Gain Compression and Above-Threshold Linewidth
Contents
1. Linewidth Enhancement Factor 0 2 4 6 8 10 Output Power mW Fig 4 Effective linewidth enhancement factor ay as a function of the output power for the QW DEB laser is due to the decrease of the differential gain from gain com pression and can be written according to the relation ay ayo 1 epP 4 where ayo is the linewidth enhancement factor at threshold Since the carrier distribution is clamped ayo itself does not change as the output power increases As an example Fig 4 shows the measured linewidth enhancement factor versus the output power for a QW DEB laser Black squares correspond to experimental data As described by 4 the effective ay factor linearly increases with the output power By curved fitting those data the a factor at threshold is found to be around 4 while the gain compression coefficient equals 0 03mW7 t Compared to QD lasers such a value of the gain compression coefficient is much lower since the enhancement of the effective a factor is not significant over the range of power In QD lasers the carrier density and distribution are not clearly clamped at threshold because the inhomogeneous broadening gain is more predominant Indeed the lasing wavelength can switch from GS to ES as the current injection increases meaning that a carrier accumulation occurs in the ES even though lasing in the GS is still occurring The filling of the ES inevitably increases the ay factor of the GS introducing a2. as well as the continuum states in the quantum wells explains the degradation of the GS ay factor 24 To the best of our knowledge we believe that such a comparison between calculations and AM FM measurements on the above threshold ay factor has not been reported yet Thus these results are of first importance because they point out the role of gain compression and that a larger maximum gain is required for getting a lower ay factor in a real laser This can be critical for the realization of chirpless devices as well as for isolator free transmission under direct modulation and without transmission dispersion penalty II DEVICE DESCRIPTION The laser under study was grown by molecular beam epitaxy MBE 23 The active region is made of three layers of self as sembled InAs QDs covered by a 5 nm InGaAs QW and sepa rated from each other by a 40 nm GaAs space layer The dot density per stack is about 3 x 10 cm The laser cavity is clad by 1 5 m Alp 7Gao 3As layers The device is a 1 950 mm long Fabry Perot ridge waveguide laser RWG with 3 y4m wide stripe Coated front and rear facet reflectivities are equal respectively to 79 and 93 at 1 3 yum In Fig 1 the N WwW fa oO Oo N Normal Compression Factor Ee oft le Ratio 9 4 Gin Fig 2 Normalized compression factor as a function of gmax gtn light current characteristic L T measured at room temperature is depicted The threshold current leading to a GS emis
3. joined Les Laboratoires de Marcoussis Alcatel Research Center He is currently with Alcatel Thales III V Lab Marcoussis France working on characterization of fast photonic sources for telecommunications applications Hui Su received the Ph D degree in optics sciences and engineering from the University of New Mexico Albuquerque in 2004 His doctoral research focused on quantum dot photonics devices During 2004 2006 he was a Postdoctoral Research Associate with Prof S L Chuang s group at the University of Illinois Urbana Champaign where he was involved with slow light and fast light in semiconductor optoelectronics devices Since 2006 he has been with EMCORE Inc Alhambra CA as a Scientist His research includes lasers for fiber to home and CATV applications Dr Su is a member of the Optical Society of America Luke F Lester SM 00 received the B S degree in engineering physics and the Ph D degree in electrical engineering from Cornell University Ithaca NY in 1984 and 1992 respectively He joined the University of New Mexico UNM Albuquerque in 1994 where he is currently a Professor with the Department of Electrical and Com puter Engineering and Associate Director of the Center for High Technology Materials He was an Engineer with the General Electric Electronics Labora tory Syracuse NY where he worked on high electron mobility transistors for mm wave applications He has over 20 years experience in I V se
