一維及二維光子晶體光學性質之計算

Abstract

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).