光子晶體是一種微結構系統，因其介電常數呈週期性變化而具有光子能隙，可藉由在光子晶體內植入缺陷，形成能循特定路徑導引光的傳遞，亦可製造能將光侷限於非常小空間的微共振腔。吾人於本論文中首先探討利用在頻率域的平面波展開法(Plane Wave Method)來計算出色散關係並找出其光子晶體能隙(Photonic Bandgap)，在時域中利用有限差分法(Finite Difference Time Domain)並搭配完美匹配層(Perfect Matching Laye: PML)的邊界條件來解決麥克斯威爾方程式亦是模擬電磁波的動態行為。利用改變光子晶體共振腔中缺陷的大小可明顯地從結構表面汲取出特定的波長，再利用光子晶體波導將光導引至其通道。吾人可利用此結構實現分波多工器的功能。此外，利用光子晶體耦合共振腔波導控制群速度達到慢光的特性，利用平面波展開法計算色散曲線圖，並且求得波導中之群速。利用群速及慢光特性設計可設計出一新型的分時多工器系統架構。另外，利用二維光子晶體環形共振腔和耦合共振腔波導來設計出一個光延遲的效果。透過排列設計後利用串接多個環形共振腔的方式，來達到更長的光延遲效果。一般常見光延遲元件是設計讓光在長波導內產生延遲現象。因此吾人在論文中提出一個環形共振腔串接的方式，不但具有更長的光延遲效果且在系統架構尺寸上也能小上許多。有鑒於奈米技術的提昇，在積體電路上實現光子晶體的元件將是一大突破，因此在超高速與超高容量的光通訊與資訊處理應用中，這些元件將扮演極重要的關鍵角色。

Photonic crystals (PCs) are nano-structured materials in which a periodic variation of the dielectric constant of the material results in a photonic band gap. By introducing defects into PCs, it is possible to build waveguides that can channel light along certain paths. It is also possible to construct micro-cavities that can localize photons in extremely small volumes. In this dissertation, to begin with, we computed the photonic crystals dispersion relations and found the photonic band gap (PBG) by the plane wave expansion method (PWE) in the frequency domain. Then, the finite difference time domain method (FDTD) along with the perfectly matched layer boundary conditions was adopted to solve Maxwell’s equations, equivalent to simulate the movement behavior of the Photonic crystals. By properly varying the size of the defect on the PCs, it could really drop the particular wavelengths and guide them to output channels by PCs waveguides. We proposed the structures that would function as Wavelength-Division-Multiplexer (WDM). Secondly, coupled cavity waveguide of PC was used to control group velocity that achieved the slow light property. By calculating dispersion curve with PWE, we obtained group velocity characteristics in PCs waveguide. Meanwhile, we designed a novel Time-Division-Multiplexer (TDM) system by controlling the group velocity characteristics. Finally, we designed cascade ring resonators and expected to obtain an extendable delay line. Conventional delay line devices are propagating in a long waveguide to obtain the delay line property. An excellent delay line and ultra-small size properties are expected in the proposed structure. Because nano-technology has been making great progress steadily, it surely can be used to demonstrate a practical breakthrough in which the devices based on the PC integrated circuits are realized. These devices will be a potential key component in the applications of ultra-high-speed and ultra-high-capacity optical communications and optical data processing systems.

