(MMI) Devices
Contents
1. m seen eee px poe pay e A t eee eee ee be ee ee ee bee ee ee seem eee ew be eee dun dl La Lao dem du dl dem mm ee eee ee ee eee eee ee dm de ee ee ee dem eee ee Soe Sb Sr Ep S207 uopasu ee ee Se E ZA ZA E EE E A G PE i sat Se er at ALS th yin im tm iy mh i a E mm mn mm Di Eee SEG 55 SG i tt EE ER na gJ Port 1 Mode 1 to Port 3 Made 1 5 Part 1 Mode 1 to Port 4 Mode 1 Er iD zc G a p t tt om O p cL EE y ip con nau G 0 q T p 55 p cL PE ue Figure 14 The insertion losses with function of MMI width MMI APN APSS Page 25 of 26 O Apollo Inc MMI DEVICE In this section the design procedure starting from material to device has been illustrated By using flexible simulation and scan function it is convenient to do the sensitivity analysis of the MMI device related to length polarization wavelength dependence port width effect MMI width and MMI pitch 5 Conclusion As demonstrated with a practical example APSS offers designers a feasible and efficient way to design and simulate an MMI device This can be accomplished by taking advantage of the knowledge based pre defined model in the APSS Device Module to create an effective functional design The theory and operational principle of the MMI device have been described Finally th2. 111 Use a tapered shape and tapered ports in the final design Compared with the rectangular shaped MMI device the tapered MMI device can improve the transverse bandwidth while keep the uniform output and loss insertion loss due to the length reduction and mode mixing in the tapered MMI area iv Fine tune the MMI device by using the scan function and dense mesh setting in the device simulations In general the user should finish the material and waveguide design using the Material Module and the Waveguide Module before starting to design an MMI device in the Device Module Although there is no bend in the MMI device you can easily build any complicated MMI device out of its subcomponents for example star coupler and connectors for example S bend in the Circuit Module of the APSS For more information about how to build complicated MMI devices in the Circuit Module please refer to APSS User Manual 3 2 Power splitter To design a power splitter 1xN symmetrical self imaging D 0 should be used to obtain the required uniform output According to Eq 1 the length of the 1XN MMI power splitter is given by L LYN The output field for each output port p p 1 2 N are described as follows 3 E D Tonia e jp VU p Eq 10 O Apollo Inc Page 10 of 26 APN APSS MMI MMI DEVICE with the output positions D W 2 W N p 1 2 3 3 Power coupler MMI devices are often used as uniform couplers which can be
3. Figure 3 The pre defined wizard of the MMI device After the device 1s defined in detail the user can then perform a simulation and scan for related variables There are many choices for the device solver settings that can be used for the simulation and analysis For example the user can select a 2 D or 3 D analytical or numerical solver with or without reflection In general for the strongly guided MMI device an analytical solver that considers reflection is sufficient for most applications For the weakly guided MMI device a numerical solver that does not consider reflection is sufficient For some specific waveguides such as silica on insulator SOI and anti Apollo Inc Page 14 of 26 APN APSS MMI MMI DEVICE reflection resonant optical waveguide ARROW the 3D simulation is recommended However in the user defined model only numerical solvers can be used Finally the user can display the simulation results to view the different performance parameters such as insertion loss phase difference and crosstalk The user can also export them in different formats such as ASCII text txt Microsoft Excel xls or as a bitmap bmp file The layout mask files can be exported in two different file formats EXF and GDSII 4 EXAMPLE This section provides an overview example of how to simulate and design an MMI device with desired properties 4 1 Material and waveguide Design As mentioned earlier general the us