4. papes dgg _ In 2 7 dN Nir 9max gg 8 where gg geh 1 p P is the uncompressed material gain increasing with the output power Equation 8 leads to Ag a0 1 epp ao 1 i255 Jmax th Jmax Ith 9 where ao is the differential gain at threshold Then using 4 6 and 9 the linewidth enhancement factor can be written as an P a9 1 epP ait 10 Jth epP Jmax Ith where o amp e ae ao The first term in 10 denotes the gain compression effect at the GS similar to QWs while the second is the contribution from the carrier filling in the ES that is related to the gain saturation in the GS For the case of strong gain saturation 10 can be reduced to OO Gmax Gth ap P 11 In Fig 5 the normalized linewidth enhancement factor ay ao is calculated through 11 and reported in the X Y plane with X P Psat and Y gmax 9th This picture acts as a stability map that simply shows that a larger maximum gain is absolutely required for a lower and stable a p ag ratio For instance let us consider the situation for which gmax 39h at low output powers i e P lt Psat the normalized ay factor remains con stant ay amp amp o 3 since gain compression is negligible On the other hand as soon as the output power approaches Psat and goes beyond the ratio azz ao is increased Gain compression effects lead to an enhancement of the normalized
5. 57 down to 30 may be explained through a modifica tion of the carrier dynamics such as the carrier transport time including the capture into the GS This last parameter affects the modulation properties of high speed lasers via a modifica tion of the differential gain 25 As a conclusion these results are of first importance because they show that the a factor can be controlled by properly choosing the ratio gmax 2th the lower gpn the higher gmax the smaller the linewidth enhance ment factor A high maximum gain can be obtained by opti mizing the number of QD layers in the laser structure while gain at threshold is directly linked to the internal and mirror losses Both gin and gmax Should be considered simultaneously so as to properly design a laser with a high differential gain and limited gain compression effects The gmax th ratio is definitely the key point in order to obtain a lower ay factor for direct modu lation in QD lasers V CONCLUSION The effects of the nonlinear gain on a 1 3 um InAs GaAs QD laser have been investigated Owing to the relaxation frequency dependence with the output power the compression factor has been determined and estimated to be significantly larger than in QW devices as previously observed Based on a theoretical approach including nonlinear gain it has been found that gain compression is systematically strengthened in QD devices be cause of the gain saturation with carrier density by a fact
6. 946 IEEE JOURNAL OF QUANTUM ELECTRONICS VOL 44 NO 10 OCTOBER 2008 Gain Compression and Above Threshold Linewidth Enhancement Factor in 1 3 um InAs GaAs Quantum Dot Lasers Fr d ric Grillot Member IEEE B atrice Dagens Jean Guy Provost Hui Su and Luke F Lester Senior Member IEEE Abstract Quantum dot QD lasers exhibit many useful prop erties such as low threshold current temperature and feedback insensitivity chirpless behavior and low linewidth enhancement factor ay factor Although many breakthroughs have been demonstrated the maximum modulation bandwidth remains limited in QD devices and a strong damping of the modulation response is usually observed pointing out the role of gain compres sion This paper investigates the influence of the gain compression in a 1 3 44m InAs GaAs QD laser and its consequences on the above threshold ay factor A model is used to explain the depen dence of the ay factor with the injected current and is compared with AM FM experiments Finally it is shown that the higher the maximum gain the lower the effects of gain compression and the lower the ay factor This analysis can be useful for designing chirpless QD lasers with improved modulation bandwidth as well as for isolator free transmission under direct modulation Index Terms Gain compression linewidth enhancement factor quantum dot semiconductor laser I INTRODUCTION UANTUM DOT QD lasers have attracted a gr
7. 97 3 G T Liu A Stintz H Li K J Malloy and L F Lester Extremely low room temperature threshold current density diode lasers using InAs dots in Ino 15 Gao g5 As quantum well Electron Lett vol 35 pp 1163 1165 1999 D G Deppe H Huang and O B Shchekin Modulation character istics of quantum dot lasers The influence of p type doping and the electronic density of states on obtaining high speed JEEE J Quantum Electron vol 38 no 12 pp 1587 1593 Dec 2002 H Saito K Nishi A Kamei and S Sugou Low chirp observed in directly quantum dot lasers JEEE Photon Technol Lett vol 12 no 10 pp 1298 1300 Oct 2000 6 A Martinez A Lemaitre K Merghem L Ferlazzo C Dupuis A Ramdane J G Provost B Dagens O Le Gouezigou and O Gauthier Lafaye Static and dynamic measurements of the a factor of five quantum dot layer single mode lasers emitting at 1 3 m on GaAs Appl Phys Lett vol 86 p 211115 2005 7 D O Brien S P Hegarty G Huyet J G McInerney T Kettler M Laemmlin D Bimberg V M Ustinov A E Zhukov S S Mikhrin and A R Kovsh Feedback sensitivity of 1 3 zm InAs GaAs quantum dot lasers Electron Lett vol 39 no 25 pp 1819 1821 2003 F Gerschiitz M Fischer J Koeth M Chacinski R Schatz O Kjebon A Kovsh I Krestinkov and A Forchel Temperature insensitive 1 3 m InGaAs GaAs quantum dot dist