Acknowledgement…............................................................i
Abstract….............................................................................iii
Contents…………………………………............................v
List of Figures.....................................................................vii
List of Tables.......................................................................xi
List of Symbols...................................................................xii
Chapter 1 Introduction........................................................1
1.1 General Review of Photonic Crystal.........................1
1.2 Motivation........................................................................2
Chapter 2 Basic Theory and Simulation Method...........4
2.1 Numerical Analysis Methods......................................4
2.1.1 Plan Wave Expansion (PWE)..................................4
2.1.2 Finite Difference Time Domain (FDTD) Method..7
2.2 Photonic Crystal Structures......................................11
2.2.1 Photonic Band Gap (PBG).....................................12
2.2.2 Photonic Crystal Waveguides...............................12
Chapter 3 A New Approach of Planar Multi-Channel Wavelength-Division-Multiplexing System using Asymmetric Super-cell Photonic Crystal Structures...22
3.1 Introduction..................................................................22
3.2 Components of WDM system..................................23
3.2.1 Micro-cavities in Photonic Crystals......................23
3.2.2 Channel Drop Filters in Photonic Crystals.........24
3.2.3 Waveguide Reflection Feedback System...........25
3.3 General Multi-channel Wavelength-Division-Multiplexing (WDM) System Design...............................27
3.4 New Approach of Multi-channel WDM System Design.................................................................................28
3.5 Summary......................................................................30
Chapter 4 Novel Time-Division-Multiplexing (TDM) System with Directional Coupling Output using Photonic Crystal Structures Slow Light Design...........49
4.1 Introduction..................................................................49
4.2 Coupled Cavity Waveguide.......................................50
4.2.1 The Structures of Coupled Cavity Waveguide....50
4.2.2 The Transmission Characteristics of Coupled Cavity Waveguide..............................................................52
4.3 Slow Light.....................................................................53
4.4 Time-Division-Multiplexing (TDM) System Design Modeling..............................................................................54
4.5 Multi-channel Time-Division-Multiplexing (TDM) System Device Design.....................................................55
4.6 New Approach of High-efficiency Multi-channel TDM system Device with Directional Coupling Output Port Design.........................................................................56
4.7 Summary......................................................................57
Chapter 5 A Novel Optical Delay Line Using Cascade Ring-type Resonators Based on Photonic Crystal Structures............................................................................85
5.1 Introduction..................................................................85
5.2 Device Structure Design Modeling..........................86
5.3 Numerical Results and Analyses............................87
5.4 Summary......................................................................88
Chapter 6 Conclusion and Future Work.....................108
Reference.........................................................................110

[1]E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, pp. 2059-2062, 1987.
[2]S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, pp. 2486-2489, 1987.
[3]S. Fan, P. R. Villeneuve and J. D. Joannopoulos, “Channel drop filters in photonic crystals,” Optics Express, Vol. 3, pp. 4-11, 1998.
[4]B. S. Song, T. Asano, Y. Akahane, Y. Tanaka, and S. Noda, “Multichannel Add/Drop Filter Based on In-Plane Hetero Photonic Crystals,” Journal of Lightwave Technology, Vol. 23, pp. 1449-1455, 2005.
[5]A. Sharkawy, S. Shi, and D. W. Pratrher, “Multichannel wavelength division multiplexing with photonic crystals,” Applied Optics, Vol. 40, pp. 2247-2252, 2001.
[6]S. Kim, I. park, H. Lim, and C. S. 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.
[7]H. Ren, C. Jian, W. Hu, M. Gao, J. Gao and J. Wangm, “Photonic crystal channel drop filter with a wavelength-selective reflection micro-cavity,” Optics Express, Vol. 14, pp. 2446-2458, 2006.
[8]K. M. Ho, C. T. Chan, and C.M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. Vol. 65, pp. 3152-3155, 1990.
[9]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.
[10]X. Wang, X. G. Zhang, Q. Yu, B. N. Harmon, “Multiple-scattering theory for electromagnetic waves,” Phys. Rev. B, Vol. 47, pp. 4161-4167, 1993.
[11]C. T. Chan, Q. L. Yu, and K. M. Ho, “Order-N spectral method for electromagnetic waves,” Phys. Rev. B, Vol. 51, pp. 16635-16642, 1995.
[12]K. S. Yee, “Numerical Solution of Initial Boundary Value Problems Involving Maxwell’s Equation In Isotropic Media,” IEEE Trans. Antennas Propagat., AP-14, pp. 302-307, 1966.
[13]S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature, Vol. 407, pp. 608-610, 2000.
[14]A. Cutinan, M. Mochizuki, M. Imada, and S. Noda, “Surface-emitting channel drop filters using single defects in two-dimensional photonic crystal slabs,” Appl. Phys. Lett., Vol. 79, pp. 2690-2692, 2001.
[15]H. A. Haus, and Y. Lai, “Theory of Cascaded Quarter Wave Shifted Distributed Feedback Resonators,” IEEE journal of Quantum Electronics, Vol. 28, No. 1, pp. 205-213, 1992.
[16]H. A. Haus, Waves and Field in Optoelectronics (Englewood Cliffs, NJ: Prentice-Hall, 1984.
[17]N. Panoiu, M. Bahl, and R. Osgood, Jr., "All-optical tunability of a nonlinear photonic crystal channel drop filter," Opt. Express 12, pp. 1605-1610, 2004.