4. APSS Apollo Application Note on Multi Mode Interference MMI Devices Design simulation and layout APN APSS MMI Apollo Inc 1057 Main Street West Hamilton Ontario L8S 1B7 Canada Tel 905 524 3030 Fax 905 524 3050 www apollophotonics com MMI DEVICE Disclaimer In no event should Apollo Inc its employees its contractors or the authors of this documentation be liable to you for general special direct indirect incidental or consequential damages losses costs charges claims demands or claim for lost profits fees or expenses of any nature or kind Document Revision July 2 2003 Copyright 2003 Apollo Inc All right reserved No part of this document may be reproduced modified or redistributed in any form or by whatever means without prior written approval of Apollo Inc Apollo Inc Page 2 of 26 APN APSS MMI MMI DEVICE Abstract This application note provides an overview and an example of how to design simulate and optimize multi mode interference MMI devices using a pre defined model in the Device Module of the Apollo Photonics Solution Suite APSS This application note describes the operation principle basic design consideration and performance parameters for MMI devices presents the basic design process for MMI based devices based on analytical and numerical methods discusses key issues related to MMI based devices such as power splitters power couplers
5. i 0 1 2 3 N where N is the number of guided modes of multi modes in the MMI area are given in the paraxial approximation by 1 i i 2 7 bo pe i 3L where Lz is defined as the beat length or coupling length between the fundamental Eq I mode i 0 and the first order mode 7 1 f IT _ 4n W i Do Bi 34 where is the free space wavelength and W is the effective width of the MMI area W Ww A eye Sn n Eq 3 IT n r Eq 2 where W is the physical width of the MMI area n and n are the effective core index and effective cladding index respectively and integer o 0 for TE modes and o 1 for TM modes According to the guided mode propagation analysis 1 three different self image phenomena can be observed 1 IxN symmetrical self imaging The coefficients of odd modes are zero when the MMI area is fed by a single central port D 0 According to Eq 1 the self imaging distance and N fold image distance are L and LYN Apollo Ine Page60f26 APN APSS MMI MMI DEVICE 11 2xN restricted self imaging The coefficients of 2nd 5th 8th etc 1s zero when the MMI area is fed by one or two input ports at D tW 6 According to Eq 1 the self imaging distance the mirror image distance and N fold image distance are 2Ln Lr and L N respectively 111 MxN general self imaging The coefficients of modes are non zero when the MMI area is fed by one or M input ports at the arbitrary
6. and respectively The beat length ratio of the MMI coupler 1s expressed R Ly a Ly g2 P g p AA Eq 18 where we find that the beat length ratio of the MMI coupler is mainly determined by the wavelength ratio For instance the 1300 1550nm demultiplexer the beat length ratio R is approximately 1 2 4 The possible combination of p and g for the minimum length L is that p 4 or 5 and g 1 The exact beat length ratio R 1 20 is obtained to adjust the width of the MMI coupler 3 6 Simulation and optimization This section provides an overview of the simulation and optimization process for the design of an MMI device Depending on the complexity of the MMI device you can build it in two different ways using the APSS Device Module using a pre defined model or a user defined model In general the pre defined model is powerful enough to cover most MMI devices Only if the designer has special requirements such as index modulation then the user defined model should be used to build the MMI device In the user defined model the MMI device is constructed using different shapes and ports In the pre defined model APSS provides a device wizard to construct the MMI device After loading the waveguide information and selecting the Device type as Multi Mode Interference the wizard will ask you to enter some information related to the device ports and MMI area or MMI shape as shown in Figure 3 The wizard provides many
7. o When the simulation is complete the user can view the S parameters and EM fields at the positions defined in the Section Position by clicking the E or button Figure 11 and Figure 12 show the X Z field and X Y field of the 3D X polarization E field respectively Figure 13 and Figure 14 show the insertion losses with function of wavelength and MMI width respectively These simulation results are in accord with the experimental results 2 Apollo Inc Page 24 of 26 APN APSS MMI MMI DEVICE HOTONICS D 4 gE J ee 4 h BE dl 1 I 1 I I I I I 4 I I I I I I I E I I 1 I I I I I 1 I I I I I 4 I b 1 I custodita clean r La Cho Sb St Bp 207 uaniesu Wavelength um i ga e mo 1 e LL ea Tm i ga e era 1 e LL Tm i ga e t e LL m Tm J T e aem 1 e LL X i ga e my p e LL a f mn i ga e e LL X Y Port 1 Mode 1 to Port 4 Mode 1 Figure 13 The insertion losses with function of wavelength C i p T E q See GE GLE Ik I 5 I I I I I I I L I I I I I I I L I I I I I I I I r I I I I I I I r I I I I I I I E I I I I I I I
