本論文的重點在於設計和分析以多模干涉效應為基礎之各式光被動元件，可分三個方面來探討：
在1.3/1.55um波長解多工器方面，使用磷化銦為基底材料，為了縮短元件長度，我們在多模干涉結構裡面放置一個週期漸變光柵。模擬結果顯示，在波長1.55um處的插入損耗為0.8dB，且隔離度為26dB，另外針對1.3um波長的插入損耗為0.03dB，而隔離度為41dB。
在耦合器方面，使用二氧化矽波導材料，藉由巧妙改變多模波導中部分區域的折射率，可以縮短N-點自我成像的間距，因此能發展新型的1XN雙波段分光器。接著，透過馬赫任德干涉的架構就可以實現1.3/1.55-um雙波段2X2光開關。此光開關共存在16種切換狀態，模擬結果顯示此光開關的插入損耗可低於0.43dB，而串音可大於27.4dB。
在四通道寬間隔波長分波解多工器方面，使用矽上絕緣體波導材料，結合了週期性區塊波導和新型任意比例多模干涉分光器的優點。它的通道間隔為24.5nm，並具有小於2.3dB的低插入損耗和高於18dB的串音。1dB的帶通頻寬為18nm，18dB的截止頻寬為12nm，所以即使雷射光源的中心波長漂移+/-6nm，還是可以正常工作。
這些元件都能應用於波長分波多工的網路中，符合低價化、體積小及易於整合的需求。

The subject of this thesis is on the design and analysis of multimode interference (MMI) based optical passive devices for wavelength-division-multiplexing (WDM) networks.
We propose a novel 1.3/1.55-um wavelength demultiplexer on the InP material system. A chirp grating is placed inside an MMI structure to shorten the device length and increase wavelength tolerance. Simulation results show that a demultiplexer with insertion losses of 0.8 dB and 0.03dB and isolation ratios of 26 dB and 41dB can be obtained at 1.55- and 1.3-um wavelengths, respectively.
An approach that can reduce the N-fold self-images interval of the MMI waveguide is presented. By placing partial index-modulation regions in a multimode waveguide, a paired-interference mechanism and a symmetric-interference mechanism will exist simultaneously. We provide a simple design principle to shorten the device length. As an example, a novel 1N dual-band optical power splitter on the silica waveguide is designed. The coupling characteristics have good tolerance on the device length and wavelength variation. We also propose a novel 1.3/1.55-um dual-band optical 2X2 switch with sixteen switching states. It consists of a Mach-Zehnder interferometer (MZI) with two dual-band 3-dB MMI couplers. The switch can have insertion loss less than 0.43dB and crosstalk larger than 27.4dB.
A 1X4 coarse wavelength division multiplexing (CWDM) demultiplexer is designed on the silicon-on-insulator (SOI) waveguide using the MZI configuration with periodically segmented waveguide (PSW) arms and novel MMI/PSW couplers. The channel spacing of the demultiplexer is chosen to be 24.5nm for applications to 10Gbps ethernet. The simulation results show that the wide-passband demultiplexer can have insertion loss less than 2.3dB and crosstalk larger than 18dB. A 1dB bandwidth of 18nm was obtained to provide good tolerance on wavelength variation.

第一章 簡介-------------------------------------------------------------------- 1
1-1 前言---------------------------------------------------------------------- 1
1-2 平面波導電路---------------------------------------------------------- 2
1-3多模干涉元件的背景理論-------------------------------------------- 3
1-3-1簡介------------------------------------------------------------------ 3
1-3-2 自我成像原理----------------------------------------------------- 3
1-3-3 一般型干涉-------------------------------------------------------- 7
1-3-4 限制型干涉------------------------------------------------------- 10
1-4 研究動機--------------------------------------------------------------- 12
第二章 1.3/1.55m波長分波解多工器------------------------------------ 14
2-1 簡介--------------------------------------------------------------------- 14
2-2 傳統MMI解多工器設計--------------------------------------------- 15
2-3 新型光柵輔助式MMI解多工器設計------------------------------ 16
2-4分析與討論-------------------------------------------------------------- 18
第三章 利用多模干涉技術研發雙波段1N分光器------------------- 26
3-1 簡介--------------------------------------------------------------------- 26
3-2 設計原理和需要條件------------------------------------------------ 28
3-3 1N雙波段MMI分光器的設計範例----------------------------- 38
3-3-1 1.3/1.55-m雙波段12分光器------------------------------- 40
3-3-2 1.3/1.55-m雙波段13分光器------------------------------- 45
3-3-3 1.3/1.55-m雙波段14分光器------------------------------- 49
第四章 新型1.3/1.55-m雙波段22光開關--------------------------- 52
4-1 簡介--------------------------------------------------------------------- 52
4-2 操作原理和結果------------------------------------------------------ 53
第五章 四通道寬間隔波長分波解多工器-------------------------------- 60
5-1 簡介--------------------------------------------------------------------- 60
5-2 寬間隔寬帶通之波長分波解多工器的設計--------------------- 61
第六章 結論與未來發展----------------------------------------------------- 76
參考文獻------------------------------------------------------------------------ 79

[1] Y. Akahori, T. Ohyama, T. Yamada, K. Katoh, T. Ito, “High-speed photoreceivers using solder bumps and microstrip lines formed on a silicon optical bench,” IEEE Photon. Technol. Lett., vol. 11, pp. 454-456, 1999.
