本論文的研究重點在利用光子晶體以及平面光波導技術，設計與分析可用於光被動網路上之被動元件，主要研究分成下列各方面。
首先，利用矽材料上之週期性六角晶格的洞或柱，我們成功展現新穎的設計在雙波段解多工器上，經由介於兩個缺陷波導間的其一光波長使其具耦合能力，及在另一光波長上具解耦合能力的光子晶體特性，模擬成功展現出元件的波長解多工功能。並且藉由適當地選擇分隔波導的孔洞列或柱列的數量及半徑大小，對其一光波長範圍將產生寬廣的頻寬特性，克服光子晶體在具解耦合功能時，結構對直通帶頻寬不夠的缺點，而以孔洞或柱形成的光子晶體，其設計上皆可實現解多工行為。
其次，我們提出一種普遍性的新方法，以縮短多模干涉耦合器上自我成像的激發長度。藉由適當地調整多點影像上的彼此相位差，模態沿展將改變並使自我成像在更短的距離上。這樣的效應可以被視作在原來的多模干涉耦合器上，分割產生成多個次多模干涉耦合器。並且這樣的效應可以應用在對稱型及成對型的干涉情形，我們應用這樣的原理設計緊密短小並可操作在雙波段的光功率分離器及解多工器，模擬展現具有縮短耦合器長度的優越效能，並可同時操作在1.3及1.55 um的頻帶上。
最後，藉由多模干涉機制與光子晶體的結合，設計實現出一種具有寬頻帶且緊密短小結構的1.3/1.55 um波長解工器，以有限差分時域分析法模擬展示出在雙波段上皆具有大於100 nm的頻寬的優越性能，而且其插入損耗將低於3 dB和隔離率大於20 dB以上。

In this thesis, we are interested in the integration of planar lightwave circuit and photonic crystals. Both analysis and design are based on the application of passive devices in optical passive network. The major wok includes three parts.
Firstly, we present a novel design of dual-band demultiplexers based on a periodic hexagonal lattice of holes or rods on silicon materials. The demultiplexing function can be applied by coupling between two defect waveguides at one wavelength and with decoupling then at another wavelength. Appropriately choosing the radius and number of separated rows yields a broad bandwidth for one range of wavelengths. Two designs that use rods or holes to generate photonic crystals are realized.
Secondly, a unified method was proposed to reduce the beat length of a multimode interference (MMI) coupler. By properly adjusting the phase difference of the N-fold images, the mode evolution is changed to generate self-images at a much shorter distance. The effect of adjusting the phase difference can be regarded as dividing the original MMI coupler into multiple sub-MMI couplers. Such an effect can be applied for both symmetric- and paired-interference cases. We applied the principle to design compact optical splitters operating at dual wavelength bands. The simulation shows that excellent performance with reduced coupler length can be obtained for splitters operating at both 1.3 and 1.55 um bands.
Thirdly, by the combination of multimode interference and photonic crystals, a broad-band 1.3/1.55-um demultiplexer can be realized with a very compact structure. Simulation with the finite-difference time domain method shows its excellent performance. Greater than 20dB an isolation ratio and the insertion loss less than 3 dB over 100nm bandwidth at both wavelength bands are obtained.

[1] S. -J. Park, C.-H. Lee, K.-T. Jeong, H.-J. Park, J.-G. Ahm, and K.-H. Song, “Fiber-to-the-Home Services Based on Wavelength-Division- -Multiplexing Passive Optical Network” J. Lightwave Technol., vol. 22, pp. 2582-2590, 2004.
[2] 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.
[3] H. Ou, “Different index contrast silica-on-silicon waveguides by PECVD,” Electron. Lett., vol. 39, pp. 212-213, 2003.
[4] D. L. Lee, “Electromagnetic Properties of Integrated Optics,” New York: Wiley, 1996.
[5] A. W. Snyder and J. D. Love, “Optical Waveguide Theory,” London, U. K.: Chapman & Hall, 1995.
[6] R. C. Alferness, R. V. Schmidt, and E. H. Tuner, “Characteristics of Ti diffused LiNbO3 optical directional couplers,” Appl. Opt., vol. 18, pp. 4012, 1979.
[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] 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.
[11] 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.
[12] 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.
[13] 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.
[14] 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.
[15] E. Yablonovitch, “Inhibited spontaneous emission in solid –state physics and electronics,” Phys. Rev. Lett. vol. 58, pp. 2059-2062, 1987.
[16] A. Sharkawy, S. Shi, and D. W. Parther, “Electro-optical switching using coupled photonic crystal waveguides,” Opt. Express, vol. 10, pp 1048-1059, 2002.
