCY OFFSET v v IN UNITS OF d EON 1 Transmittance of a Fabry Perot etalon for various mirror reflectances The dissipative loss of the mirrors is assumed to be 0 2 Note from 1 that the difference in frequency between two transmission fringes called the free spectral range of the etalon is given by FSR 5 3a The ratio of the freespectral range to the instru mental bandwidth is called the finesse of the eta lon Using 4 and 5 we find for the finesse F uqcg 6 The ratio of the transmission frequency to the
234. s the same intensity from one end of the cell to another This is okay for a first approximation but calculating what really happens is an interesting problem Consider a simple laser beam the pump shining through a vapor cell If the laser intensity is weak and the atoms are all pretty much in the ground state then the laser intensity changes according to the equation d dx alI where a a v depends on the laser frequency but not on position inside the cell a7 is called the absorption length in this case This equation has the solution I x Linie where init is the initial laser intensity The transmission through the cell e Where L is the length of the cell is what we called e above Your job in this problem is to work out what happens when the input laser beam is not weak and thus we cannot assume that the atoms are all in the ground state In this case a a v x which makes the differential equation somewhat more interesting Assume the laser is on resonance for simplicity Then the attenuation coefficient at any position x is proportional to P P5 which in turn is proportional to Page 6 Saturated Absorption Spectrum of 2 Level Atom Probe Transmission 400 200 0 200 400 v Vo MHz Figure 6 Calculated saturated absorption spectra for two level atoms for T I Isat 1 0 1 1 1 1 10 1 100 and 1 1000 Note at large laser intensities the saturated absorption feature is p
235. sec so that the photodiode is fast enough to record the full peak If not use a slower scan Measure the height of the transmitted peaks and com pare with the input beam intensity to produce a peak transmitted fraction Keep in mind the photodiode gains which may be different and how many times the various beams went through the beam splitter You should be able to produce a transmitted fraction between 596 and 1096 If your measurement is above 1096 you probably made an error somewhere or your cavity alignment is amazingly good If Page 10 Optical Isolator Photodiode1 Confocal Cavity 50 50 beamsplitter Photodiode2 Figure 7 Optics set up for the confocal cavity your measurement gives you something below 5 again check for simple errors If that s not it tweak the cavity length and alignment until the peak transmitted fraction is above 5 When everything looks good print out the spectrum showing sharp peaks Measure the Cavity Finesse Capture a single sweep on the oscilloscope and use the built in cur sors to measure the effective finesse of the cavity Measure the spacing between the peaks the free spectral range and then change the time base on the scope and measure the full width at half maximum of the peaks The effective finesse is then F Avrsn Avrwmuw You should get F gt 100 or even F gt 200 if the cavity is well aligned Why is the transmitted peak intensity only 5 when in principle it cou
236. sed it becomes clear that the atom s excited states also display hyperfine splittings formerly invisible because of the Doppler broadening but now cleanly resolved Lots more can be done on a tabletop scale Given this ultrahigh resolution for example it s very easy to see the Zeeman effect of even modest magnetic fields further splitting the atomic energy levels And beyond these simple experiments very glamorous things have been done with diode laser spectroscopy including laser cooling magneto optical trapping and even Bose Einstein condensation What s truly remarkable is how far along this path one can proceed on a tabletop scale and with real time accessibility of the optical phenomena And it is all made possible by the techniques of diode laser spectroscopy Diode Laser Spectroscopy David Van Baak July 2009 Rubidium Atomic Energy Level Diagrams woo P 3 4 we N if 0 287 GHz B i F 2 0 157 GHz x F z1 5P35 SPsi v 0 072 GHz Pa T Fz0 y I S Pi pog ELE i ba i cS a 780 2nm 780 2 nm E 384 000GHz 384 000 GHz i 1 57 eV E 1 57 eV bg I I j I F 2 m 2to 2 59 5 F 3 m 3to 3 5S1 3 036 GHz 6 835 GHz F 2 m 2to 2 Fat oum m 1 t0 85 Rb 72 87 Rb 28 Energy Diagram shows D2 transitions only The D1 transitions at 794 8 nm are not shown Transmitted Light vs Laser Frequency Tek _ Trig d M Pos 40 00ms SAVE REC PRINT ll ELTERN IILI Seen OBESSE g
237. sed to generate the signals required in this paper In the case of interest the y parameter has the fixed and small value of about 0 0102 and the x parameter reaches about 33 for detuning v v of 10 GHz lMichael Faraday Experimental Researches in Electricity paragraphs 2146 2242 in Vol III of the reprint edition Dover New York 1965 E Scott Barr Men and milestones in optics V Michael Faraday Appl Opt 6 631 637 1967 3E D Palik and B W Henvis A bibliography of magnetooptics of sol ids Appl Opt 6 603 630 1967 D Macaluso and O M Corbino On a new effect on light traversing certain metallic vapors in a magnetic field C R Acad Sci 127 548 1898 5Poch Yeh Dispersive magnetooptic filters Appl Opt 21 2069 2075 1982 5Frank J Loeffler A Faraday rotation experiment for the undergraduate physics laboratory Am J Phys 51 661 663 1983 Frank L Pedrotti and Peter Bandettini Faraday rotation in the under graduate advanced laboratory Am J Phys 58 542 545 1990 5L J Aplet and J W Carson A Faraday effect optical isolator Appl Opt 3 544 545 1964 Daryl W Preston and Eric R Dietz The Art of Experimental Physics Wiley New York 1991 pp 355 366 10This labeling avoids the troublesome and contradictory conventions asso ciated with right and left handed circular polarizations Amnon Yariv Optical Electronics HRW N
238. serve the signal from Detector on the scope Adjust the gain on Detector so that you have a large signal several volts but not so large as to saturate the detector maximum signal less than 10 volts Now set the plus balance to one and the minus balance to zero and observe the signal form Detector 2 It will be inverted with negative voltage values Again adjust the gain of Detector 2 for a signal level that is comparable to that seen by Detector 1 Because the beam going to Detector 2 is not attenuated by the 50 50 beam splitter the gain needed on Detector 2 will be less than that of Detector 1 Typically Detector 1 needs a gain setting of 1 0 MQ and Detector 2 a gain of 330 kQ Rev 2 0 11 09 Now set both balance knobs to one and then reduce the balance on the larger signal so that the Doppler broadened background is removed This subtraction is never perfect so there will always be some residual broad absorption signal remaining You may now raise the gain setting on the difference signal and bring the SAS spikes up to the volt level You are now ready to record some beautiful SAS traces Tek JL Trig d M Pos 32 50ms SAVEZA Tek KIM Trig d M Pos 26 00ms SAVE R Pee ee ee eee eee NM ETT yt itis Peel Be Ot SEO Bat anes File File AE NS NE Woe eo Forma Forma eben eei ene mene Jeceeleeelee BMP BMP f i About About Savin Savind Image Image 2 Select Select Folder ook Folder Sa