[2] T. W. Ang, G. T. Reed, A. Vonsovici, A. G. R. Evans, and P. R. Routley, “0.15 dB/cm loss in unibond SOI waveguides,” Electron. Lett., vol. 35, pp. 977-978, 1999.
[3] H. Ou, “Different index contrast silica-on-silicon waveguides by PECVD,” Electron. Lett., vol. 39, pp. 212-213, 2003.
[4] A. Yariv, Introduction to Optical Electronics, 2nd ed. New York Holt, Rinehart and Winston, 1976.
[5] S. L. Lee, D. S. L. Mui, and L. A. Coldren, “Explicit formulas of normalized radiation modes in multilayer waveguides,” J. Lightwave Technol., vol. 12, pp. 2073-2079, 1994.
[6] L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol., vol. 13, pp. 615-627, 1995.
[7] O. Bryngdahl, “Image formation using self-imaging techniques,” J. Opt. Soc. Amer., vol. 63, pp. 416-418, 1973.
[8] R. Ulrich and G. Ankele, “Self-imaging in homogeneous planar optical waveguides,” Appl. Phys. Lett., vol. 27, pp. 337-339, 1975.
[9] R. Ulrich and T. Kamiya, “Resolution of self-images in planar optical waveguides,” J. Opt. Soc. Amer., vol. 68, pp. 583-592, 1978.
[10] M. Bachmann, P. A. Besse, and H. Melchior, “General self-imaging properties in NN multimode interference couplers including phase relations,” Appl. Opt., vol. 33, pp. 3905-3911, 1994.
[11] R. M. Jenkins, R. W. J. Deveraux, and J. M. Heaton, “Waveguide beam splitters and recombiners based on multimode propagation phenomena,” Opt. Lett., vol. 17, pp. 991-993, 1992.
[12] R. M. Jenkins, R. W. J. Deveraux, and J. M. Heaton, “A novel waveguide Mach-Zehnder interferometer based on multimode interference phenomena,” Opt. Commun., vol. 110, pp. 410-424, 1994.
[13] T. Hashimoto, T. Kurosaki, M. Yanagisawa, Y. Suzuki, Y. Akahori, Y. Inoue, Y. Tohmori, K. Kato, Y. Yamada, N. Ishihara, and K. Kato, “A 1.3/1.55-μm wavelength-division multiplexing optical module using a planar lightwave circuit for full duplex operation,” J. Lightwave Technol., vol. 18, pp. 1541-1547, 2000.
[14] K. Hattori, T. Kitagawa, M. Oguma, Y. Ohmori, and M. Horiguchi, “Erbium-doped silica-based waveguide amplifier integrated with a 980/1530 nm WDM coupler,” Electron. Lett., vol. 30, pp. 856-857, 1994.
[15] H. Sasaki, E. Shki, and N. Mikoshiba, “Propagation characteristics of optical guided wave in asymmetric branching waveguides,” IEEE J. Quantum Electron., vol. QE-17, pp. 1051-1058, 1981.
[16] C. Kostrzewa, and K. Petermann, “Bandwidth optimization of optical add/drop multiplexers using cascaded couplers and Mach-Zehnder sections,” IEEE Photon. Technol. Lett., vol. 7, pp. 902-904, 1995.
[17] B. Li, G. Li, E. Liu, Z. Jiang, J. Qin, and X. Wang, “Low-loss 1×2 multimode interference wavelength demultiplexer in silicon-germanium alloy,” IEEE Photon. Technol. Lett., vol. 11, pp. 575-577, 1999.
[18] K. D. Schock, F. E. Prins, S. Strahle, and D. P. Kern, “Resist process for low-energy elecron-beam lithography,” J. Vac. Sci. Technol. B 15, p.2323, 1997.