8. um ane ur Figure 6 The modal profile E of the ridge waveguide MMI APN APSS Page 17 of 26 O Apollo Inc MMI DEVICE 4 2 Creation of predefined device The design parameters are taken from 2 to build a 2x2 3 dB coupler MMI width W 18 um port width w 3um and MMI length L 530um After loading the waveguide project and selecting a predefined MMI as shown in Figure 3 with M N 2 number of input and output ports and asymmetrical at the port position we create a device project D _MMI2x2 as shown in Figure 7 ee 0 00 275 00 550 00 0 00 Y 10 50 21 60 Y 16 39 548 69 Object D_MMI_2x2 Geometry Materials W Auto Refresh Refresh Mame Variable Expression Comment Length of left ports L1 10 0000 OK L1 OK 530 0000 OK width of coupler w 18 0000 OK 3 0000 m OK Port pitch w 3 OK Min D 5 L1 2 OK Min 0 5 LA OK Min 0 5 LM OK Min 0 5 L2 2 OK wT 00 10 m OK Figure 7 The 2x2 device project for the 2x2 MMI 3dB coupler Apollo Inc Page 18 of 26 APN APSS MMI MMI DEVICE 4 3 Solver settings of predefined device After the creation of the MMI 2x2 coupler the user must select the appropriate solver setting for the simulation by clicking the button Figure 8 shows the Device Solver Setting window which has three tabs General Information Solver Selection and Variable Sele
9. be used as a coarse wavelength multiplexer demultiplexer MUX DeMUX as shown in Figure 2 Although the MMI device has a relatively large optical bandwidth it still can be used to realize two wavelength multiplexing in two wavelength bands 25 i e 1 3 um 1 55 um or 0 98um 1 55um The MMI coupler operates as a cross bar coupler in wavelength a bar cross coupler in wavelength In general the 1x2 MMI device should be based on restricted and general self imaging A a Restricted MMI coupler b General MMI coupler Figure 2 A schematic view of the 1x2 MMI wavelength multiplexer According to the above mentioned MMI self imaging theory an input field in the MMI device can be reproduced along the MMI coupler at certain periodic intervals 2pkL bar state direct image and 2p J kL cross state mirror image respectively In other words because an MMI device can operate as a bar coupler for one wavelength and a cross coupler for the other wavelength it can perform the signal separation between two wavelengths and A gt Therefore the total length of the MMI device meets the following equation L pkL 4 p q kLr 22 Eq 17 where integer p is a positive integer natural number integer q is an odd integer and integer is 3 for the general coupler and 1 for the restricted coupler L and Lz 20 are O Apollo Inc Page 12 of 26 APN APSS MMI MMI DEVICE the beat lengths of the MMI coupler at the wavelength
10. position W 2 lt D lt W 2 According to Eq 1 the self imaging distance the mirror image distance and N fold image distance are 6L 3L and 3L N respectively Therefore the input field profile can be reproduced in single or multiple images at periodic intervals along the propagation direction of the guide As can be seen in the above discussion for the same width or beat length the MMI device based on symmetrical self imaging is four times shorter than one based on general self imaging and the MMI device based on restricted self imaging is three time shorter than one based on general self imaging 2 2 Basic design considerations After understanding the operation principle of MMI devices depending on different materials such as silica or InP and design requirements such as splitter coupler or mode converter it 1s possible to apply some related analytical and numerical solvers to design MMI based devices From the above analysis we know that the MMI device that is based on symmetrical self imaging is the shortest one and shorter devices have better tolerance For this reason the device should generally be designed to be as short as possible However the final device configuration will be determined by device functions material systems and even fabrication technologies For example for the power splitter in which the phase of the output is not important the MMI device based on symmetrical self imaging could be use