239. side of the spectrum marked by N3 The center of the 85b line is at N2 The feature at N1 is an artifact of the laser scanning Next block the arm of the interferometer without the rubidium cell in order to observe the rubidium absorption line without any interferometer effects If all is going well you should see a nice strong Doppler broadened absorption line without any serious mode hops The ND filter is necessary to avoid saturating the line which makes it broader Tune the laser to get a nice strong 85b line with the 87b line on the side Have your TA check it out and save a spectrum Now unblock the second arm of the interferometer and watch the oscilloscope As you push on the optical bench you can see different points in the interferometer fringe pattern and you should see an output something like what you calculated in Problem 2 for low 7 Play around with the interferometer until you understand what s going on and your spectra agree reasonably well with theory Have your TA take a look at the spectra to see that everything looks good Capture three good traces corresponding roughly to points B C and D in Figure 3 Lastly heat the rubidium cell by turning the controller setting to 100C Watch the spectra as the cell heats up It will take about 15 minutes but then you should begin seeing spectra that look like what you calculated for high 7r Figure 5 shows some typical results for one phase The data will probably not be a perf
240. sorption signal predicted for the sample Figure 7 b shows the results where the horizontal axis and the vertical scale and baseline slope have been scaled to match the data but in which no other parameters are adjusted Comparing the data and the model we see fine agreement in the shape of the absorption signals showing that the computed Doppler broadening is really being observed but the agreement in absolute and relative intensities is not so good This may perhaps be attributed to optical pumping of the sample though the light intensity is low enough to avoid saturation depletion of the ground state population it may not be low enough to avoid optical pumping redistribution of the ground state magnetic sublevels population Now there are only two experimental changes needed to display Faraday rotation with this system The first is to ro tate the polarization analyzer to the 45 position to view the signals from both photodetectors to invert one of them and to display both on a dual trace oscilloscope The result ing displays are shown in Fig 8 where the two signals are shown before and after algebraic addition on the scope As expected the two separate signals are nearly identical and the sum signal is nearly zero on the scope The second change is to raise the magnetic field from its previous zero value to a succession of fixed values The results for the previously vanishing sum signal on the scope are
241. t drives the frequency sweep of the laser S max min IV DATA AND DISCUSSION We turn now to data derived from diode laser spectro scopy of rubidium vapor and a discussion of it in terms of the model so far developed For purposes of orientation it is important first to acquire simple absorption data this can be easily done with the ap paratus described above by turning the magnetic field off and by orienting the polarization analyzer to the 0 position so that the incoming linearly polarized light is entirely trans mitted to one of the two photodetectors Then the intensity of the transmitted light as a function of laser diode current exhibits a graph like that of Fig 7 This graph and those to follow was obtained by operating the diode laser with a sum of a fixed dc and a sawtooth modulated ac injection current Increasing current is to the right the diode laser responds to greater current by exhibiting greater output power and larger output wavelength The increasing output power is displayed in the linearly rising signal in the figure the increasing wavelength or decreasing opt cal frequency is chosen to scan over the rubidium D resonance line at 780 nm The upsloping optical signal interpolated through the narrow ab sorption features displayed is exactly the signal Sy defined above since it is obtained for polarimeter angle 0 for no absorption and for zero magnetic field knowledge of So and its unint
242. t for now For pure frequency modulation we can write the electric field of the laser beam at some fixed location as E t Eo exp iwot id t where g t is the modulated phase of the laser output We always assume that t is slowly varying compared to the unmodulated phase change wot since wo is at optical frequencies and our modulation will be at radio frequencies If we re putting in a single sinusoidal phase modulation we have t Bsin 2t where Q is the modulation frequency and 6 called the modulation index gives the peak phase excursion induced by the modulation If we note that the instantaneous optical frequency is given by the instantaneous rate of change of the total phase we have Winstant Wo dd dt wo BQcos Nt wo Awcos Nt where Aw is the maximum frequency excursion Note that 8 Aw Q is the dimensionless ratio of the maximum frequency excursion to frequency modulation rate It is useful to expand the above expression for the electric field into a carrier wave and a series of Page 6 sidebands E t Epexp iwot iB sin Qt Ey Y Ja 8 exp wo n 2 t Eo vo exp iwot Jn 8 exp t wo nQ t 1 exp i wo E This transformation shows that our original optical sine wave has now developed a comb like structure in frequency space The Jo term at the original frequency wo is the optical carrier frequency in analogy g y with radio terminol
243. te rotation in space of the plane of polarization of the transmitted light The absorption dispersion and Faraday rotation signals computed thus far are complicated in experimental practice by the Doppler effect Rather than a sample of atoms all at rest and all sharing a common resonant frequency or its Zeeman shifted equivalent the experimenter confronts a sample of atoms of mass m sharing common rest frequency Vo but spread out in velocity component v according to the one dimensional Maxwell distribution a Gaussian 728 Am J Phys Vol 64 No 6 June 1996 zm Q9 stee COE where kg is Boltzmann s constant and T is the absolute tem perature of the sample The effect of this distribution in ve locity is to create a distribution of apparent resonant frequen cies v where the first order Doppler shift gives Vo v ll t v c so U A o vg voo 30 Thus the sample effectively contains a whole collection of distinguishable kinds of atoms with distribution of resonant frequencies m 39 amp wen Ak Ao vo wl 31 Defining the Doppler width Avp as the full width at half maximum of this distribution we get 8kgT In 2 ae ae 32 0 Vp and the Doppler distribution normalized to unit area be comes 1 2 een e n 1 im 33 The utility of this normalized distribution is that results pre viously calculated for motionless atoms all of one resonant frequen
244. ter the laser warms up briefly you should have essentially the same spectrum you had when you turned the laser current off We do not recommend leaving the controller on overnight and unattended even if the laser current has been turned off Rev 2 0 11 09 III Observing Saturated Absorption A The Optical Plan There are countless ways in which the optics could be configured to do observe the Saturated Absorptions Spectrum SAS of Rubidium A complete diagram of the configuration we will guide you in building is shown below in Figure 1 A different layout is used in the lab notes from Caltech which are at the end of this manual Detector 2 Detector 1 to INPUT to INPUT Photo Photo diode diode Detector Detector Figure 1 Complete SAS setup B Some Basics Before We Begin 1 Keep the beam height above the table constant as you bounce the beam off the mirrors Since the center of the absorption cell and the laser are 4 10 cm above the table top the beam should be there also You can use the viewing card to check the beam height Place the viewing card in the neutral density beam holder so that the marked line matches the top of the holder Now set the height so that the top edge of the holder and thus the