8. DOT LASERS 947 N Q Output Power mW _ 0 50 100 150 200 250 Current mA Fig 1 L I characteristic of the InAs GaAs QD laser under study At room temperature the threshold current for the GS is 13 mA and the external differ ential efficiency is about 0 02 W A on high frequency semiconductor current modulation that gen erates both amplitude AM and optical frequency FM modu lation The ratio of the FM over AM gives a direct measurement of the ay factor This method has already demonstrated that an ay factor as high as 57 can be obtained in QD devices 23 The aim of this study is to investigate the influence of gain compression and its consequence on the above threshold ay factor of the 1 3 um InAs GaAs QD laser published in 23 After deriving the gain compression coefficient from relaxation frequency measurements a theoretical approach in cluding an effective gain compression factor is used The model explains the dependence of the ay factor with the injected current the occurrence of the giant ayy factor and even its collapse down to negative values due to the transition from the ground state GS to the excited state ES The increase of the ay factor with current is attributed to the enhancement of the gain compression through the gain saturation with the carrier density in QDs As shown in the paper a qualitative agreement with AM FM experiments is obtained Thus taking into ac count the ES in the dots
9. HRESHOLD LINEWIDTH ENHANCEMENT FACTOR IN 1 3 um InAs GaAs QUANTUM DOT LASERS 951 21 A A Ukhanov Study of the carrier induced optical properties in II V quantum confined laser nanostructures Ph D dissertation Opt Sci Eng Dept Univ New Mexico Albuquerque 2004 22 S Melnik and G Huyet The linewidth enhancement factor a of quantum dot semiconductor lasers Opt Exp vol 14 pp 2950 2955 2006 23 B Dagens A Markus J X Chen J G Provost D Make O Le Gouezigou J Landreau A Fiore and B Thedrez Giant linewidth enhancement factor and purely frequency modulated emission from quantum dot laser Electron Lett vol 41 no 6 pp 323 325 2005 24 H Su L Zhang A L Gray R Wang P M Varangis and L F Lester Gain compression coefficient and above threshold linewidth enhance ment factor in InAs GaAs quantum dot DFB lasers in Proc SPIE 5722 2005 vol 5722 11 25 H Su and L F Lester Dynamic properties of quantum dot distributed feedback lasers High speed linewidth and chirp J Phys D Appl Phys vol 38 2005 26 D Bimberg N Kirstaedter N N Ledentsov Z I Alferov P S Kop ev and V M Ustinov InGaAs GaAs quantum dot lasers IEEE J Sel Top Quantum Electron vol 3 no 2 pp 196 205 Apr 1997 27 K Petermann Laser Diode Modulation and Noise Kluwer 1988 28 W V Sorin K W Chang G A Conrad and P R Hernday Fr
10. a factor which can go up to 10 for P 2P level of injection for which the ES occurs On the other hand assuming gmax 59th Fig 5 shows that the effects of gain compression are significantly attenuated since the ratio ay o remains almost constant over a wider range of output power The level at which gain compression starts being Ratio Ayl Oy Ratio Gmax Sth O 0 4 B 2 25 3 36 4 45 5 Ratio P P sat Fig 5 Stability map based on the normalized linewidth enhancement factor a p p in the P Psat Gmax 9tn plane GS O Factor 50 100 150 200 250 300 Bias Current mA Fig 6 Calculated GS a1 factor versus the bias current black dots Superim posed red stars correspond to experimental data from 23 critical is now shifted to P 3P instead of P Psat Let us also stress that at a certain level of injection the normalized GS ay factor can even become negative This effect has already been experimentally reported in 23 and they occur when the GS gain collapses e g when ES lasing wavelength occurs In Fig 6 the calculated GS ay factor black dots of the QD laser under study is depicted as a function of the bias current Red stars superimposed correspond to data measurements from 23 which have been obtained via the AM FM technique This method consists of an interferometric method the output optical signal from the laser operated under small signal direct mod ulation is filtered in a 0 2