[19] K. O. Hill, and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol., vol. 15, pp. 1263-1276, 1997.
[20] Y. Shibata, S. Oku, Y. Kondo, T. Tamamura and M. Naganuma, “Semiconductor monolithic add-drop multiplexer using a grating switch integrated with coupler structure,” Electron. Lett., vol. 35, pp. 489-491, 1999.
[21] T. Augustsson, “Bragg grating-assisted MMI-coupler for add-drop multiplexing,” J. Lightwave Technol., vol. 16, pp. 1517-1522, 1998.
[22] G. Przyrembel, B. Kuhlow, E. Pawlowski, M. Ferstl, W. Furst, H. Ehlers, and R. Steingruber, “Multichannel 1.3m/1.55m AWG multiplexer/ demultiplexer for WDM-PONs,” Electron. Lett., vol. 34, pp. 263-264, 1998.
[23] Y. P. Li, C. H. Henry, E. J. Laskowski, H. H. Yaffe, and R. L. Sweatt, “Monolithic optical waveguide 1.31/1.55 μm WDM with -50 dB crosstalk over 100 nm bandwidth,” Electron. Lett., vol. 31, pp. 2100-2101, 1995.
[24] U. Hilbk, M. Burmeister, B. Hoen, T. H. Hermes, J. Saniter, and F. J. Westphal, “Selective OTDR measurements at the central office of individual fiber links in a PON,” Proc. OFC’97, Paper TUK.3, 1997.
[25] D. B. Mortimore, “Wavelength-flattened fused couplers,” Electron. Lett., vol. 21, pp. 742-743, 1985.
[26] J. V. Wright, “Wavelength dependence of fused coupler,” Electron. Lett., vol. 22, pp. 320-321, 1986.
[27] K. Okamoto, “Theoretical investigation of light coupling phenomena in wavelength-flattened couplers,” J. Lightwave Technol., vol. 8, pp. 678-683, 1990.
[28] M. Zirngibl, C. Dragone, C. H. Joyner, M. Kuznetsov, and U. Koren, “Efficient 116 optical power splitter based on InP,” Electron. Lett., vol. 28, pp. 1212-1213, 1992.
[29] S. S. Choi, J. P. Donnelly, S. H. Groves, R. E. Reeder, R. J. Bailey, P. J. Taylor, A. Napoleone, and W. D. Goodhue, “All-active InGaAsP-InP optical tapered-amplifier 1  N power splitters,” IEEE Photon. Technol. Lett., vol. 12 , pp. 974-976, 2000.
[30] H. Sasaki, E. Shki, and N. Mikoshiba, “Propagation characteristics of optical guided wave in asymmetric branching waveguides,” IEEE J. Quantum Electron., vol. QE-17, pp. 1051-1058, 1981.
[31] M. Belanger, G. L. Yip, and M. Haruna, “Passive planar multibranch optical power divider: Some design considerations,” Appl. Opt., vol. 22, pp. 2283-2289, 1983.
[32] M. Haruna and J. Koyama, “Electrooptic branching waveguide-switch and the application to 1  4 optical switching network,” J. Lightwave Technol., vol. LT1-1, pp. 233-247, 1983.
[33] R. Baets and P. E. Lagasse, “Calculation of radiation loss in integrated-optic tapers and Y-junctions,” Appl. Opt., vol. 21, pp. 1972-1978, 1982.
[34] O. Mikami and S. Zembutsu, “Coupling-length adjustment for an optical direction coupler as a 2  2 switch,” Appl. Phys. Lett., vol. 35, pp. 38-40, 1979.
[35] H. A. Haus and C. G. Fonstad, “Three waveguide couplers for improved sampling and filtering,” IEEE J. Quantum Electron., vol. QE-17, pp. 2321-2325, 1981.
[36] M. Rajarajan, B. M. A. Rahman, and K. T. V. Grattan, “A rigorous comparison of the performance of directional couplers with multimode interference devices,” J. Lightwave Technol., vol. 17, pp. 243-248, 1999.
[37] H. Yanagawa, S. Nakamura, I. Ohyama, and K. Ueki, “Broad-band high-silica optical waveguide star coupler with asymmetric directional couplers,” J. Lightwave Technol., vol. 8, pp. 1292-1297, 1990.
[38] A. Takagi, K. Jinguji, and M. Kawachi, “Silica-based waveguide-type wavelength-insensitive couplers (WINC’s) with series-tapered coupling structure,” J. Lightwave Technol., vol. 10, pp. 1814-1824, 1992.