[18]J. Huh, J. K. Hwang, H. Y. Ryu, and Y. H. Lee, “Nondegenerate monopole mode of single defect two-dimensional triangular photonic band-gap cavity,” Appl. Phys.92, pp. 654-659, 2002.
[19]H. A. Haus, Waves and Fields in Optoelectronics (Englewood Cliffs, NJ: Prentice-Hall, 1984), Chap. 7.
[20]F. Bouef et al., "0.248 μm^2 and 0.334 μm^2 Conventional Bulk 6T-SRAM bit-cells for 45nm node Low Cost-General Purpose Applications," in Proceedings of IEEE Conference on VLSI (Institute of Electrical and Electronics Engineers, Kyoto, pp. 130-131, 2005.
[21]A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett., vol. 24, pp. 711-713, 1999.
[22]S. Olivier, C. Smith, M. Rattier, H. Benisty, and C. Weisbuch, T. Krauss, R. Houdré and U. Oesterlé, “Miniband transmission in a photonic crystal coupled-resonator optical waveguide,” Opt. Lett., vol. 26, pp. 1019-1021, 2001.
[23]W. J. Kim, W. Kuang, and J. D. O’Brien, “Dispersion characteristics of photonic crystal coupled resonator optical waveguides,” Opt. Lett., vol. 11, pp. 3431-3437, 2003.
[24]A. Martínez, A. García, P. Sanchis, and J. Martí, “Group velocity and dispersion model of coupled-cavity waveguides in photonic crystals,” J. Opt. Soc. Am. A, vol. 20, pp. 147-150, 2003.
[25]M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely Large Group-Velocity Dispersion of Line-Defect Waveguides in Photonic Crystal Slabs,” Phys. Rev. Lett., vol. 87, pp. 253902-1-4, 2001.
[26]J. P. Dakin, “Multiplexed and distributed optical fiber sensors,” in Distributed Fiber Optic Sensing Handbook, (Ed. UK: IFS, 1990).
[27]A. D. Kersey, “Multiplexed fiber optic sensors,” in Distributed and Multiplexed Fiber Optic Sensors II, Proc. SPIE, vol. 1797, pp. 161-185, 1993.
[28]C. W. Kuo, C. F. Chang, M. H. Chen, S. Y. Chen, and Y. D. Wu, “A new approach of planar multi-channel wavelength division multiplexing system using asymmetric super-cell photonic crystal structures, ”Opt. Express, vol. 15, No. 1, pp. 198-206, 2007.
[29]S. C. Huang, W. W. Lin, M. H. Chen, S. C. Huang and H. L. Chao, “Crosstalk Analysis and system Design of Time-Division Multiplexering of Polarization-Insensitive Fiber Optic Michelson Interferometric Sensors, ”J. Light-wave Technol., vol. 14-6, pp. 1488-1500, 1996.
[30]J. L. Brooks, B. Boslehi, B. Y. Kim, and H. J. Shaw, “Time-domain addressing of remote fiber-optic interferometric sensor arrays,” J. Light-wave Technol., vol. LT-5, pp. 1014-1023, 1987.
[31]A. D. Kersey, A. Dandridge, and A. B. Tveten, “Time-division multiplexing of interferometric fiber sensors using passive phase-generate carrier interrogation,” Optics Lett., vol. 12, pp. 775-777, 1987.
[32]S. Lan, S. Nishikawa, H. Ishikawa, and O. Wada, “Design of impurity band-based photonic crystal waveguides and delay lines for ultrashort optical pulses,” J. Appl. Phys., Vol.90, pp.4321-4327, 2001.
[33]A. Martinez, J. Marti, J. Bravo-Abad, and J. Sanchez-Degesa,” Wavelength Demultiplexing Structure Based on Coupled-Cavity Waveguides in Photonic Crystals,” Fiber and Integrated Optics, Vol.22, pp. 151-160, 2003.
[34]M. Bayindir, B. Temelkuran, and E. Ozbay,” Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett., Vol.84, pp. 2140–2143, 2000.
[35]K. Guven, and E. Ozbay, “Coupling and phase analysis of cavity structures in two-dimensional photonic crystals,” Phys. Rev. B, Vol.71, pp. 085108-1-7, 2005.