11. ance including width tolerance W W length tolerance L L and wavelength tolerance 4 A which are given by 2 as 31W _SIL _6ln _ 612 Eq 7 W L n where the width tolerance W W is calculated by 2 Red lt Z L Eq 8 W SW where d is the mode width of the input port and Z L is a function depending on the excess Le which is expressed as Z L 4 57 4577 167 16 87 Eq 9 where L dB 10log T As shown in Eq 7 fabrication tolerances such as the device width variations OW W are inversely proportional to the coupler length L For the restricted 2x2 MMI 3dB coupler on InP index n 3 44 at 1 55 um where length L L 2 if W 12 d 3m and the length L 213um the result is 0W 0 08um dL 2 89 um and dA 2 1 nm for 0 5 dB excess loss Obviously the wavelength tolerance dW represents the most critical value Note that tapered input and output ports of the MMI devices relax the wavelength tolerance Apollo Inc Page 9 of 26 APN APSS MMI MMI DEVICE 3 Design and simulation 3 1 Overall design This section introduces a general design procedure for creating an MMI device According to related design experiences the following process should be used 1 Decide the type of the self imaging required according to the materials and device function 11 Use a sample rectangular shaped MMI to check device performance using analytic solvers and to discover possible sizes for the device
12. and wavelength multiplexers outlines design steps specific to the design of MMI based devices such as import projects solver settings and display of simulation results provides a typical example and simulation results which can then be compared with published papers The APSS application consists of four different modules Material Waveguide Device and Circuit Because each module specializes in different specific design tasks APSS can handle almost any kind of device made from almost any kind of material Keywords APSS device module multi mode interference MMI device power splitter coupler switch multiplexer excess loss crosstalk strongly and weakly guided waveguides analytical method numerical method Apollo Inc Page 3 of 26 APN APSS MMI MMI DEVICE Table of Contents 1 INTRODUCTION i 3525989249080082589 0 55493 520 0099 49 8 59009309 9990200 04980259 998929500090 90 29902 5 ZEE 01 6 REC RR EE IRINA 5 2 1 OPERATION PRINCIPLE cceccececccececcecescececcececeececescecuscececescecssecesescucuscecesceceees 5 2 2 BASIC DESIGN CONSIDERATIONS cccccccececececcecececcscecececescecececesestecesucesescececeseecs 7 2 3 PERFORMANCE PARAMETERS cceccccececcecescececcecccececcececescecestscessscecescecsceceseeceees 8 3 DESIGN AND SIMULATION 2 2 2 266552 2220055 974529522565 949022 40656972930 525 205 0436693672 10 3 1 OVERALEI DESIGN rinite 10 3 2 POWER SPLITTER ccccceccececcececcececc
13. ccececcecesesceceececeececstscustecscescecessscusescesuseecacees 10 3 3 POWER COOPER ea 11 3 4 NON UNIFORM POWER SPLITTER oerornevernenernenennenennnnennnnennnnenennenennenennnnennnnenennene 11 3 5 WAVELENGTH MULTIPLEXER ccceccccecccceccccececcececcececcececeececescecstscusescesescecacees 12 3 6 SIMULATION AND OPTIMIZATION cccecceccececceccecescecceccecesceccecescessscesceseecesceseces 13 2 FN OPER hd 15 4 1 MATERIAL AND WAVEGUIDE DESIGN cccccoccececcececcececcsceccececescecucesceseccecesees 15 42 CREATION OF PREDEFINED DEVICE cerci rire cirie cirie cirie cirie rei e cinici ie 18 4 3 SOLVER SETTINGS OF PREDEFINED DEVICE reranernrnenennvnvnenennnnrnenennnnnnenenennnnnnenenee 19 4 4 RUN AND DISPLAY EGG 21 5 CON CUSTI N a E A AE 26 6 REFRENG 26 Apollo Inc Page 4 of 26 APN APSS MMI MMI DEVICE 1 Introduction Multi mode interference MMI devices have been extensively studied and are of considerable interest as key optical components in photonic integrated circuits PICS The principle of the MMI devices is based on destructive constructive interferences occurring in the MMI area with a large number of multi modes Because of its unique properties such as low insertion loss large optical bandwidths compactness polarization insensitivity low crosstalk and excellent fabrication tolerances the MMI device has many potential applications such as couplers splitters combiners mode converters fil