[39] A. Takagi, K. Jinguji, and M. Kawachi, “Design and fabrication of broad-band silica-based optical waveguide couplers with asymmetric structure,” IEEE J. Quantum Electron., vol. 28, pp. 848-855, 1992.
[40] L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol., vol. 13, pp. 615-627, 1995.
[41] K.-C. Lin and W.-Y. Lee, “Guided-wave 1.3/1.55m wavelength division multiplexer based on multimode interference,” Electron. Lett., vol. 32, pp. 1259-1261, 1996.
[42] Y.-J. Lin and S.-L. Lee, “InP-based 1.3/1.55m wavelength demultiplexer with multimode interference and chirped grating,” Opt. and Quantum Electron., vol. 34, pp. 1201-1212, 2002.
[43] Y. Ma, S. Park, L. Wang, and S. T. Ho, “Ultracompact multimode interference 3-dB coupler with strong lateral confinement by deep dry etching,” IEEE Photon. Technol. Lett., vol. 12, pp. 492-494, 2000.
[44] Y. Gottesman, E. V. K. Rao, and B. Dagens, “A novel design proposal to minimize reflections in deep-ridge multimode interference couplers,” IEEE Photon. Technol. Lett., vol. 12, pp. 1662-1664, 2000.
[45] M. Bachmann, P. A. Besse, and H. Melchior, “General self-imaging properties in NN multimode interference couplers including phase relations,” Appl. Opt., vol. 33, pp. 3905-3911, 1994.
[46] E. R. Thoen, L. A. Molter, and J. P. Donnelly, “Exact modal analysis and optimization of NN1 cascaded waveguide structures with multimode guiding sections,” IEEE J. Quantum Electron., vol. 33, pp. 1299-1307, 1997.
[47] H. Ou, “Different index contrast silica-on-silicon waveguides by PECVD,” Electron. Lett., vol. 39, pp. 212-213, 2003.
[48] M. Hoffmann, P. Kopka, and E. Voges, “Low-loss fiber-matched low-temperature PECVD waveguides with small-core dimensions for optical communication systems,” IEEE Photon. Technol. Lett., vol. 9, pp. 1238-1240, 1997.
[49] Y. Hibino, F. Hanawa, H. Nakagome, M. Ishii, and N. Takato, “High reliability optical splitters composed of silica-based planar lightwave circuits,” J. Lightwave Technol., vol. 13, pp. 1728-1735, 1995.
[50] H. H. Yaffe, C. H. Henry, R. F. Kazarinov, and M. A. Milbrodt, “Polarization-independent silica-on-silicon Mach-Zehnder interferometers,” J. Lightwave Technol., vol. 12, pp. 64-67, 1994.
[51] Y. Inoue, K. Katoh, and M. Kawachi, “Polarization sensitivity of a silica waveguide thermooptic phase shifter for planar lightwave circuits,” IEEE Photon. Technol. Lett., vol. 4, pp. 36-38, 1992.
[52] M.-H. Lee, Y. H. Min, J. J. Ju, J. Y. Do, and S. K. Park, “Polymeric electrooptic 22 switch consisting of bifurcation optical active waveguides and a Mach-Zehnder interferometer,” IEEE J. Select. Topics Quantum Electron., vol.7, no. 5, pp. 812-818, 2001.
[53] U. Hilbk, M. Burmeister, B. Hoen, T. H. Hermes, J. Saniter, and F. J. Westphal, “Selective OTDR measurements at the central office of individual fiber links in a PON,” Proc. OFC’97, Paper TUK.3, 1997.
[54] B. H. Verbeek, G. H. Henry, and N. A. Olsson, “Integrated four-channel Mach-Zehnder Multi/Demultiplexer fabricated with phosphorous doped SiO2 waveguides on Si,” J. Lightwave Technol., vol. 6, pp. 1011-1015, 1988.
[55] L. A. Buckman, B. E. Lemoff, A. J. Schmit, R. P. Tella, and W. Gong, “Demonstration of a small-form-factor WWDM transceiver module for 10-Gb/s local area networks,” IEEE Photon. Technol. Lett., vol. 14, pp. 702-704, 2002.
[56] Y. Hibino, F. Hanawa, H. Nakagome, M. Ishii, and N. Takato, “High reliability optical splitters composed of silica-based planar lightwave circuits,” J. Lightwave Technol., vol. 13, pp. 1728-1735, 1995.