245. th Professor Kenneth Libbrecht of the California Institute of Technology Caltech Having used TeachSpin s Pulsed NMR and Optical Pumping in his advanced lab Professor Libbrecht was convinced that TeachSpin would be able to build an apparatus that would make these experiments which were a favorite with his students available to the entire advanced laboratory community And the collaboration continues shortly after DLSI A was finished Professor Libbrecht worked with us to create the Fabry Perot Cavity accessory And we are hoping to add even more Both the DLSI A apparatus and this manual were produced in collaboration with Professor Libbrecht The varied voices will be apparent as your read the manual Senior Scientist Dr George Herold was responsible for much of the TeachSpin contribution to both the instrument design and this manual The first three student laboratory instruction manuals in the Experiments section come from the Caltech advanced lab You will find pdf versions of these documents on the Caltech advanced lab website The fourth experiment is in an article that was written for the American Journal of Physics by Professor David Van Baak of Calvin College who is also a TeachSpin collaborating physicist We know you will be creating instruction manuals for this apparatus which are tailored to the specific needs of your own institution We hope that as you do so you will make them available through your own lab websit
246. th a color center laser Appl Phys B 34 179 185 1984 Zpolarizing beamsplitter 03 PBS 065 by Melles Griot Irvine CA Photodiodes VTB 6061 from EG amp G Vactec St Louis MO Using dual op amp LM833 from National Semiconductor with feedback resistors of 3 9 KO and parallel capacitors of 220 pF for high frequency roll off G P Barwood P Gill and W R C Rowley Frequency measurements on optically narrowed Rb stabilized laser diodes at 780 nm and 795 nm Appl Phys B 53 142 147 1991 777 Wu M Kitano W Happer M Hou and J Daniels Optical determi nation of alkali metal vapor number density using Faraday rotation Appl Opt 25 4483 4492 1986 In this paper it is shown that an exact treatment gives a Faraday rotation far from resonance larger by a factor of 7 6 than the one computed using the simple model described here 5X Chen V L Telegdi and A Weis Magneto optical rotation near the cesium D line Macaluso Corbino effect in intermediate fields I Linear regime J Phys B 20 5653 5662 1987 26 I Kanorsky A Weis J Wurster and T W Hansch Quantitative investigation of the resonant nonlinear Faraday effect under conditions of optical hyperfine pumping Phys Rev A 47 1220 1226 1993 2C Wieman and T W H nsch Doppler free laser polarization spectros copy Phys Rev Lett 36 1170 1173 1976 3 Kazuyuki Muroo Takeshi Matsunobe Yukio Shishido Y
247. th a hole punched in it to observe the reflected beam from each of the mirrors Adjust the business card and card holder so that the incoming beam goes through the hole Use the CCD camera to observe the beam reflected from the mirror Adjust the mirror to send the out going beam back through the same hole Do this for both mirrors as shown in Figure 2 Rev 2 0 11 09 Mirror 1 50 50 Beam Splitter Business Card w hole in Card Holder NS 50 50 Beam H Splitter Business Card w hole in Card Holder Mirror 2 Figure 2 Use a business card with a hole punched in it to roughly align two mirrors Rev 2 0 11 09 Mirror 1 Business Card in Card Holder Mirror Mirror 2 5 4 a E 50 50 Beam 4 Splitter Mirror 1 Business Card 7 in Card Holder Mirror Mirror 2 8 50 50 Beam Splitter Figure 3 Iterative procedure to get two beam co linear Now move the Card holder to the p
248. th other methods of producing laser light Diode lasers have many uses primary among these are retrieving data stored on optical disks for instance all compact disk players use diode lasers and sending light pulses down optical fibers for telecommunications At present one can purchase diode lasers that operate at wavelengths from the blue to the infrared there is a big push in industrial labs to produce shorter wavelength lasers in order to increase the density of optical disk storage Power levels for single mode diode lasers are typically a few mW but can be as high as 1 Watt The TeachSpin diode lasers Sanyo DL 7140 201S emit up to 70 mW of output power near 785 nm The back surface of the tiny semiconductor laser cavity is highly reflecting while the front surface is often coated with a thin antireflection layer to enhance its transmission Only the manufacturer knows exactly how the facets are prepared such details are often carefully guarded industrial trade secrets It is possible to get an approximate measure of the reflection coefficient R 16 5 596 See section A4 2 for details Rev 2 0 11 09 II LASERS WITH GRATING FEEDBACK or External Cavity Diode Lasers ECDL A Introduction Bare diode lasers have two undesirable properties 1 their linewidths Av 50 MHz are large compared to the linewidths of atomic transitions in our case I 5 MHz and 2 they are extremely sensitive to optical feedback as little
249. that the atoms being illuminated are not at rest but instead are free flying in vacuum The relevant velocity is that component v of the atom s velocity along the direction of the light beam because that motion causes a Doppler shift of the laser light s frequency In the rest frame of the atom the laser frequency is shifted from is lab value f to a received frequency of fg f 1 v C It is only when the received frequency fg matches the atomic energy level difference according to h fp AE that a transition will occur So a laser of fixed frequency in the lab frame will pick out only one velocity class of atoms namely the atoms having the v needed according to the equation above and it will interact only with that class of atoms Kinetic theory tells us how many atoms should have various v values In fact there ll be a Gaussian distribution in v with mean v value of zero but with mean square value given by equipartition according to 12 m lt v gt 1 2 kp T And that s why there s a Gaussian distribution in frequency too in the curve that gives the intensity of the fluorescence as a function of laser frequency Diode Laser Spectroscopy David Van Baak July 2009 Even here the list of things to be observed spectroscopically is not nearly complete Using the methods of laser spectroscopy it is even possible to surpass the limits of Doppler broadening and to achieve spectroscopic resolution far better than the
250. that they will produce and not by the maximum current For each individual diode the current that will produce this specified power is different with values ranging from 80 mA min 110mA typ and 140mA max See spec sheet in appendix Your instrument has a current limit that has been set to approximately 80 mA This value has been chosen so that no diodes can be damaged by excess current from the controller However this also means that the typical diode will not reach its maximum specified output power 70 mW For the typical student experiment the current limit will not be a problem because the diode has excess power and one is typically attenuating the beam when taking data A user needing the full power may adjust this current limit See section LB 2 The current limit does not affect the currents injected either through the front panel current modulation input or through the SMA connector on the laser head The front panel has a maximum modulation amplitude of 11 mA This means that a maximum current of 91 mA the sum of the modulation input and DC current can be applied to the diodes by the students It is possible that this may be enough current to damage a few select diodes Please warn your students There is no over current protection limiting the amount of current that can be sent through the RF connector The RF input is for advanced users only LC 2 c Applying Power Before turning on the AC line power to the electronics make s