11. dence of the relaxation oscillation frequency shows a deviation from the expected proportionality on the square root of the optical output power As shown in the inset a curve fit based on 2 is used to express the gain com pression in terms of a saturation power Psat 3 3 mW where egS epP P P az where ep is the gain compression co efficient related to the output power P This value means that at this level of output power nonlinear effects start to be signif icant Owing to the value of the saturated power Psat the gain compression coefficient related to the output power is estimated to be ep 1 Pyat 0 3 mW7 The maximum of the reso nance frequency can be directly deduced from the curve fitting as 2 APsat and is expected to be 5 GHz not shown in Fig 3 Taking into account the facet reflectivity as well as the modal volume of the laser the order of magnitude for the gain compression factor g is in the range from 5 x 10718 cm to 1 x 10716 cm This value is in good agreement with those already reported for QD lasers 25 26 on GaAs remaining much larger than those measured on QW lasers typically around 107 cm 27 IV ON THE ABOVE THRESHOLD amp y FACTOR In QW lasers which are made from a homogeneously broadened gain medium the carrier density and distribution are clamped at threshold As a result the change of the a factor IEEE JOURNAL OF QUANTUM ELECTRONICS VOL 44 NO 10 OCTOBER 2008
12. e quency domain analysis of an optical FM discriminator J Lightw Technol vol 10 no 6 pp 787 793 Jun 1992 Norwell MA Fr d ric Grillot M 06 was born in Versailles France on August 22 1974 He received the M Sc degree in physics from the University of Dijon Dijon France in 1999 and the Ph D degree in elec trical engineering from the University of Besancon Besan on France in 2003 His doctoral research activities were conducted within the Optical Com ponent Research Department Alcatel Marcoussis France He studied the effects of the optical feed back in semiconductor lasers and the impact this phenomenon has on optical communication systems for high bite rate transmissions From May 2003 to August 2004 he held a postdoctoral position with the Institut d Electronique Fondamentale University of Paris Sud Paris France where he focused on integrated optics modeling and on Si based passive devices for optical interconnects and telecommunications On September 1 2004 he was appointed to the Institut National des Sciences Appliqu es INSA Rennes France where he is currently Associate Professor within the Materials and Nan otechnologies MNT Department His main research activities are on advanced laser diodes emitting at 1 55 um using new materials like quantum dots for low cost applications Since the beginning of 2008 he is also a Visiting Re search Professor of Electrical and Computer Enginee
13. eat Q deal of interest in the last decade owing to their ex pected remarkable properties arising from charge carrier confinement in three spatial dimensions 1 Low threshold current densities and high material gain 2 3 temperature insensitivity 4 and near zero linewidth enhancement factor a y factor at the lasing wavelength 5 6 have been reported This latter property combined with a high damping factor 7 is of utmost importance because it should increase the tolerance to optical feedback in these devices and may offer potential ad vantages for direct modulation without transmission dispersion penalty Directly modulated QD lasers may hence play a major role in next generation telecommunication links for cooler less and isolator free applications Much effort has been devoted to the GaAs based QD material system for emission in the 1 3 um Manuscript received April 21 2008 revised June 18 2008 F Grillot and L F Lester are with the Center for High Technology Mate rials The University of New Mexico Albuquerque NM 87106 USA e mail fgrillot chtm nm edu luke chtm unm edu B Dagens is with the Institut d Electronique Fondamentale Universite Paris Sud 91405 Orsay France e mail beatrice dagens ief u psud fr J G Provost is with Alcatel Thales II V Lab 91461 Marcoussis Cedex France e mail jean guy provost 3 5lab fr H Su is with Emcore Inc Alhambra CA 91803 USA e mail Hui_Su Em core com Co