[57] B. H. Verbeek, G. H. Henry, and N. A. Olsson, “Integrated four-channel Mach-Zehnder Multi/Demultiplexer fabricated with phosphorous doped SiO2 waveguides on Si,” J. Lightwave Technol., vol. 6, 1011-1015, 1988.
[58] M. Kuznetsov, “Cascaded coupler Mach-Zehnder channel dropping filters for wavelength-division-multiplexed optical systems,” J. Lightwave Technol., vol. 12, 226-230, 1994.
[59] H. H. Yaffe, C. H. Henry, M. R. Serbin, and L. G. Cohen, “Resonant couplers acting as add-drop filters made with silica-on-silicon waveguide technology,” J. Lightwave Technol., vol. 12, 1010-1014, 1994.
[60] C. Kostrzewa, and K. Petermann, “Bandwidth optimization of optical add/drop multiplexers using cascaded couplers and Mach-Zehnder sections,” IEEE Photon. Technol. Lett., vol. 7, pp. 902-904, 1995.
[61] B. J. Offrein, G. L. Bona, F. Horst, H. W. M. salemink, R. Beyeler, and R. Germann, “Wavelength tunable optical add-after-drop filter with flat passband for WDM networks,” IEEE Photon. Technol. Lett., vol. 11, pp. 239-241, 1999.
[62] T. W. Ang, G. T. Reed, A. Vonsovici, A. G. R. Evans, and P. R. Routley, “0.15 dB/cm loss in unibond SOI waveguides,” Electron. Lett., vol. 35, pp. 977-978, 1999.
[63] D. Ortega, R. M. De La Rue, and J. S. Aitchison, “Cutoff wavelength of periodically segmented waveguides in Ti:LiNbO3,” J. Lightwave Technol., vol. 16, pp. 284-290, 1998.
[64] R. Scarmozzino and R. M. Osgood, “Comparison of finite-difference and fourier-transform solutions of the parabolic wave equation with emphasis on integrated-optics applications,” J. Opt. Soc. Am. A., vol. 8, pp. 724-731, 1991.
[65] P. D. Trinh, S. Yegnanarayanan, F. Coppinger, and B. Jalali, “Silicon-on-insulator (SOI) phased-array wavelength multi/demultiplexer with extremely low-polarization sensitivity,” IEEE Photon. Technol. Lett., vol. 9, pp. 940-942, 1997.
[66] J. Aarnio, P. Heimala, M. D. Giudice, and F. Bruno, “Birefringence control and dispersion characteristics of silicon oxynitride optical waveguides,” Electron. Lett., vol. 27, pp. 2317-2318, 1991.
[67] K. Jinguji and M. Kawachi, “Synthesis of coherent two-port lattice-form optical delay-line circuit,” J. Lightwave Technol., vol. 13, pp. 73-82, 1995.
[68] Y. Inoue, M. Oguma, T. Kitoh, M. Ishii, T. Shibata, Y. Hibino, H. Kawata and T. Sugie, “Low-crosstalk 4-channel coarse WDM filter using silica-based planar-lightwave-circuit,” OFC 2002 Technical Digest., pp. 75-76, 2002.
[69] K. Jinguji and M. Oguma, “Optical half-band filters,” J. Lightwave Technol., vol. 18, pp. 252-259, 2000.
[70] M. Rajarajan, B. M. A. Rahman, and K. T. V. Grattan, “A rigorous comparison of the performance of directional couplers with multimode interference devices,” J. Lightwave Technol., vol. 17, pp. 243-248, 1999.
[71] User guide of FimmWave program, version 3.4, Photon Design, 2001. http://www.photond.com
[72] R. Mestric, H. Bissessur, B. Martin, and A. Pinquier, “1.31-1.55-m phase-array demultiplexer on InP,” IEEE Photon. Technol. Lett., vol. 8, pp. 638-640, 1996.
[73] M. Kawachi, “Recent progress in silica-based planar lightwave circuits on silicon,” IEE Proc.-Optoelectron., Vol. 143, pp. 257-262, 1996.
[74] M. Kawachi, “Silica waveguides on silicon and their application to integrated-optic components,” Optical and Quantum Electronics, vol. 22, pp. 391-416, 1990.
[75] M. Okuno, A. Sugita, K. Jinguji, and M. Kawachi, “Birefringence control of silica waveguides on Si and its application to a polarization-beam splitter/switch,” J. Lightwave Technol., vol. 12, pp. 625-633, 1994.
[76] Q. Lai, W. Hunziker, and H. Melchior, “Low-power compact 22 thermooptic silica-on-silicon waveguide switch with fast response,” IEEE Photon. Technol. Lett., vol. 10, pp. 681-683, 1998.