使用分波多工技術 (wavelength-division multiplexing) 之通訊系統可以對頻寬作較有效率的運用。由於光子晶體的介電常數成周期性變化而具有能隙，頻率落在此能隙中的光子無法在光子晶體中傳輸。因而可藉由在光子晶體內置入缺陷結構來控制光在特定的路徑傳播。
本論文討論了耦合腔波導(CCWs)和濾波器的一些特性。然後我們利用耦合腔波導來設計多通道的分波多工器。其可以濾出1310/1490/1550 nm等波長並應用在光纖到家(FTTH)系統上，且可以使輸出波長的頻寬變窄以便濾出更多的波段。此外，由於調整光子晶體中共振腔的大小，可以擷取出特定的波長，所以我們利用此特性設計一個半高寬為0.8 nm的多通道擷取濾波器。此架構具有100%的擷取效率、高Q值和極低的耦合干擾，並符合粗分波多工技術(CWDM)的規格。這種積體化光子晶體之解多工器和擷取濾波器相當適用於分波多工的光通訊系統中。

The communication system using Wavelength-division multiplexing (WDM) allows for better utilization of the spectral bandwidth. Photonic crystals (PhCs) exhibit photonic bandgap (PBG) due to the periodic variation of the dielectric constant and photons with a range of frequencies within the PBG cannot travel through the crystal. By introducing defects into PhCs, it is possible to control the light propagation along certain paths.
In this thesis, the characteristics of coupled cavity waveguides (CCWs) and drop filter are discussed. Then we propose a multi-channel WDM system based on CCWs. It can be applied in FTTH to filter the wavelengths of 1310, 1490 and 1550 nm in different CCWs and also can make the bandwidth of output wavelength become narrow to filter more wavelengths. In addition, by modulating the size of the resonator on the PhCs, it can drop the particular wavelength into the waveguide. Finally, we proposed a multi-channel drop filter with FHWM 0.8 nm. This device design is leading the way to achieve CWDM specification with 100% drop efficiency, high quality factor and almost no crosstalk. The operations of such an ultra-compact demultiplexer and drop filter based on PhCs are suitable to be used in WDM optical communication systems.

Acknowledgements i
Abstract iii
Contents v
List of Figures vii
List of Tables xvi
List of Symbols xvii

Chapter 1： Introduction
1.1 General Reviews of Photonic Crystals 1
1.2 Photonic Crystal Components 3
1.2.1 Defects 3
1.2.2 Photonic Crystal Waveguides 4
1.2.3 Coupled Cavity Waveguides 4
1.3 Applications of Photonic Crystals 7
1.3.1 FTTH 7
1.3.2 CWDM and DWDM 7
1.4 Organizations of the Thesis 9
Chapter 2： Basic Theory and Simulation Method
2.1 Introduction 17
2.2 Plane Wave Expansion Method (PWE) 17
2.3 Finite Difference Time Domain Method (FDTD) 22
Chapter 3： The Study of N-channel Demultiplexer Based on Two-Dimensional Photonic Crystals with Coupled Cavity Waveguides
3.1 Introduction 33
3.2 A T-branch 1310/1550 nm Wavelength Demultiplexer Based on Two-Dimensional Photonic Crystals 36
3.2.1 Analysis 36
3.2.2 Numerical Results and Discussions 38
3.3 A New Approach of Multi-channel Wavelength Division Multiplexing with Coupled Cavity Waveguides 41
3.3.1 Analysis 41
3.3.2 Numerical Results and Discussions 43
3.4 Summary 45
Chapter 4： Multi-Channel Drop Filters Based on Two-Dimensional Photonic Crystals
4.1 Introduction 67
4.2 Theoretical Modeling and Analysis 70
4.3 Numerical Results and Discussions 63
4.4 Summary 77
Chapter 5： Conclusions
5.1 Summary 94
5.2 Suggestions for Future Researches 95
References 96

[1] S. John, “Strong localization of phonics in certain disordered dielectric superlattice,” Phys. Rev. Lett., Vol.58, pp.2486-2489, 1987.
[2] E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics electrons,” Phys. Rev. Lett., Vol.58, pp.2059-2062, 1987.
[3] N. Moll, G.L. Bona, “Comparison of three-dimensional photonic slab waveguides with two-dimensional photonic crystal waveguides: Efficient butt coupling into these photonic crystal waveguides,” J. Appl. Phys., Vol.93, pp.4986, 2003.