14. lor versions of one or more of the figures in this paper are available online at http ieeexplore ieee org Digital Object Identifier 10 1109 JQE 2008 2003 106 band owing to a better material maturity 2 6 allowing the demonstration of temperature insensitive 10Gb s transmission 8 9 Although many breakthroughs have already been demonstrated the maximum modulation bandwidth remains limited to 10 12 GHz for lasers operating in the 1300 1550 nm bands much below the best values reported for quantum well QW lasers At the same time a strong damping of the modu lation response is usually observed in QD devices pointing to the role of the gain compression which physically comes from the redistribution of carriers Only devices exploiting tunnel injection 10 p doping 4 11 gain lever effect 12 13 or injection locking 14 may improve the modulation bandwidth Among the various properties of QD lasers the ay factor is one of the most important and is used to distinguish the behavior of semiconductor lasers with respect to other types of lasers 15 The ay factor influences several fundamental aspects of semiconductor lasers such as the linewidth 16 or the laser behavior under optical feedback 17 In the case of QD lasers several models at the early stages have predicted a near zero ay factor due to the discrete density of states Different groups have reported different values of the ay factor associated with diffe
15. miconductor materials and devices and was a cofounder and Chief Technology Officer of Zia Laser Inc a startup company using quantum dot laser technology to de velop products for communications and computer microprocessor applications He has published 80 journal articles and over 100 conference papers Dr Lester is an active organizer of the IEEE Lasers and Electro Optics So ciety LEOS conferences workshops and journals He was a US Air Force Summer Faculty Fellow in 2006 and 2007 His other awards and honors include the 1998 UNM School of Engineering Research Award the 1994 Martin Mari etta Manager s Award and the 2007 UNM ECE Teaching Award
16. n additional dependence with the injected current Thus taking into account the gain variation at the GS and at the ES the index change at the GS wavelength can be written as follows n Ak Jk 5 k g e where k g e are the indices of summation for GS and ES respectively Equation 5 leads to he n a5 as Ogg QH g 6 g In 6 6g and 6n are the changes of the gain and refractive index at the GS respectively g is the linewidth enhancement factor actually measured in the device ae and ag are the differential gains at the ES and at the GS respectively e describes the GRILLOT et al GAIN COMPRESSION AND ABOVE THRESHOLD LINEWIDTH ENHANCEMENT FACTOR IN 1 3 um InAs GaAs QUANTUM DOT LASERS 949 change of the GS index caused by the ES gain and ag is re lated to the GS index change caused by the GS gain variation When the laser operates above threshold a keeps increasing according to 4 as previously shown for the case of QW de vices Let us note that the differential gain at GS a can also be simply expressed as a function of the gain compression co efficient as well as gmax and gn Indeed it has been shown in 25 that the gain saturation in a QD media can be described by the following equation y Gace f TOCE 7 where N is the carrier density and N is the transparency carrier density When the laser operates above threshold the differen tial gain for the GS lasing is defined as follows
17. newidth of semiconductor lasers IEEE J Quantum Electron vol QE 18 no 2 pp 259 264 Feb 1982 16 H Su L Zhang R Wang T C Newell A L Gray and L F Lester Linewidth study of InAs InGaAs quantum dot distributed feedback quantum dot semiconductor lasers JEEE Photon Technol Lett vol 16 no 10 pp 2206 2208 Oct 2004 17 H Su L Zhang A L Gray R Wang T C Newell K J Malloy and L F Lester High external feedback resistance of laterally loss coupled distributed feedback quantum dot semiconductor lasers IEEE Photon Technol Lett vol 15 no 11 pp 1504 1506 Nov 2004 18 A V Uskov E P O Reilly D McPeake N N Ledentsov D Bim berg and G Huyet Carrier induced refractive index in quantum dot structures due to transitions from discrete quantum dot levels to con tinuum states Appl Phys Lett vol 84 pp 272 274 2004 19 T C Newell D J Bossert A Stintz B Fuchs K J Malloy and L F Lester Gain and linewidth enhancement factor in InAs quantum dot laser diodes IEEE Photon Technol Lett vol 11 no 12 pp 1527 1529 Dec 1999 20 P M Smowton E J Pearce H C Schneider W W Chow and M Hopkinson Filamentation and linewidth enhancement factor in In GaAs quantum dot lasers Appl Phys Lett vol 81 pp 3251 3253 2003 4 5 8 9 GRILLOT et al GAIN COMPRESSION AND ABOVE T
