本論文主要在探討如何藉著將光子晶體波導與各種不同型態之點缺陷耦合以產生濾波效果。藉由觀察不同結構之穿透率頻譜圖將可設計最佳化的寬頻濾波器。
論文之分析步驟如下。首先以平面波展開法求出所欲分析光子晶體之頻帶，以找出帶隙，接下來導入缺陷態，再使用多重散射法求出帶有缺陷光子晶體結構的頻率－穿透率圖及場圖，進而由頻率－穿透率圖可求出點缺陷共振腔的Q factor，最後針對模擬的結果分析各結構的場圖狀況、缺陷所造成頻率－穿透率圖的變化以及共振腔Q factor等等，以找出最佳的設計。
而思考邏輯基本上依循著Plan-Do-Check-Act的cycle持續對寬頻濾波器的濾波效果做改善。

In this thesis we study the problem of how to design a wideband band-pass filter by using waveguide-defect coupling mechanism. The filter consists of a photonic crystal waveguide and several point defects. By observing the transmission-frequency curves of various configurations , we can modify the structure and finally find the optimized design of the filter.
The analytic procedure is as follows:
1. Using plane-wave expansion method to determine the photonic crystal structure’s band gap, which is the working frequency region for the defects and the waveguide.
2. Using multiple scattering method to determine the field pattern and transmission-frequency diagram for photonic structures with defects. We can calculate the cavity’s Q factor according to transmission-frequency diagram.
3. Finally, we analyze the simulation results of field patterns, the transmission-frequency diagram, and the relations between the defect sizes and transmission-frequency diagram and cavity’s Q factor to find the optimal design.
Basically, we follow the “Plan-Do-Check-Act” PDCA cycle to contineously improve the performance of the photonic band-pass filter.

[1] 李正中， “ 自然界與科技領域中的光學薄膜 - 從色彩顯示談起 ” 科儀新知 , 第二十五卷 , (2004), pp. 6-13
[2]E. Yablonovith, “Inhhibited Spontaneous Emission in Solid-State Physics and Electronics” Phys. Rev. Lett. 58,2059(1987)
[3]S. John, “Strong localization of photons in certain disordered dielectric superlattices” 58,2486(1987)
[4]Yoel Fink, Joshua N. Winn, Shanhui Fan, Chiping Chen, Jurgen Michel, John D. Joannopoulos, Edwin L.Thomas*, “A Dielectric Omnidirectional Reflector”
[5] ”Microcavities in photonic crystals: Mode symmetry, tenability, and coupling efficiency” VOLUME54, NUMBER11 / PHYSICAL REVIEW B
[6] “Coupling characteristics of localized photons in two-dimensional photonic crystals” PHYSICAL REVIEW B 67, 073103 (2003)
[7] “Waveguides, resonators and their coupled elements in photonic crystal slabs” 19 April 2004 / Vol. 12, No. 8 / OPTICLA EXPRESS
[8] “Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals” PHYSICAL REVIEW B, VOLUME 64, 155113
[9] “Ministop bands in single-defect photonic crystal waveguides” PHYSICAL REVIEW E, VOLUME 64, 055603(R)
[10] “Mini-stopbands of a one-dimensional system: The channel waveguide in a two-dimensional photonic crystal” PHYSICAL REVIEW B, VOLUME 63, 113311(2001)
[11]”Coupled-resonator optical waveguide: a proposal and analysis “ June 1,1999/Vol. 24, No.11/OPTICAL LETTERS
[12] “Mach-Zehnder interferometer employing coupled-resonator optical waveguides” March 15, 2003 / Vol. 28, No. 6 / OPTICLAL LETTERS
[13] “Experimental Results on Adiabatic Coupling Into SOI Photonical Crystal Coupled-Cavity Waveguides” IEEE PHOTONICS TECHNOLOGY LETTERS, VOL.17, NO. 6, JUNE 2005
[14] “Microring Resonator Channel Dropping Filters” JPURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 15, NO. 6, JUNE 1997
[15] “Channel Drop Tunneling through Localized States” PHYSICS REVIEW LETTERTS VOLUME 80, Number 5, 2 February 1998
[16] “Channel drop filters in photonic crystal” 6 July 1998 / Vol. 3, No. 1 / OPTICAL EXPRESS
[17] “Theoretical analysis of channel drop tunneling process” PHYSICAL REVIEW B / VOLUME 59, NUMBER 24 / 15 JUNE 1999
[18] Pi-Gang Luan and Zhen Ye, Two dimensional photonic crystals, preprint,http://140.115.40.128/publication/P03.pdf (July 10, 2004)
[19] Bikash C. Gupta, Chao-Hsien Kuo, and Zhen Ye, Propafation inhivition and localization of electromagnetic waves in two dimensional random dielectric systems, Phys. Rec. E69, 066615(2004)
[20] 欒丕綱&陳啟昌,光子晶體(從蝴蝶翅膀到奈米光子學).五南出版社,台灣,2005.
[21] G. R. Fowles, Introduction to modern optics, Dover Publications,2nd Ed.,1989
[22] “Introduction to Solid State Physics” Charles Kittel 8th edition
[23] L. S. Chen, C. H. Kuo, Z. Ye, “Acoustic miaging and collimating by slabs of sonic crystals made from arrays of rigid cylinders in air”, Applied Physics Letters, (2004)
[24] George B. Arfken, Hans J. Weber, “Mathematical Methods for physicists”, ACADEMIC, (1966)
[25] “Band-dropping via coupled photonic crystal waveguides” 4 November / Vol. 10, No.22 / OPTICS EXPRESS
[26] “光子晶體簡介” 光學工程第九十五期
[27] “A Dispersion Compensator Using Coupled Defects in a Photonic Crystal” IEEE J. Quantum Electron. 38, 825(2002)
[28] “Microcavities in photonic crystals: Mode symmetry, tunability, and coupling efficiency” PHYSICAL REVIEW B VOLUME 54, NUMBER11(1996)
[29] “Coupling characteristics of localized photons in two-dimensional photonic crystals” PHYSICAL REVIEW B 67, 073103 (2003)
[30] “Higher Order Optical Resonant Filters Based on Coupled Defect Resonators in Photonic Crystals” JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 23, NO. 5, MAY 2005
[31] “Tunable Study of Frequency Selective Filter Based on Photonic Crystal” Progress In Electromagnetics Research Symposium 2005