14. ct Field the Import Port Wavelength and exit point Mode number or User defined must be selected in the Input Selection area of the tab These parameters define the 2 D slice view of the EM fields that will be used for dynamic showing and for file saving in the Section Position area of the Apollo Inc Page 20 of 26 APN APSS MMI MMI DEVICE window as shown in Figure 9 Note that those positions also can be used to view the index distribution in the mesh setting part of the corresponding solvers fa Section Position Editor Y H6 2 Ma v Display Position Z Display Position Display Position v Close 4 Help Figure 9 The Section Position setting for the 2x2 MMI 3dB coupler On the Device Solver Setting tab the user must select appropriate variables for the variable scan The user can also do a Structure Check for selecting scan parameters In the current version of the APSS application the maximum number of variables for the variable scan is two 4 4 Run and Display After selecting the solver settings the user can simulate the S parameters and fields of the device by clicking Run button For example if you select Field Port 1 Mode 1 1 5um 3D Numerical X Y Dynamic Showing Y Z and 1 05 the Apollo Inc Page 21 of 26 APN APSS MMI MMI DEVICE dynamic showing window as shown in Figure 10 will appea
15. ction On the General Information tab the user can select appropriate Polarization check Port Information Based on Effective Index Values and Single Mode Width and view all related port mode profiles by clicking View Mode Profile The Solver Selection tab allows the user to specify for the Output Selection S parameter and Field as shown in Figure 8 If the user selects S parameter the user must then select the appropriate solvers either analytical or numerical depending on accuracy requirements and time constraints Table 1 shows possible solvers for simulation of the 2x2 MMI 3dB coupler Apollo Inc Page 19 of 26 APN APSS MMI MMI DEVICE Ei Device Solver Setting General Information Solver Selection Variable Selection Uutput Selection 5 Parameter f Field Reflection Input Selection Import Port Porti F Folarization Eoupling Mode Mode1 UserDetine Wave Function ee KE ii Wavelength 158 Solver Dimensio Solver Typ fr 3D f Mur 52 Section Fosition v Dynamic Showing Plane rz Position 1 05 Fjeld Ex Hun Close ax Help Figure 8 The device solver setting for the 2x2 MMI 3dB coupler Table 1 Possible solvers for simulation of the 2x2 MMI 3dB coupler Solver type Solver type Analytical Analytical 2D BPM 2D BPM FDTD Yes 3D BPM 3D BPM FDTD Yes As shown in Figure 8 when you sele
16. d To build a 3dB coupler in which the phase difference between the outputs is 7 2 the MMI device based on restricted or even general self imaging could be used To build a wavelength multiplexer in which the mirror image is used the MMI device based on O Apollo Inc Page 7 of 26 APN APSS MMI MMI DEVICE restricted or even general self imaging should be used because the one based on symmetrical self imaging does not have a mirror image The minimum gap size that 1s the difference between the pitch and the port width is determined by material systems and fabrication technologies Generally the gap size of the MMI device based on general self imaging is larger than the one for an MMI device based on restricted self imaging The insertion loss and bandwidth of the MMI device can also be improved by increasing the port width However a wider port may support high order modes High order modes of input ports cannot be imaged properly for symmetrical and restricted self imaging because it does not satisfy image conditions Eq 1 Eq 3 Tapered ports can be used to avoid this shortcoming According to Eq 2 the length of the MMI device is mainly determined by the effective width of the device If we make the MMI shaped like a butterfly the effective width of the device can be decreased and the length of the MMI device can be shortened MMI devices are generally easy to design and are compatible with both strongly guided and weakly gui
17. ded structures Depending on the required accuracy and available simulation time there are several analytical and numerical solvers that can be used in APSS some of which consider reflection In general for the strongly guided MMI device an analytical solver that considers reflection is sufficient for most applications For the weakly guided MMI device a numerical solver that does not consider reflection is sufficient 2 3 Performance parameters Except some commonly used performance parameters such as insertion loss L dB and return loss L dB this section will discuss performance parameters more specifically related to MMI based devices The excess loss L dB of the device is defined by the difference between the sum of the powers exciting the outputs and the power entering the devices L dB 1010g o XP Fn Eq 4 J Apollo Inc Page 8 of 26 APN APSS MMI MMI DEVICE As a coupler two performance parameters the crosstalk and power imbalance should be evaluated The crosstalk L dB is a ratio of the desired power output P4 to unwanted outputs P and the power imbalance L dB is a ratio between two the desired outputs L dB 10log 9 P B Eq 5 Ly dB 10logio i Faz Eq 6 where the crosstalk and the power imbalance of the coupler is also evaluated by the extinction ratio or contrast and the coupling ratio respectively One of the most critical issues in designing MMI devices is the design toler