18. nm resolution monochromator and sent in a tunable Mach Zehnder interferometer From separate measurements on opposite slopes of the interferometer transfer function phase and amplitude deviations are extracted against the modulating frequency in the 50 MHz 20 GHz range 28 The LEF is given by the phase to amplitude responses ratio at the highest frequencies in the limits of the device modulation bandwidth Thus a qualitative agreement between simulations and mea surements is obtained As expected the GS ay factor increases with the injected current due to the filling of the excited states as well as carrier filling of the nonlasing states higher lying energy 950 levels such as the wetting layer which results in a differential gain reduction above threshold Although the a y factor is en hanced at lower output powers this increase stays relatively lim ited until the bias current remains lower than 150 mA e g such that as P lt Psat Beyond that compression effects start being significant and the a factor reaches a maximum of 57 at 200 mA before collapsing to negative values As previously men tioned the collapse in the ay factor is attributed to the occur rence of the ES as well as to the complete filling of the available GS states In other words as the ES stimulated emission requires more carriers it affects the carrier density in the GS which is significantly reduced As a result the GS a y factor variations from
19. or of 2 in the laser under study Regarding the a factor a qualita tive analysis has been performed based on an analytical model taking into account the filling both in the GS and in the ES A good agreement with measurements published in the litera ture has been obtained the model reproduces the increase of the ay factor with current the giant value reported close to the transition GS ES as well as the collapse down to negative values after the transition To the best of our knowledge this is the first time that such behaviour is reported in the literature Results also show that the optimization of the ratio 2max 2th is the key point for the realization of state of the art QD devices A higher max imum gain is definitely required for getting a lower ay factor which is really decisive for the realization of chirpless devices and isolator free transmission ACKNOWLEDGMENT The authors would like to acknowledge Prof A Fiore as well as Dr A Markus for providing the structure IEEE JOURNAL OF QUANTUM ELECTRONICS VOL 44 NO 10 OCTOBER 2008 REFERENCES 1 Y Arakawa and H Sakaki Multidimensional quantum well laser and temperature dependence of its threshold current Appl Phys Lett vol 40 pp 939 941 1982 2 D Bimberg N Kirstaedter N N Ledentsov Z I Alferov P S Kop ev and V M Ustinov InGaAs GaAs quantum dot lasers IEEE J Sel Topics Quantum Electron vol 3 no 2 pp 196 205 Apr 19
20. ration by a factor of gmax Jmax gen In Fig 2 the evolution of the normalized gain compression Eseff Es is plotted as a function of the ratio gmax 9th This shows that the higher the ratio gmax gtn the lower the effects of gain compression If gmax gt gt gtn the graph tends to an asymptote such that eseg es 1 On the other hand if Jmax gth gain compression effects are strengthened the ratio increases drastically and can even be extremely large if 948 e gt o Relaxation Frequency GHz A 0 0 0 5 1 0 1 5 2 0 Output Power mW Fig 3 Square of the resonance frequency versus the output power The curve fitting equation is shown in the inset and leads to A 7 5 0 2 GHz mW t and Psat 3 3 0 3 mW not enough gain is provided within the structure gmax 9th As an example for the QD laser under study gmax 9th 2 meaning that the effects of gain compression are doubled causing critical degradation to the laser bandwidth In order to extract the intrinsic properties of this InAs Gas QD laser microwave frequency properties have been investigated In Fig 3 the square of the measured resonance frequency is plotted as function of the output power which is linked to the photon density through the relation P hvyVvgan 5 where hy is the energy per photon V is the cavity volume and av is the energy loss through the mirrors where m is the mirror loss The experimental depen
21. rent techniques for instance a negative value to about 2 has been reported 18 19 On the other hand an ay factor as low as 0 1 has been measured in single stack QD lasers 20 while a minimum of about 1 0 has been observed in a multistack sample 21 It has been shown that the various techniques commonly used to measure the a factor can lead to different values when applied to QD lasers 22 It is well known that the so called linewidth enhancement factor can be written as AT dn dN 4ndn dN _ 4Ur A dGret dN dg dN H 1 where g is the material gain The y factor depends on the ratio of the evolution of the refractive index n with the carrier den sity N to that of the differential gain dg dn I is the optical confinement and Gnet L g a is the net modal gain where a is the internal loss coefficient In most cases the a factor is de tected by using the Hakki Paoli method which relies on direct measurement of the refractive index change and the differen tial gain as the carrier density is varied by slightly changing the current of a semiconductor laser in subthreshold operation This method is applicable only below threshold and does not corre spond to an actual lasing condition A more reliable technique to measure the ay factor is the AM FM method which relies 0018 9197 25 00 2008 IEEE GRILLOT et al GAIN COMPRESSION AND ABOVE THRESHOLD LINEWIDTH ENHANCEMENT FACTOR IN 1 3 um InAs GaAs QUANTUM