[17] Martinez, A. Griol, P. Sanchis, and J. Marti, “Mach-Zehnder interferometer employing coupled-resonator optical waveguides,” Opt. Lett., vol. 28, pp. 405-407, 2003.
[18] M. Koshiba, “Wavelength division multiplexing and demultiplexing with photonic crystal waveguide couplers,” J. Lightwave Technol., vol. 19, pp. 1970-1975, 2001.
[19] M. Loncar, D. Nedelijkovic, T. Doll, and T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett., vol. 77, pp. 1937-1939, 2000.
[20] A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimentional photonic crystal slabs,” Phys. Rev. B., vol. 62, pp. 4488-4492, 2000.
[21] T. Baba, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, and A. Sakai, “Light propagation characteristics of straight single-line-defect waveguides in photonic crystal slabs fabricated into a silicon-on-insulator substrate,” J. Quantum Electron., vol. 38, pp. 743-752, 2000.
[22] A. Chutinan, M. Okano, and S. Noda, “Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs,” Appl. Phys. Lett., vol. 80, pp. 1698-1700, 2002.
[23] M. Imada, S. Noda. A. Chutinan, M. Mochizuki and T. Tanaka, “Channel drop filter using a single defect in a 2-D photonic crystal slab waveguide,” J. Lightwave Tech., vol. 20, pp. 873-878, 2002.
[24] R. Costa, A. Melloni and M. Martinelli, “Bandpass resonant fitlers in photonic-crytal waveguides,” Photon. Tech. Lett., vol. 15, pp. 401-403, 2003.
[25] M. Koshiba, “Wavelength division multiplexing and demultiplexing with photonic crystal waveguide couplers,” J. Lightwave Tech., vol. 19, pp. 1970-1975, 2001.
[26] A. Sharkawy, S. Shi and D. W. Prather, “Electro-optical switching using coupled photonic crystal waveguides,” Optics Express, vol. 10, pp. 1048-1059, 2002.
[27] A. Martinez, F. Cuesta and J. Marti, “Ultrashort 2-D photonic crystal directional couplers,” Photon. Tech. Lett., vol. 15, pp. 694-696, 2003.
[28] S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis,” Optics Express vol. 8, pp. 173-190, 2001.
[29] F. S.-S. Chien, Y. J. Hsu, W.-F. Hsieh and S.-C. Cheng, “Dual wavelength demultiplexng by coupling and decoupling of photonic crystal waveguides” Optics Express, vol. 12, pp. 1119-1125, 2004.
[30] M. Bayindir, B. Temelkuran and E. Ozbay, “Tight-binding description of the coupled defect modes in the three-dimensional photonic crystals,” Phys. Rev. Lett., vol. 84, pp. 2140-2143, 2000.
[31] 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.
[32] 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.
[33] 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.
[34] 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.
[35] 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.
[36] 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.
[37] 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.
[38] 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.
[39] 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.
[40] 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.
[41] 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.
[42] 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.
[43] J. M. Heaton and R. M. Jenkins, “General matrix theory of self-imaging in Multimode Interference (MMI) couplers,” IEEE Photon. Technol. Lett., vol. 11, pp. 212-214, 1999.
[44] J. M. Heaton, R. M. Jenkins, D. R. Wight, J. T. Parker, J. C. H. Birbeck and K. P. Hilton, “Novel 1-to-N way integrated optical beam splitters using symmetric mode mixing in GaAs/AlGaAs multimode waveguides,” Appl. Phys. Lett., vol. 61, pp. 1754-1756, 1992.
[45] 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.
[46] Y.-J. Lin, “Integrated-optics devices based on the multimode interference effect,” National Taiwan University of Science and Technology, Taipei, Taiwan, P. H. D, 2003.
[47] B. Li, G. Li, E. Liu, Z. Jiang, J. Oin and X. Wang, “Low-loss 1 2 multimode interference wavelength demultiplexer in silicon-germanium alloy,” IEEE Photonics Technol. Lett., vol. 11, pp. 575-577, 1999.
[48] 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.
[49] C. Kostrzewa and K. Petermann, “Bandwidth optimization of optical add/drop multiplexers using cascaded couplers and Mach-Zehnder sections,” IEEE Photonics Technol. Lett.,vol. 7, pp. 902-904, 1995.
[50] T. Augustsson, “Bragg grating–assisted MMI-coupler for add-drop multiplexing,” J. Lightwave Technol., vol. 16, pp. 1517-1522, 1998.