251. the Faraday effect is to dispersion what the Zeeman effect is to absorption or emission Given the small magnitude of Faraday rotation in bulk condensed matter it might seem impossible to detect the effect for a much more dilute gas sample It is the connection between absorption and dispersion that contradicts this ex pectation both effects are subject to enormous enhancements near atomic resonances This paper will work out the theory of Faraday rotation for light interacting with a simple model system and will derive the behavior of the Verdet constant both far from and very near an atomic resonance The cal culation in turn is motivated by the possibility of observing resonant Faraday rotation in an atomic vapor in this case by the interaction of 780 nm diode laser radiation with a room temperature sample of rubidium vapor The notable and de tailed agreement between observed rotation signals and those computed from a theory involving atomic dispersion demonstrates the reality of dispersion and its intimate con nection with absorption Since the absorption and fluores cence of rubidium vapor under diode laser excitation is an 1996 American Association of Physics Teachers 724 emerging classic experiment in diode laser optics and since only very modest extra equipment is needed to display Far aday rotation a growing number of students will be able to appreciate directly this probe of the dispersion that always accompan
252. the end of the chip serve as the cavity mirrors and output couplers These can be coated to increase or decrease the facet reflectivity Rev 2 0 11 09 SCHEMATIC STRUCTURE OF VISIBLE LASER DIODES a Gain Guided Laser b index Guided Laser Figure 3 Schematic picture of the internal semiconductor structure of some typical laser diodes This view is looking into one facet of the laser cavity By careful construction of the diode cavity the laser can be made to emit in a single longitudinal cavity mode i e a standing wave inside the cavity with a fixed number of nodes along the cavity axis and no nodes in the transverse direction A bare diode laser has a linewidth of typically Av 50 MHz The spatial mode of the laser and thus the shape of the output beam is defined by the narrow channel that confines the light Since the channel is rectangular and not much larger than the light wavelength the output beam is elliptical and strongly diverging see Wieman and Hollberg 1991 At low levels of injection current the optical losses exceed the gain and a population inversion is not achieved The light output is then broad band spontaneous emission similar to that of an LED But above a threshold current the laser emits a coherent beam which increases in intensity linearly with injection current The output power in coherent radiation can be as high as 50 percent of the input electrical power which is very efficient compared wi
253. the vertical position Once again try to minimize the reflected beam s intensity by adjusting both the X and Z rotations This time you should find a nice minimum The alignment of your poor man s optical isolator is now optimized The isolation is far from perfect but it is good enough to perform all the measurements that have been outlined in the Fabry Perot manual It may also be the case that by empirically adjusting the isolator I was able to compensate for the polarization change caused by the mirror 15 TeachSpin Fabry Perot Manual Fabry Perot Cavities and FM Spectroscopy Student Laboratory Manual Pg 1 12 California Institute of Technology Dr Eric Black and Professor Kenneth Libbrecht Followed by Scanning Spherical Mirror Interferometers for the Analysis of Laser Mode Structure Spectra Physics Laser Technical Bulletin Number 6 Ph 77 ADVANCED PHYSICS LABORATORY ATOMIC AND OPTICAL PHYSICS Expt 71 Fabry Perot Cavities and FM Spectroscopy I BACKGROUND Fabry Perot cavities also called Fabry Perot etalons are ubiquitous elements in optical physics and they are used for such applications as sensitive wavelength discriminators as stable frequency references and for building up large field intensities with low input powers Also lasers are all made from optical cavities For our diode lasers the cavity is made from a semiconductor material a few millimeters in length and the light propagates i
254. tic field V CONCLUSIONS AND APPLICATIONS We have shown that the Faraday effect is readily detected in a diode laser experiment in rubidium vapor and that it has both an unusually large size and a particularly interesting structure in the immediate vicinity of the D resonance line We have also shown that a relatively simple theory can de scribe most of the features of the resonant structure and this illustrates the intimate connection between absorption and dispersion in this resonant interaction of light and matter It is worth contemplating how the theoretical and experi mental work discussed in this paper could be extended An obvious extension to the theory would be to replace the simple atomic model used above with a quantum mechanical model of actual rubidium complete with the hyperfine struc ture of both the ground and excited states and the correct magnetic field dependence of all the energy levels This has been done for the analogous D line in cesium in connection with experiments in parity violation and affords a useful exercise in matrix diagonalization This however would still not give a perfect description of the experiment since at easily accessible levels of laser intensity there arise nonlinear effects such as optical pumping saturation and velocity redistribution On the experimental side one could imagine a Doppler free Faraday effect experiment using a pump beam to isolate one velocity class a
255. tions but the derivation is a bit too involved to repeat here Most good books on statistical mechanics derive it For example you can find it in Reif s book see references below which is still an excellent introduction to the subject Assuming the rubidium gas behaves like an ideal gas a good assumption the vapor density is propor tional to e T and thus so is the optical depth 7 w The light transmitted through the cell is equal to Iou w ime in the limit that Iin the light incident on the cell is much less than the saturation intensity which was introduced in the previous lab equal to about 2 mW cm for rubidium Thus we have Lout w Ii where the function A w contains the Doppler broadened absorption profile of the gas If we measure the exp A w exp KT Page 5 intensity of the line center only then I out wo Ti where here Ao is a constant for a given atomic transition The goal of the first part of the lab will be to exp Ao exp KT measure Zou wo 1 at several different values of the cell temperature and from these data extract the latent heat of vaporization of rubidium gas Start with the cell at room temperature about 25C on the cell temperature controller Scan the laser frequency and send the beam through the rubidium cell and onto a photodiode Reduce the laser intensity by about 3 4 orders of magnitude by using absorption filters in order to reduce the intens
