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研究生: 劉正禮
論文名稱: 一維及二維光子晶體光學性質之計算
Numerical Studies of Optical Properties of One-Dimensional and Two-Dimensional Photonic Crystals
指導教授: 吳謙讓
學位類別: 碩士
Master
系所名稱: 光電工程研究所
Graduate Institute of Electro-Optical Engineering
論文出版年: 2009
畢業學年度: 97
語文別: 英文
論文頁數: 79
中文關鍵詞: 光子晶體
英文關鍵詞: Photonic Crystals
論文種類: 學術論文
相關次數: 點閱:221下載:12
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  • 本篇論文主要是採用數值模擬的方法,研究一維及二維光子晶體的光學特性及應用。對於一維結構的光子晶體,我們透過轉移矩陣法來計算由超導層、介電層相互交替排列的週期組成,並求得其透射及反射的光學頻譜。利用模擬的結果,我們分析不同的相對週期厚度及入射角度對能帶分佈的影響,進一步歸納出各個變量在整體的結構中,所可能扮演的角色及造成的效應。在處理二維組成的光子晶體時,我們利用平面波展開法探求其能帶結構;並應用時域有限差分法,以光學模擬上常被使用的FDTD套裝軟體,進一步透析其電場、磁場、及能量在光子晶體中的傳播方式,以及各個分量在行進中隨時間和空間的變化。最後,我們將探討光通訊系統中,由光子晶體組成的小尺寸光學元件,例如:二維光子晶體波導、耦合共振光學波導、以及指向耦合器,其特有的電磁特性與相關的光學應用。

    In this thesis, we theoretically study the optical properties and their applications for one-dimensional and two-dimensional photonic crystals. In the one-dimensional photonic crystals (1DPCs) we use the transfer matrix method to calculate the transmittance and reflectance spectra for a superconductor-dielectric photonic crystal (SDPC). Based on the calculated results we investigate the photonic band structures as a function of film thickness and the angle of incidence as well. As for the two-dimensional photonic crystals (2DPCs), the optical properties will be explored by not only the plane wave expansion but FDTD method. In the final part, we design some useful two-dimensional photonic devices such as the photonic crystal waveguides (PCWs), coupled-resonator optical waveguides (CROWs), and director couplers (DCs).

    Chapter 1 Introduction 1.1_Foreword 06 1.2_Introduction to Photonic Crystals 07 Reference 08 Chapter 2 Basic Theories 2.1_Theory of Photonic Crystals 10 2.2_Plane Wave Expansion Method 11 2.3_Transfer Matrix Method 13 2.4_FDTD Method 16 2.5_An Introduction to Photonic Band Gaps 16 2.6_More on Photonic Band Gaps 20 Reference 22 Chapter 3 One-Dimensional Photonic Crystals---Using TMM 3.1_Analysis of Thickness-Dependent Optical Properties in a One-Dimensional Superconducting Photonic Crystal 24 3.2_Angle-Dependent Transmittance Spectra in a One- Dimensional Superconducting Photonic Crystal 33 Chapter 4 Two-Dimensional Photonic Crystals---Using FDTD 4.1_Introduction to FDTD 43 4.2_FDTD Method 44 4.3_Cell Size and Time Step 48 4.4_Absorbing Boundary Condition 49 4.5_Cases Study 50 4.6_Anti-Reflection Film of 1-D PC 72 4.7_Negative Refraction in HTSC PC 75 Reference 78 Chapter 5 Conclusion and Future Works 5.1_Conclusion 79 5.2_Future Works 79

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