[4] T. Bada, A. Motegi, T. Iwai, N. Fukaya, Y. Watanabe, A. Sakai, “Light Propagation Characteristics of Straight Single-Line-Defect Waveguides in Photonic Crystal Slabs Fabricated Into a Silicon-on-Insulator Substrate,” IEEE J. Quantum Electronics, Vol.38, pp.743, 2002.
[5] M.Loncar, J. Vuckovic, A. Scherer, “Methods for controlling positions of guided modes of photonic-crystal waveguides,” J. Opt., Vol.18, pp.1362, 2001.
[6] A. Scherer, O. Painter, J. vuckovic, M. Loncar, T. Yoshie, “Photonic Crystals for Confining, Guiding, and Emitting Light,” IEEE trans Nanotechnology, Vol.1, pp.4, 2002.
[7] J. Moosburger, M. Kamp, A. Forchel, U. Oesterle, and R. HoudrHoudré, “Transmission
spectroscopy of photonic crystal based waveguides with resonant cavities,” J.
Appl.Phys., Vol.92, pp.4791, 2002.
[8] J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D.
Joannopoulos, L. C. Kimerling, H. I. Smith, E. P. Ippen, “Photonic-bandgap
microcavities in optical waveguides,” Nature, Vol.390, pp.143, 1997.[9] S. Noda, A Chutinan, M. Imada, “Trapping and emission of photons by a single
defect in a photonic bandgap structure,” Nature, Vol.407, pp.608, 2002.
[10] M. Bayindir, E. Ozbay, “Band-dropping via coupled photonic crystal
waveguides,” Opt. Express, Vol.10, pp.1279, 2002.
[11] M. Koshiba, “Wavelength Division Multiplexing and Demultiplexing With
Photonic Crystal Waveguide Couplers,” IEEE J. Lightwave. Tech., Vol.19, pp.733,
2001.
[12] J. Sharee, McNab, Nikolaj Moll, and Yurii A. Vlasov, “Ultra-low loss photonic
integrated circuit with membrane-type photonic crystal waveguides,” Opt.
Express, Vol.11, pp.2927-2939, 2003.
[13] Kartik Srinivasan, Oskar Painter, “Momentum space design of high-Q photonic
crystal optical cavities,” Opt. Express, Vol.10, pp.670-684, 2002.
[14] Tomoyuki Yoshie, Jelena Vučković, “High quality two-dimensional photonic
crystal slab cavities,” Axel Scherer, H. Chen, Dennis Deppe, Appl. Phys. Lett.,
Vol.79, pp.4289-4291, 2001.
[15] Thomas F. Krauss, “Planar photonic crystal waveguide devices for integrated
optics,” Phys. Stat. Sol., Vol.197, pp.688-702, 2003.
[16] R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, K.
Kash, “Novel applications of photonic band gap materials: Low-loss bends and
high Q cavities,” J. Appl. Phys., Vol.75, pp.4753-4755, 1994.
[17] S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear
waveguides in photonic-crystal slabs,” Phys. Rev. B, Vol.62, pp.8212-8222, 2000.
[18] G. P. Nordin, S. Kim, J.Cai, J. Jiang, “Hybrid integration of conventional
waveguide and photonic crystal structures,” Opt. Express, Vol.10, pp.1334, 2002.
[19] T. Sondergaard, K. H. Dridi, “Energy flow in photonic crystal waveguides,” Phys.
Rev. B, Vol.61, pp.15688, 2000.
[20] S. Boscolo, M. Midrio, “Y junctions in photonic crystal channel waveguides:
high transmission and impendence matching,” Opt. Lett., Vol.27, pp.1001, 2002.
[21] M. Bayindir, B. Temelkuran, E. Ozbay, “Photonic-crystal-based beam splitters,”
Appl. Phys. Lett., Vol.77, pp.3902, 2000.
[22] S. G. Johnson, C. Manolatou, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, H. A.
Haus, “Elimination of cross talk in waveguide intersections,” Opt. Lett., Vol.23,
pp.1855, 1998.
[23] S. Lan, K. Kanamoto, T. Yang, S. Nishikawa, Y. Sugimoto, N. Ikeda, H.
Nakamura, K. Asakawa, H. Ishikawa, “Similar role of waveguide bends in
photonic crystal circuits and disordered defects in coupled cavity waveguides: An
intrinsic problem in realizing photonic crystal circuits,” Phys. Rev. B, Vol.67,
pp.115208, 2003.