256. tive horizontal alignment Before beginning your alignment it is important that you have read the first section of this manual Diode Laser Physics It will be much easier to follow the procedure if you have some idea of the physics behind these adjustments This may be the most difficult procedure you will need to follow in this experiment For the uninitiated it is very easy to totally misalign the laser which can be both frustrating and time consuming If you are not familiar with diode laser adjustment we ask that you follow each step closely If you have trouble or do not observe what is described in a given step do not go on to the next step We have tried to anticipate possible problems and direct you to the solution We also do not want to make you overly timid by this statement Alignment of the external laser cavity is something that any experimental physicist can accomplish You will need to become facile in the alignment not only because your students may misalign the cavity but also because eventually your diode will burn out and you will have to replace it This will involve an alignment of the cavity starting from scratch Figure 2 Picture showing TOP and SIDE Knobs used to align grating Allen wrench is shown in Side Knob Rev 2 0 11 09 6 Vertical Alignment Remove the plastic cover from the laser and set the current so that the laser is just above threshold Adjust the TOP knob while watching the laser spot on the card usi
257. to 377 000 GHz Recall 1 GHz 1000 MHz 10 optical cycles per second In the simplest diode laser systems it s feasible to sawtooth scan over only about 10 not 7 000 GHz of optical frequency which is only about a 30 part per million variation in frequency Clearly you want this relatively narrow scan to include the 780 nm target wavelength but once it does what a wealth of spectroscopic information waits to be revealed How will it show up The two mechanisms most easily displayed are absorption and fluorescence Absorption that s the removal of energy from the beam of laser light as it passes through the cell The exiting beam s power is easily measured by conversion to an electrical current in a solar cell sort of photodiode and it s easy to arrange a real time oscilloscope display which shows transmitted power on a vertical scale as a function of the diode laser s frequency control voltage a surrogate for its frequency on a horizontal scale Absorption will be indicated by a local drop in the amount of transmitted power The process is easy to see since fractional absorptions of 10 50 are easily achieved but only at the right wavelength Fluorescence that s the production of light from inside the cell For if absorption happens then assuredly energy is being removed from the light beam transferred to the atoms as they are elevated to excited states Since these atoms are in free flight in vacuum there s no way
258. tomic resonance Note the index change is proportional to the first derivative of the absorption An electromagnetic wave in the medium propagates according to e iwt nkz e hnokz e ileot knoz 3 where k w c From this it can be seen that no corresponds to the usual index of refraction equal to c v while describes the attenuation of the wave Note that a relation ng 1 2 Nw amp y exists between the index of refraction and the attenuation which is independent of the oscillator strength of the atomic transition This relation showing that no v and amp v can be derived from one another is an example of the more general Kramers Kronig relations A full quantum mechanical treatment also yields the same relation for the absorption and refractive index of a gas near an atomic resonance The goal of this lab Page 2 is to measure both the absorption and index of refraction variations of rubidium gas around the S P resonance lines While absorption is easy to observe refractive index changes are not so an interferometric technique will be used to observe it 50 50 Beamsplitter Photodiode Rubidium Cell Figure 2 The basic experimental set up consisting of a rubidium vapor cell in one arm of a Mach Zehnder interferometer The dotted lines represent 50 50 beamsplitters The input laser scans across the Doppler broadened rubidium absorption line Let us examine the experimental set up shown in Figure 2 co
259. toms sees extra absorption For the other velocity class the pump laser excites g2 e gl gets overpopulated and again the probe laser which now excites g1 e for these atoms sees more absorption Quantitative Picture of Saturated Absorption Spectroscopy 2 Level Atoms One can fairly easily write down the basic ideas needed to calculate a crude saturated absorption spectrum for 2 level atoms which demonstrates much of the underlying physics The main features are 1 the transmission of the probe laser beam through the cell is e 7 r v is the optical depth of the vapor 2 the contribution to T v from one velocity class of atoms is given by dr v v P P3 F v v dn v where P is the relative population of the ground state P5 is the relative population of the excited state Pi P 1 dn e 2T dqy is the Boltzmann distribution for v along the beam axis and T 27 v vo vov c T 4 is the normalized Lorentzian absorption profile of an atom with natural linewidth T including the Doppler F v v shift Putting this together we have the differential contribution to the optical depth for laser frequency v and atomic velocity v dr v v oP P3 F v v e m 2T dy The overall normalization comes in with the P factor which is the optical depth at the center of resonance line i e To f dr vo v with no pump laser the integral is over all velocity classes 3 The populations of the excited and
260. tor Beam Block Glass ND Filter Figure 2 Start of SAS setup with 1 wedged beam splitter in place We have used the 1 wedged beam splitter which yields two reflected beams one from each face The small angle of the wedge causes the beams to diverge slowly so that both beams can travel through the cell to the two photodetectors The second photodetector PD is not needed to see the SAS It is used in the final electronic subtraction to remove the absorptive background signal If you do not intend to use this electronics trick you can leave the second detector out of the setup Position the PD s to maximize the signal level from each Rev 2 0 11 09 Monitoring the output of the Detectors you should observe the now familiar Rb absorption spectrum on your scope 3 Now add the two turning mirrors to the setup as shown in Figure 3 Move the Beam Blocker to the new location shown Detector 2 Detector 1 to INPUT to INPUT Photo Photo diode diode Detector Detector Beam Block S sl O g o WO LJ
261. tor while the horizontal axis indicates frequency On an actual oscilloscope trace the transition frequency would be hard to determine with much accuracy 1 of 4 When using saturated absorption spectroscopy SAS however the oscilloscope trace for atoms with a single transition shows a sharp spike within the Doppler dip when the laser frequency matches fp The process of SAS like many great insights seems obvious in retrospect The laser beam is split into two unequal portions The weaker portion the probe beam with only 10 of the initial intensity is directed through the gas cell to the detector The stronger or pump beam is directed around the cell and sent back through it in the opposite direction of but collinear to the probe beam The upper section of Figure 2 shows the z velocity vs frequency plot for particles that will absorb pump photons as a heavy line while the plot for atoms that will absorb probe photons is thinner Notice that the two lines cross at v 0 f fo For most frequencies within the Doppler range the pump and probe beams interact with groups of atoms moving in opposite directions When the laser frequency is fa for instance atoms moving toward the probe beam at a velocity we can call v 4 absorb the probe beam photons However for the pump beam it is the atoms moving at v 4 which see the pump beam frequency as elevated to fo At this frequency the presence of the pump beam has no effect on the amount of l