18. e design process has been outlined and the simulation results agree well with experimental results 6 References 1 L B Soldano and C M Pennings Optical multimode interference devices based on self imaging principles and applications J Lightwave Technol vol 13 no 4 pp 615 627 April 1995 2 P A Besses M Bachmann H Melchior L B Soldano and M K Smit Optical bandwidth and fabrication tolerances of multimode interference couplers J Lightwave Technol vol 12 no 6 pp 1004 1009 June 1994 3 M Bachmann P A Besses and H Melchior Overlapping image multimode interference couplers with a reduced number of self images for uniform and nonuniform power splittering Appl Opt vol 34 no 30 pp 6898 6910 Oct 1995 4 K C Lin and W Y Lee Guided wave 1 3 1 55 um wavelength division multiplexer based on multimode interference Electronics Lett vol 32 no 14 pp 1259 1261 July 1996 Apollo Inc Page 26 of 26 APN APSS MMI
19. er should finish the material and waveguide design using the Material Module and the Waveguide Module before starting to design an AWG device in the Device Module In the Material Module there are two pre defined material systems InP and silica There are five pre defined waveguides ridge channel ridge channel buried channel and multi step ridge in the Waveguide Module These cover most applications but APSS also provides a user defined model to accommodate special or more complicated requirements The user can simulate and design according to the performance parameters such as single mode condition effective index dispersion effective area spot size bending loss confinement loss In this section for the sake of simplicity and to compare the simulation results with a published paper the structure provided in 2 is used as our material and waveguide design The first step is to create a material project M InGaAsP lambda 1 25 with two materials for wavelength range of 1 4 1 7 um One 1s InP index 3 190 from to 3 154 and another one is InGaAsP Bandgap 1 25um index 3 375 from to 3 353 After Apollo Inc Page 15 of 26 APN APSS MMI ae AUS MMI DEVICE loading the material project by selecting a predefined Ridge with N number of layers we create a waveguide project W Ridge MMI as shown in Figure 4 Note that the waveguide project was built using a half structure because APSS ca
20. n take advantage of the geometric symmetry However the whole structure is needed to simulate performance parameters related to the waveguide bend x 162 Y 3 87 Object Substrate Geometry Materials vw Auto Refresh Refresh Mame Variable Expression Comment JA Ridge width 3 0000 al DE 5 0000 oof OK 1 5000 wt OK 30 0000 g OK 0 0000 y DK 2 0000 off OK 1 5000 wt OK 0 6000 g OK 2 0000 eM DK Figure 4 The ridge waveguide project for the MMI device In order to achieve accurate results the mesh boundaries must be coincident with the dielectric boundaries and similar size in both directions To accomplish this use the multi section mesh I button The calculated dispersion curves for both X and Y polarizations and the modal profile E for the X polarization are shown in Figure 5 and Figure 6 respectively O Apollo Inc Page 16 of 26 APN APSS MMI m O gt m A gt gt PEE 1 I 1 1 I 1 1 I 1 T 1 I 1 I 1 I 1 L I 1 I 1 I 1 T I I 1 I L 1 I 1 CEE Pr E S Loan nn ln La dn La m rrr R ax EE gc de e PSY sapu SAJPSPI Wavelength um amp Model Mode 1 Figure 5 The effective index of the ridge waveguide Y urn 0 08 Optical Field un x Value Y uim Y um 0 08 tum 0 3439 Value 13 6769749793757 0 3495 amp
21. possible combinations for the following parameters e ports for example port width port position port pitch and port type but does not allow specifying the number of ports and port default width e shape for example shape type function and taper type e array waveguides for example shape type width and pitch O Apollo Inc Page 13 of 26 APN APSS MMI MMI DEVICE There are two major types of MMI devices regular rectangular shape and taper function shape The ports and MMI shape can have the following tapers rectangular 99 66 99 66 99 66 linear sine cosine parabolic or user defined Note For more information about building an MMI device or the definition of taper functions please refer to APSS manual Also note more compact and low loss MMI devices can be built and simulated more easily by incorporating the pre defined star coupler device available in the Device Module of the APSS MMI Selection Por Position Port Type Number of ports Lett Right sh s Ports Default Width Symmetrical Rectangular Asymmetrical Linear Arbitrary Cosine f Equal Right Left equal Pitch f Equal C Right Left equal Parabolic C UserDefined C Unequal C Unequal Function Taper Type Linear Cosine C Triangle C Sine C Parabolic C User defined f Symmetrical C Arbitrary Partial taper