[36]E. Ozbay, M. Bayindir, I. Bulu, and E. Cubukcu, “Investigation of Localized Coupled-Cavity Modes in Two-Dimensional Photonic Bandgap Structures,” IEEE J. Quantum Electron., Vol.38, pp. 837-843, 2002.
[37]G. P. Agrawal, Fiber-Optic Communication System (Wiley-Interscience, 1997).
[38]P. W. Milonni, Fast Light Slow Light and Left-Handed Light (MPG, 2005).
[39]L. H. Frandsen, A. V. Lavrinrnko, Jacob Fage-Pedersen, and Peter I. Borel, “Photonic crystal waveguide with semi-slow light and tailored dispersion properties,” Opt. Express, vol. 14, pp. 9444-9450, 2006.
[40]D. Mori, and T. Baba, “Wideband and low dispersion slow light by chirped photonic crystal coupled waveguide,” Opt. Express, vol. 13, pp. 9398-9408, 2005.
[41]T. Baba and D. Mori, “Slow light engineering in photonic crystals,” J. Phys. D: Appl. Phys., Vol. 40, No. 9, pp. 2659-2665, 2007.
[42]J. Li, T. P. White, L. O’Faolain, A. Geomez-Iglesias, and T. F. Krauss, “System design of flat band slow light in photonic crystal waveguides,” Opt. Express, vol. 16, pp. 6227-6232, 2008.
[43]T. Kawasaki, D. Mori, and T. Baba, “Experimental observation of slow light in photonic crystal coupled waveguides,” Opt. Express, vol. 15, pp. 10274-10281, 2007.
[44]S. Kim, I. Park, and H. Lim "Proposal for ideal 3-dB splitter-combiners in photonic crystal," Opt. Lett., 30, 257, 2005.
[45]M. Y. Teleste, and J. M. Yarrison-Rice "high efficiency photonic crystal based wavelength demultiplexer," Opt. Expr., 14, 7931, 2006.
[46]S. G. Johnson, J. D. Joannopoulos “Designing synthetic optical media: Photonic Crystals,” Acta Materialia 51, pp. 5823-5835, 2003.
[47]T. A. Birks, J. C. Knight, and P. St. J. Russell "Endlessly single-mode photonic crystal fiber," Opt. Lett. 22, pp. 961-963, 1997.
[48]R. Ramaswami and K. N. Sivarajan ”Optical Networks: A Practical Perspective”. San Francisco, CA: Morgan Kaufmann, 1998.
[49]C. W. Kuo, C. F. Chang, M. H. Chen, S. Y. Chen, and Y. D. Wu, “A new approach of planar multi-channel wavelength division multiplexing system using asymmetric super-cell photonic crystal structures, ”Opt. Express, vol. 15, No. 1, pp. 198-206, 2007.
[50]Y. D. Wu, K. W. Hsu, and T. T. Shih, “Thirty-two-channel Dense-Wavelength-Division Multiplexer based on Cascade Two-Dimensional Photonic Crystals Waveguide Structure,” J. of Optical Socity of America B, Vol. 24, No. 9 , pp. 2075-2080, 2007.
[51]W. Bogaerts, R. Baets, P. Dumon et al., "Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology", J. of Lightwave Technology, Vol. 23, pp. 401-412, 2005.
[52]K. L. Hall, J. D. Moores, K. A. Rauschenbach, W.S. Wong, E. P. Ippen and H. A. Haus “All-optical storage of a 1,25 Kb packet at 10 Gb/s”, IEEE Photonics Tech. Lett., Vol. 7, pp. 1093-1095, 1995.
[53]A. Liu, C. Wu, Y. Gong, P. Shum “Dual-loop optical buffer (DLOB) based on a 3 x 3 collinear fiber coupler” , IEEE Photon. Technol. Lett., Vol. 16, pp. 2129-2131, 2004.
[54]Z. Wang, and S. Fan “Compact all-pass filters in photonic crystals as the building block for high-capacity optical delay lines” Phys. Rev. E, 68, 066616, 2003.
[55]D. Mori, T. Baba “Dispersion-controlled optical group delay device by chirped photonic crystal waveguides”, Appl. Phys. Lett., Vol. 85, pp. 1101-1103, 2004.
[56]J. Joannopoulos, R. Meade, J. Winn “Photonic Crystals”, Princeton University Press, Princeton, 1995.