262. ty of order 0 5 A W it is convenient to use operational amplifiers as current to voltage converters to generate voltage outputs of order 1 V per milliwatt of incident optical power Such detector amplifier combinations can easily have response times under 10 ys and display output noise equivalent to optical inputs well under 1 uW The ancillary electronics needed for this sort of experi ment include the servomechanism for diode laser tempera 730 Am J Phys Vol 64 No 6 June 1996 ture control the stable but agile current source of order 0 100 mA 0 3 V needed to drive the diode laser and an audio frequency oscillator to modulate the diode laser cur rent and thus its output frequency Remarkably most of the experiments of interest can be accomplished with signal capturing electronics no more complicated than a dual trace oscilloscope given the laser power and detector noise levels available even nonlinear optical effects such as saturated absorption can be displayed in real time on an oscilloscope display Given such capabilities only modest additional equipment is needed to perform the Faraday rotation experiment de scribed here one needs only a source of magnetic field and a somewhat more complicated polarization sensitive optical detector system The magnetic fields required are of moder ate size up to perhaps 20 mT 200 Gauss and are easily produced by air core solenoidal coils The homogeneity re quirements are
263. u may now try to maximize the size of these spikes by tweaking the adjustment screws on the mirrors and the 50 50 BS Tek JL H Trad MPos3250ms SAVE Al Tek JL H Trad a File Forma BMP About rara daa raa denn nni nr nni Savin i ZI E J imaoe M Pos 32 50ms SAVE R Select Folder Save Save 7 TEKOOI 1 TEK0012 1 M 2 50ms Ext X 4 00m CH1 2 00VBy CH2 1 00VBy M 2 50ms Ext 4 00m Vv CH1 2 00vBy CH2 1 00VBy 1 12 Nov 08 04 54 lt 10Hz 12 Nov 08 04 54 lt 10Hz a b Figure 5 Observation of SAS features a Beams are partially overlapped and some SAS signal is visible b Signal after tweaking of mirrors and 50 50 beamsplitter If you are too good at this alignment the two beams may be so perfectly anti parallel that the strong pump beam comes through the cell and bouncing off the 10 90 is reflected back into the laser When this happens the laser will no longer scan through the spectrum continuously but in a series of steps You may observe a spectrum that looks like that shown 3 23 Rev 2 0 11 09 in Figure 6 This feedback is undesirable but it does show that you have perfected the alignment of the two beams Now you can slightly misalign the two beams such that the feedback does not corrupt the smooth scan of the laser You may have noticed that the Caltech lab notes show an opto isolator right after the laser The opto isolator
264. uilding both our Diode Laser Spectroscopy apparatus and this Fabry Perot cavity In it you will find a detailed discussion of the physics of this instrument as well as descriptions of a variety of student experiments Here we offer a brief Overview of the Physics of a Fabry Perot Cavity instructions for Unpacking the Instrument and detailed instructions for Setting Up the Fabry Perot Cavity for the First Time Overview of the Physics A Fabry Perot cavity is created by mounting a matched pair of highly reflective mirrors at either end of a tube As seems logical light aimed at the back of the near end mirror is generally reflected immediately and not transmitted through its length and out the other end However as the analysis in the appendix explains at certain resonant frequencies monochromatic laser light is actually transmitted The distance between the mirrors mounted at the two ends of a Fabry Perot cavity determine its resonant frequencies A detector just past the far end monitors the transmission Non resonant Input light is scarcely transmitted As the frequency C of a tunable laser is swept through the resonant frequencies of the cavity distinct maxima in 3 L transmission occur For a properly adjusted cavity the resonant frequencies are given by c f j 1 1 1 4nL In this equation j is an integer c is the vacuum speed of light L is the distance between the two mirrors defining th
265. ure that the laser power toggle is off that the Current ten turn pot is set to zero and that there is no external modulation Once AC power is applied you may turn on the laser power toggle and then finally increase the Current with the ten turn pot When shutting off the unit the steps should be followed in reverse First set the current to zero disconnect any external modulation turn the laser power toggle off and finally shut off the AC power to the electronics box AII these steps are meant to ensure a maximum lifetime for your diode laser This is for operation at 25 C At higher temperatures more current is needed to reach a specified output power See Diode spec sheet Rev 2 0 12 09 1 C 3 Current Controller Advanced Details The current control is based on the design of K G Libbrecht and J L Hall Rev Sci Instrm 64 8 2133 1993 zi B E f E E E 3 3 zd A H a Figure 5 Picture showing current limit trim pot and test points LC 3 a Current Limit Adjustment Advanced users may want to change the current limit so that they can get more power from an individual diode Increasing the current limit could lead to overdriving of the laser diode and permanent damage This procedure is only for those who understand this and can set an appropriate current limit The circuit limits the current by setting the supply voltage The supply voltage is dropped across the 50 ohm current sensing resistor the 5 ohm cur
266. v 2 0 11 09 Grating FeedBack and b External Cavity 777777 Internal Cavity q Mode Hop 1 0 q Int O m 1 04 P hint 0 8 0 8 S c oy a 9 0 6 h 0 64 0 4 0 4 02 7 Abe 02 MM e 2 e 1 e0 e1 e2 e3 e4 e 2 e 1 e0 el e2 e3 e4 0 0 T Y T a T T T T T Y T M 1 0 0 T V T Y T Y T T T T T n 1 80 100 120 140 160 180 200 80 100 120 140 160 180 200 12 Relative Frequency GHz 15 Relative Frequency GHz c d Mode Hop 40 lt q Mode Hop 0 8 1 S 06 S G 3 0 4 0 24 41 Nee e 2 e 1 e0 e1 e2 e3 e4 e 2 e 1 e0 e1 e2 e3Ve4 0 0 r 0 0 s T T T T T T d T Y T y T T T 1 80 100 120 140 160 180 200 80 100 120 140 160 180 200 Relative Frequency GHz Relative Frequency GHz Figure 9 Series of graphs showing showing how the external and grating feed back mode shifts as the grating angle is changed Figure 9 shows a series of pictures of the External and Internal cavity modes as the grating angle is decreased The pictures show only two of the internal modes labeled Int 0 and Int 1 For reference we have also labeled some of the external modes e 2 e 1 eO el e4 In Figure 9 Graph a is for the same grating angle shown in Figure 8 where the laser is oscillating in external mode e0 As the grating angle is decreased mode e0 is shifted to higher frequency shorter wavelength until the point shown in graph b At this point the overall gain in external mode e 1 is about equal to that in m