22. r You can cancel pause or resume during the simulation period ED mmI 242 EN ao Target 3D X Polanzation Semi vector Field Ex Elapsed time 00 04 41 0 00 274 50 549 00 H Resume 0 00 0 00 n Pause 10 80 10 80 a Cancel 21 60 21 60 0 00 274 50 545 00 W Display Dynamic showing Panel Progress Bars Figure 10 The dynamic showing for 3D X polarization BPM solver Apollo Inc Page 22 of 26 APN APSS MMI MMI DEVICE Ei Result amp Post Processing Field Parameters Folarization x i Plane type Fjeld Ex Section position 10 8 Polarization Coupling Show Solver 3D BPM Wavelength 1 550000 Date 7 3 2003 Z um 437 3 50 100 150 200 250 300 350 400 450 500 Z CUm z um 437 3 amp Cum 0 2082 Value 5 6306267 X urn 0 2082 Value Value 50 100 150 200 250 300 350 400 450 500 umm Close m Help Figure 11 The X Z field display at Y 10 8 um for 3D X polarization Ex field AX Axis um 4 B 10 12 14 16 18 20 Y Axis um a Z 5um O Apollo Inc Page 23 of 26 APN APSS MMI MMI DEVICE Solver 30 BPM Wavelength 1 550000 Date 7 3 2003 Cum 10 12 14 16 19 20 um b Z 275um Solver 3D BPM Wavelength 1 550000 Date 7 3 2003 c r2 Ta ca um 2 4 B B 10 12 14 16 15 20 Y um c Z 545um Figure 12 The X Y field display at different Z positions for 3D X polarization Ex field
23. realized by using 2xN restricted self imaging According to Eq 1 the length of the 2xN MMI power coupler is given by L L N The output field for each output port p p 1 2 N are described as follows 3 exp jd j 8N 1 3p 2N 2 3p podd E Dp a Eq 11 N expl j i BN 6N 4 3p 2N 4 3p peven with the following output positions W 2 WIN p 1 3 podd vada Po W 2 W N p 2 3 peven p 3 4 Non uniform power splitter In some cases the MMI device may be designed to function as a non uniform splitter which can be realized by using NxN general self imaging According to Eq 1 the length of the NxN MMI power coupler is given by L 3L7N Note that there are many combinations of power splitting ratios for the different N input and N output positions For instance if we set the N input and N output positions to meet the following conditions DI W 2 pWIN Eq 13 D W 2 iW N Eq 14 where p 0 I 2 N 1 N and i 0 1 2 N 1 N with p i even the output field for each output port i from the input port p is described as follows 3 expLj y p 2 ji jb for cos N i p b gt E y AN 2 2 2N 2 Ea 15 EN q EL I no A pio Z P 4N J 2 J 5 J PN 2 with the following output intensities O Apollo Inc Page 11 of 26 APN APSS MMI MMI DEVICE 3 4 9 v x T r pi cos CN i p b Ea 16 pi N Pi d q 3 5 Wavelength multiplexer A 1x2 MMI device can
24. ters and routers 1 They can also be easily fabricated in more complex PICs such as ring lasers optical modulators MZI Mach Zehnder interferometer switches dense wavelength multiplexers and wavelength converters 2 Theory In this section the operation principle of the MMI devices is described Basic design considerations and performance parameters for MMI based devices are also provided 2 1 Operation principle The operation principle of the MMI device is based on self imaging which is a property of multimode waveguides For sake of simplicity the simple 1x1 rectangular shape MMI device as shown in Figure 1 is used to illustrate the operation principle The MMI device generally consists of three parts input ports or left ports a MMI area output ports or right ports The typical practical MMI device is usually an M input and N output device with tapered functions There are three kinds of MMI devices which allow different interferences Note For more information about the detailed categories and basic solver setting of the MMI devices please refer to the MMI pre defined model in the Device Module section of APSS manual Apollo Inc Page 5 of 26 APN APSS MMI MMI DEVICE Figure 1 Schematic diagram of a MMI device Here the guided mode propagation method MPA one of the analytical methods is used to illustrate the self imaging effect in the MMI device In this approach the propagation constants
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