22. ributed feedback lasers for 10 Gbit s transmission over 21 km Electron Lett vol 42 pp 1457 1459 2006 B Dagens O Bertran Pardo F Gerschutz J Koeth I Krestnikov A Kovsh O Le Gouezigou and D Make Uncooled directly modu lated quantum dot laser 10 Gb s transmission at 1 3 44m with constant operation parameters presented at the ECOC Cannes France 2006 Postdeadline ECOC Th4 5 7 10 S Gosh P Battacharya Z K Wu T Norris J Singh and B Kochman Quantum dot tunnel injection lasers with large modulation bandwidth at room temperature in Proc 60th Device Res Conf 2002 pp 137 138 11 Z Mi and P Battacharya DC and dynamic characteristics of P doped and tunnel injection 1 65 um InAs quantum dash lasers grown on InP 001 IEEE J Quantum Electron vol 42 no 12 pp 1224 1232 Dec 2006 12 N A Naderi Y Li C Dziak Y C Xin V Kovanis and L F Lester Quantum dot gain lever laser diode in Proc 20th IEEE LEOS An nual Meeting Montreal QC Canada 2006 pp 52 53 13 Y Li N A Naderi Y C Xin C Dziak and L F Lester Multi section gain lever quantum dot lasers in Proc SPIE 6468 2007 vol 646819 14 Y Li N A Naderi V Kovanis and L F Lester Modulation response of an injection locked 1550 nm quantum dash semiconductor laser in Proc 20th IEEE LEOS Annual Meeting 2007 pp 498 499 15 C H Henry Theory of the li
23. ring with the University of New Mexico Albuquerque where he is leading research in optical science and optoelectronics at the Center for High Technology Materials CHTM Dr Grillot is a member of the IEEE Lasers and Electro Optics Society and also la Soci t Francaise d Optique B atrice Dagens received the M S degree in physics and chemistry from ESPCI Paris France in 1992 and the Ph D degree in optoelectronics from the University Paul Sabatier Toulouse France in 1995 She joined the Optical Component Research Department Alcatel Mar coussis France in 1996 where she was first responsible for the design realization and measurement of SOA based interferometers for all optical and high bit rate wavelength conversion and regeneration Then her activity was focused on advanced laser diodes emitting at 1 3 and 1 55 pm using new materials like quantum dots dilute nitride based active layers and metallic ferromagnetic layers Since the end of 2007 she has been a Senior Researcher with Institut d Electronique Fondamentale Orsay France Her current research includes magneto optical magneto photonic and plasmonic nanostructured waveguides for compact integrated photonic circuits She has authored and coauthored more than 120 international publications and communications and 12 patents Jean Guy Provost received the Ph D degree from Ecole Nationale Sup rieure des T l communication Paris France in 1989 In 1989 he
24. sion is 13 mA and the external differential efficiency is about 0 02 W A The GS and ES transitions emit respectively at 1290 and 1210 nm 23 Let us note that the ES lasing emission occurs for a threshold current equal to 220 mA at room temperature The QD size distribution as well as the Fabry Perot cavity leads to a widely multimode emission as shown in 23 HI EVALUATION OF GAIN COMPRESSION Measuring the frequency response as a function of the output power is a common method to evaluate gain compression in semiconductor lasers In the case of the QD laser it has been shown that effects of gain compression are more important than those measured on quantum well devices 24 25 In order to explain this phenomenon a modified nonlinear gain coefficient has been introduced leading to a new expression for the relax ation frequency under strong gain saturation such as 24 pe Vga Ugao S i ame a e 2 AT Tp 1 EsS 4n 7 14 Eses A where v is the group velocity a is the differential gain ao is the differential gain at threshold unsaturated value S is the photon density Tp is the photon lifetime s is the gain compression factor related to the photon density and seg is the effective gain compression factor defined as follows 1 ESeff CST tin 3 i Jmax where gp is the gain at threshold and gmax 1s the maximum gain for GS lasing Equation 3 indicates that the gain compression is enhanced due to gain satu
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