267. ve Save 1 TEKOO13 4 i TEKOO14 I CH1 2 00V By CH2 1 00VBy M 2 50ms Ext X 4 00m CH1 2 00 By CH2 1 00VBy M 500us Ext 4 00mV 12 Nov 08 04 55 lt 10H2 CH2 vertical position 2 12 divs 2 12 a b Figure 7 SAS traces with background subtraction a Rb F2 and Rb F 3 b Expanded view of Rb F 2 It is interesting to study these signals as a function of the intensity in each of the beams The above traces are power broadened To observe the narrowest linewidths you will have to work at very low optical power levels in both the pump and the probe beams You can use neutral density filters to attenuate the beams You will also need to darken your room to minimize ambient light falling into your photodetectors Rev 2 0 11 09 IV Aligning a Michelson Interferometer Photo diode Detector Splitter Pick off portion of strong beam Figure 1 Overview of un equal arm Michelson Find a spot on the table to lay out the Michelson interferometer MI You must use the filter holder to hold the 50 50 Beam Splitter BS A mirror mount will not allow the beam to come in and exit from all four directions This complicates the alignment as one can only make coarse adjustments of the 50 50 BS Keep Mirror 1 as close to the 50 50 BS as possible Use a wedged or flat piece of glass as the 10 90 BS to pick off a fraction of the laser beam Now look at Figure 2 below We will use a business card wi
268. ve control algorithm 5 25 Rev 2 0 12 09 II B CELL HEATER AND COLD FINGER IILB 1 Description A cross sectional view of the Cell Heater is shown in Figure 17 The spring loaded cold finger makes contact between Rb cell tip and the outer glass cylinder A white piece of thermal adhesive is placed around the cell tip to increase the contact area between the cell and cold finger The thermocouple temperature sensor has been placed between the cell and the foam near the cell tip The junction is soldered together and the wires are covered with black heat shrink tubing III B 2 Removal of Cell Heater and Cold finger To remove the cell and cold finger first turn off the power and let the unit cool to room temperature Loosen the Nylon setscrew on the side of the rotatable cell mount and remove the heater assembly with attached aluminum holder from the base Set the assembly on the table We will describe the removal of the cell and cold finger while leaving the glass cylinder attached to the aluminum holder Remove the foam ends caps When you remove the end cap with the wires for the heater and thermocouple TC the TC will come out with the end cap Slowly push the foam and cell assembly out of the glass cylinder Push towards the end where the heater wires come out Be prepared to catch the bottom of the spring loaded cold finger as it clears the end of the glass cylinder when the assembly is half way out When the foam and cell ass
269. w square milli meters means that optical signals in rubidium can be readily saturated For experiments such as Doppler free saturated ab sorption this is desirable but for Faraday rotation experi ments this can be avoided either by using a less tightly fo cused laser beam or by using neutral density filters to attenuate the laser beam A suitable level of attenuation is easily found empirically by noting with decreasing values of laser beam intensity an approach to a asymptotic value for the fractional absorption at a rubidium resonance The rubidium cell used in such experiments can be of 1 to 3 cm diameter and 5 to 10 cm length for polarization sensitive experiments it is very convenient for the cell to have flat end windows at near normal incidence Since typi cal experiments can be done with the rubidium near room temperature exotic glass is not required The data below were all obtained with a cell of 25 mm outside diameter 51 mm inside length made of Pyrex glass and filled with rubidium of natural isotopic abundance in vacuum no buffer gas The simplest optical detectors for use near 780 nm are silicon photodiodes These are available in a wide range of shapes and sizes but all share the remarkably high quantum efficiency 75046 of silicon p n photojunctions at these near infrared wavelengths The detectors can be operated at zero potential difference such that they act like ideal current sources with responsivi
270. w stronger and richer Gilbert Highet The Art of Teaching Vintage Books New York 1989 originally published by Alfred A Knopf 1950 pp 83 84 735 Am J Phys Vol 64 No 6 June 1996 D A Van Baak 735 DIODE LASER SPECTROSCOPY APPARATUS SECTION Rev 2 0 11 09 Chapter 5 Apparatus Table of Contents I Laser I Laser continued A 9 pin cable and connector 5 1 E Piezo Stack 5 21 B Laser Temperature 5 2 1 Piezo electronics 1 Specifications F Ramp generator 5 22 2 Laser Head II Photodiode Detectors and a Plexiglas cover Detector Electronics 5 23 3 Laser temperature electronics 4 Advanced Details III Absorption Cell Assembly 5 25 a Changing the PID control A Specifications parameters B Cell heater and Cold finger 1 Description C Laser Current Controller 5 8 Specifications 2 Current electronics 2 Removal a Diode protection 3 b Current Limit c Applying power 3 Advanced Details a Current limit adjust b High Freq Mod Installation C Thermocouple Position D Condensation of Rb on Cell Windows E Cell Temperature Controller F Magnetic Field Coils D Laser Optics and Diode 5 12 IV Optics 5 30 1 Laser Diode A Mirrors 2 External Cavity B Beam Splitters a Finding the retro reflection C Neutral Density Filters b Aligning external cavity D Linear Polarizers c Measuring the Threshold E Quarter Wave Plates rent F Assembly and Care of Optical 3 D
271. we could photograph it easily Depending upon the space you have available and the kinds of experiments you wish to do other configurations may be far more useful The photograph shows the location of the linear polarizer and 4 wave plate which were not included in the schematic These are not used in the initial set up and are added somewhat into the process of tuning the cavity As you can see 4 wave plate is tilted around its vertical axis This is one of the degrees of freedom you can use when adjusting this poor man s optical isolator to prevent the light reflected off the Fabry Perot surfaces from returning to the laser See page 9 of this discussion 5 TeachSpin Fabry Perot Manual Rev 2 0 11 09 Now it is time to turn on the laser and get the beam near center of two steering mirrors Use the mirrors to make the beam parallel with the top of the breadboard and at a height of about 4 inches The iris provided will make this task easier Tune the laser to the Rb spectrum and use one photodiode to monitor the absorption This is not necessary to run the FP but the cleanness of the absorption spectra will be used a diagnostic to tell you when reflections for the FP are getting back into the laser and changing its wavelength The upper trace in Figure 2 is a normal spectrum below is one corrupted by feedback Well stocked optics labs may have an optical isolator that can be used to eliminate the back reflections We will also d
272. will read SP2 e Press the leftmost button twice The display will read RUN momentarily then it will read the cell temperature f The cell temperature should read near the set point after several minutes You may proceed with the next step before the final temperature is reached The Cell Temperature controller is not critical to operation of your diode laser It merely improves the signal strength by increasing the rubidium density in the cell See Theory section for a plot of Rb pressure versus temperature A starting temperature of 50 C was chosen to give a nice strong absorption signal about 90 Once you become familiar with the system you may want to work at a lower temperature 3 3 Rev 2 0 11 09 Trouble shooting If the controller is not working as described please refer to the Apparatus section of the manual under Cell Temperature Controller for how to configure and set your controller It is possible your controller became reset during shipping or by a student the ever present scapegoat C Starting up the Laser Operating note The diode laser frequency depends on temperature If not set correctly you may not be able to get your laser to tune to the Rb resonance lines The optimal temperature was determined at TeachSpin and is recorded on the data sheet 1 Check the Diode Laser temperature a Use a voltmeter to read the TEMPERATURE SET POINT in the MONITORS section of the controller chassis This voltage should equa