[24] Mehmet Bayindir, B. Temelkuran, and E. Ozbay, “Freezing by Heating in a
Driven Mesoscopic System,” Phys. Rev. Lett., Vol.84, pp.2140, 2000.
[25] C. Martijn de Sterke, “Superstructure gratings in the tight-binding
approximation,” Phys. Rev. E, Vol.57, pp.3502, 1998.
[26] N. Stefanou and A. Modinos, “Impurity bands in photonic insulators,” Phys. Rev.
B, Vol.57, pp.12127, 1998.
[27] E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis,
“Tight-Binding Parametrization for Photonic Band Gap Materials,” Phys. Rev.
Lett., Vol.81, pp.1405, 1998.
[28] A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator
opticalwaveguide:a proposal and analysis,” Opt. Lett., Vol.24, pp.711, 1999.
[29] Ekmel Ozbay, Mehmet Bayindir, Irfan Bulu, and Ertugrul Cubukcu,
“Investigation of Localized Coupled-Cavity Modes in Two-Dimensional
Photonic Bandgap Structures,” IEEE J. Quantum Electronics, Vol.38, pp.7, 2002.
[30] Mehmet Bayindir, B. Temelkuran, and E. Ozbay, “Photonic-crystal-based beam
splitters,” Appl. Phys. Lett., Vol.77, pp.24, 2000.
[31] P. R. Villeneuve, D. S. Abrams, S. Fan, and J. D. Joannopoulos, “Single-mode
waveguide microcavity for fast optical switching,” Opt. Lett., Vol.21, pp.
2017–2019, 1996.
[32] A. MARTINEZ, J. MARTÍ, J. BRAVO-ABAD, and J. SÁNCHEZ-DEHESA,
“Wavelength Demultiplexing Structure Based on Coupled-Cavity Waveguides in
Photonic Crystals,” Fiber and Integrated Optics, Vol.22, pp.151–160, 2003.
[33] Francis Nedvidek, Marcus Nebeling and Daniel Mailloux, “Deploying CWDM
to Overcome Bandwidth Limitations of FTTH Access Networks,” 2006 FTTH
Conference & Expo.
[34] C. Bouchat, C. Dessauvages, F. Fredricx, C. Hardalov, R. Schoop, and P. Vetter,
“WDM-upgraded PONs for FTTH and FTTBusiness.”
[35] K. M. Ho, C. T. Chan, and C. M. Soukouils, “Existence of a photonic gap in
periodic dielectric structures,” Phy. Rev. Lett., Vol.65, pp.3152-3155, 1990.
[36] K. M. Leung, and Y. F. Liu, “Photon band structures: The plane-wave method,”
Phys. Rev. B, Vol.41, pp.10188-10190, 1990.
[37] Z. Zhang and S. Satpathy, “Electromagnetic wave propagation in periodic
structures: Bloch wave solution of Maxwell’s equations,” Phys. Rev. Lett., Vol.65,
pp.2650-2653, 1990.
[38] B. C. Gupta, C. H. Kuo, and Z. Ye, “Propagation inhibition and localization of
electromagnetic waves in two-dimensional random dielectric systems,” Phys. Rev.
E., Vol.69, pp.06615-1-6, 2004.
[39] P. M. Bell, J. B. Pendry, L. M. Moreno, and A. J. Ward, “A program for
calculating photonic band structures and transmission coefficients of complex
structures,” Comput. Phys. Commun., Vol.85, pp.306-322, 1995.
[40] K. S. Kunz and R. J. Luebbers, “The finite difference time domain method for
electromagnetics,” Boca Raton FL: CRC Press, 1993.
[41] G. S. Smith, M. P. Kesier, J. G. Maloney, and B. L. Shirely, “Antenna design with
the use of photonic band-gap materials as all-dielectric planar reflectors,”
Microwave and optical technology letters, Vol.11, pp.169-174, 1996.
[42] J. G. Maloney, M. P. Kesier, B. L. Shirely, and G. S. Smith, “A simpled
description for waveguiding in photonic bandgap materials,” Microwave and
optical Technology Letters, Vol.14, pp.261-266, 1997.
[43] K. S. Yee, “Numerical solution of initial boundary value problems involving
Maxwell’s equations in isotropic media,” IEEE Trans. Antenna Propagat. Vol. 14,
pp. 302-307, 1966.
[44] J. Adhidjaja and G. Horhmann, “A finite-difference algorithm for the transient
electromagnetic response of a three-dimensional body,” Geophysics J. Int., Vol.
