二維光子晶體全反射帶隙結構之研究

Abstract

本文主要以平面波展開法討論二維系統中的不同結構、不同元素變化對於光子晶體全方向能隙所產生的影響。首先，對於二維系統的光子晶體其基本理論做介紹以及平面波展開法在光子晶體能帶分析中的運作方式，而後利用平面波展開法針對不同晶格以及元素探討其不同的能隙特性。而對於每種不同的參數設定，可以發現在其中具有一些相似性及趨勢，而這些特性可以提供在設計元件上很大的助益，能針對不同性能需求很快的找到發生全方向能隙的參數設定。在二維光子晶體中，較典型的晶格型狀可以分為方形晶格、三角形晶格以及蜂巢狀晶格；在結構方面，也可以分成是柱狀或是孔洞結構；極化方式可以分為TE mode以及TM mode;在元素選擇方面，分別討論圓形元素、方形元素以及六角形元素。再來，對於近年來蓬勃發展的複雜形式的單位晶胞定義形式介紹，以及其能帶結構的討論。最後則是提出結論以及未來展望的部分。

The main purpose of this thesis is to observe and discuss the results obtained by changing different structures and elements of two-dimensional photonic crystals using plane wave expansion method (PWEM). First, the basic introduction of photonic crystals and method of calculating the band structures by PWEM will be presented. Then, the discussion of results of different structures and different elements will be introduced. For all kinds of parameters, we discover the familiar characteristics of them, these characteristics can provide benefits when designing is requested. The typical lattices of two dimensional photonic crystals are square lattice, triangular lattice and hexagonal lattice(honeycomb). The structure types can be hole or dielectric rod, the shape of elements can be circle, square and hexagon , and there are also two different kinds of polarization: TE mode and TM mode. Third, introductions of several kinds of complex structures and their band diagrams are presented.