273. xis condition As the beam becomes closer to on axis you will see a drop in the intensity of every other mode of the c 4L spacing At the same time as we can see from Figure 14 the magnitude of the alternate peaks increases If you were able to be exactly on axis you would be exciting even but not odd transverse modes and you would get complete suppression of every other peak in the mode spectrum In addition to doubling the free spectral range exciting these on axis modes also maximizes feedback to your laser Can you explain why This places the highest demands on isolation of the laser from the cavity 13 Rev 2 0 11 09 Tek SAVE REC IM Tria d M Pos 55 5 rns Action Select Folder A Save TEKOO6 BMP CHiw2 mw CH2 100m ey Mi 100m Ext Bar Current Folder is 4 4 FP MAN 4 Figure 13 Normal input signal FSR c AL Tek Al Trig d M Pos 55 5 ms SAVE REC Action Select Folder Save TEK0015 6MF 26 Jan OF 3 23 Figure 14 On axis input FSR c 2L lt 10Hz TeachSpin Fabry Perot Manual Appendix A The Poor Man s Optical Isolator The poor man s optical isolator is a means by which specular reflections may be reduced It consists of a linear polarizer followed by a 1 4 wave plate If the axis of the polarizer is placed at 45 degrees with respect to the axes of the 1 4 wave plate the light beam will emerge from the 1 4 wave plate circularly polarized T
274. y skip the following step Usually this step is only necessary if you are installing a new collimation tube or if the lens position has been grossly misadjusted Coarse adjustment involves collimating the laser beam so that the beam size does not change with distance Turn the laser power on and adjust the laser current above threshold Use the IR viewing card or the viewing screen CCD camera and TV monitor to observe the spot size first near the output of the laser and then at a point several meters away If the beam size changes use the spanner wrench to adjust the lens until the beam is collimated LD 4 c 2 Fine Lens Adjustment Fine lens adjustment involves measuring the threshold current as a function of the lens position At the optimal lens position the threshold current is a minimum The following steps need to be repeated until the minimum threshold current is found Align the external cavity and measure the threshold current section I D 2 b amp c Remove the grating section I D 3 a Adjust and record the lens position LD 4 c 3 Reinstall the grating LD 3 b Align the external cavity and then measure the new threshold current You may be tempted to remove the collimation tube from the tube holder adjust the lens position and then reinstall the collimation tube in the holder thus skipping the removal and installation of the grating However the threshold current is a strong function of the electric field polarization direction and we
275. ye lasers they are still very expensive options The recent development of tunable narrow bandwidth semiconductor diode lasers dramatically changed this picture These lasers are inexpensive easy to operate and produce high power tunable narrow bandwidth radiation Av lt 1 MHz AA lt 1 5x10 nm For these reasons tunable diode lasers have rapidly become commonplace in modern research laboratories Interior Diagram of TOLD9200 Series Figure 1 Cut away view of a typical laser diode can like those used in the TeachSpin laser The basic physics of diode lasers is presented in several review articles and books such as Wieman and Hollberg 1991 and Camparo 1985 Figure 1 shows a cut away view of a typical diode laser similar to the ones used in this experiment The actual semiconductor device is a small chip LD chip in Figure 1 bonded to a heat sink Tiny wires connect the Rev 2 0 11 09 chip to the outside world Most of the light emitted by the laser comes out the front facet and a small amount also comes out the back facet The two facets are constructed to have different reflectivities Often a photodiode is placed at the back of the can to monitor the laser output power The main laser beam which is elliptical and strongly diverging comes out a window in the front of the laser diode can Figure 2 shows a more detailed view of a typical laser diode chip Current is driven from the top to the bottom of the chip see
276. you notice Rb condensing on just one of the end windows of the cell adjust the cell and foam support to expose slightly more of the heater on the side where the Rb is condensing Push gently on the foam and cell from the side where the metal is condensing See the addendum at the end of this section for detailed instructions on how to transfer the Rb from the end windows to the tip I E CELL TEMPERATURE CONTROLLER IILE 1 Operation of Cell Temperature Controller The Omega temperature controller is mounted on the front panel A manufacturer s manual for the controller has been included Reading from left to right across the face of the unit the four keys used to program the controller are MENU UP DOWN and ENTER When the controller is in the normal or RUN mode the temperature is displayed in degrees Celsius Under normal operation you will be changing only the temperature set point In the RUN mode the controller will display the current temperature To get into the Configuration Mode press the MENU key once SP1 will be displayed Now press the ENTER key The display will show the current Setpointl Use the UP and DOWN arrow keys to change the value Once the correct value has been selected press the ENTER key again to store the value The display will show StRd briefly indicating your value has been registered Return to the MENU key and continue pressing until RUN is displayed IILE 2 Configuration of Cell Temperature Contr
277. ys readily apparent when a laser needs to be replaced The telltale signs of a damaged laser are The laser power as a function of current is reduced from nominal values The laser threshold is not abrupt and obvious at the nominal threshold current The output beam profile of the diode may also change I D 2 External Cavity To align the external cavity you must adjust the angular orientation of the grating so that the beam diffracted from the grating is sent back into the diode The beam labeled Secondary Output is also called the retro reflected beam Figure 8 diagrams the process Secondary Output Beam Reflected from Grating and Diode Front Facet Primary Laser Beam Front Facet Back Facet R 15 R 100 em Beam Diffracted from Grating Beams have been spacially separated for clarity Columating lens is not shown Figure8 Diagram Showing Origin of both the Primary and Secondary Retro Reflected beam Spots Rev 2 0 12 09 LD 2 a Finding the Retro Reflection Use the blank backside of a business card as a viewing screen Place the card in front of the laser and use the CCD camera and video monitor to view the output beam as shown in Figure 9 Turn on the laser power and set the laser current two to three milliamps above threshold Check that the Laser TEMPERATURE SET POINT is correct Refer to section L B 3 Laser Temperature Electronics for how to change temperature set point The picture of the TV monitor

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