98, pp.233, 1989.
[45] M. Piket-May and A. Taflove, “Electrodynamics of visible-light interactions with
the vertebrate retinal rod,” Optics Letter, Vol.18, pp.568-570, 1993.
[46] M. Celuch-Marcysiak and W. Gwarek, “Higher order modeling of media
interfaces for enhanced FDTD analysis of microwave circuits,” in 24th European
Microwave Conference, Vol.24, pp.1530, 1994.
[47] Chongjun Jin, Shouzhen Han, Xiaodong Meng, Bingying Cheng, and Daozhong
Zhang, “Demultiplexer using directly resonant tunneling between point defects
and waveguides in a photonic crystal,” J. Appl. Phys., Vol.91, pp.7, 2002.
[48] Shanhui Fan, S. G. Johnson, and J. D. Joannopoulos, “Waveguide branches in
photonic crystals,” J. Opt. Soc. Am. B, Vol.18, pp.2, 2001.
[49] Tapio Niemi, Lars Hagedorn Frandsen, Kristian Knak Hede, Anders Harpøth,
Peter Ingo Borel, and Martin Kristensen, “Wavelength-Division Demultiplexing
Using Photonic Crystal Waveguides,” IEEE Photonics Technology Letters,
Vol.18, pp.1, 2006.
[50] Shanhui Fan, P. R. Villeneuve, J. D. Joannopoulos, “Channel drop filters in
photonic crystals,” Optics Express, Vol.3, pp. 4-11, 1998.
[51] Bong-Shik Song, Takashi Asano, Yoshihiro Akahane, Yoshinori Tanaka, and
Susumu Noda, “Multichannel Add/Drop Filter Based on In-Plane Hetero
Photonic Crystals,” Journal of Lightwave Technology, Vol.23, pp.1449-1455,
2005.
[52] Ahmed Sharkawy, Shouyuan Shi, and Dennis W. Pratrher, “Multichannel
wavelength division multiplexing with photonic crystals,” Applied Optics, Vol.40,
pp.2247-2252, 2001.
[53] Sangin Kim, Ikmo park, Hanjo Lim, and Chul-Sik Kee, “Highly efficient
photonic crystal-based multi-channel drop filters of three-port system with
reflection feedback,” Optics Express, Vol.12, pp.5518-5525, 2004.
[54] Honglian Ren, Chun Jian, Weisheng Hu, Mingyi Gao, Jingyuan Gao and
Jingyuan Wangm, “Photonic crystal channel drop filter with a
wavelength-selective reflection micro-cavity,” Optics Express, Vol.14,
pp.2446-2458, 2006.
[55] Chih-Wen Kuo, Chih-Fu Chang, Mao-Hsiung Chen, and Shih-Yuan Chen, “A
new approach of planar multi-channel wavelength division multiplexing system
using asymmetric super-cell photonic crystal structures,” Optics Express, Vol.15,
pp.1, 2007.
[56] T. Lang, J.-J. He, S. He, "Cross-oder arrayed waveguide grating design for
triplexers in fiber access networks," IEEE Photonics Tech. Lett., Vol.18,
pp.232-234, 2006.
[57] X. Li, G-R Zhou, N-N Feng, W. Huang, "A novel planar waveguide wavelength
demultiplexer design for integrated optical triplexer transceiver," IEEE Photonics
Tech. Lett., Vol.17, pp.1214-1216, 2005.
[58] H. A. Haus, “Waves and Field in Optoelectronics,” 1984.
[59] H. A. Haus and Y. Lai, “Theory of cascaded quarter wave shifted distributed
feedback resonators,” J. Quantum Electron, Vol.28, pp.205-213, 1992.
[60] David M. Pustai, Ahmed Sharkawy, Shouyuan Shi, and Dennis W. Prather,
“Tunable photonic crystal microcavities,” Appl. Opt., Vol.41, pp.5574-5579,
1992.
[61] Hitomichi TAKANO, Bong-Shik SONG, Takashi ASANO and Susumu NODA,
“Highly Effective In-Plane Channel-Drop Filters in Two-Dimensional
Heterostructure Photonic-Crystal Slab,” Japanese Journal of Applied Physics,
Vol.45, pp.6078-6086, 2006.
[62] Hitomichi TAKANO, Bong-Shik SONG, Takashi ASANO and Susumu NODA,
“Highly efficient multi-channel drop filter in a two-dimensional hetero photonic
crystal,” Optics Express, Vol.14, pp.3491, 2006.