臺灣博碩士論文加值系統

在本文中我們使用平面波展開法(plane-wave expansion)來求取二維光子晶體中的光子能態密度(Density of States)和本徵模態的場分佈(Distribution of Eigenmode)。光子能態密度與光子晶體的透射率及光學性質有密切的關係，而本徵模態的場分佈不但有助於分析能隙的形成，結合光子能態密度後，還可以得到局部光子能態密度(Local Density of States)的分佈。局部光子能態密度和位於光子晶體內活性介質的自發輻射衰減率有密切的關係，它對於活性介質(active medium)的嵌入位置提供了相當重要的參考，這種利用改變空間結構來影響活性介質電偶極自發輻射衰減率的方法，即為Purcell effect。在本文中我們對能帶結構上應用價值較高的特定能態，計算出相對應的本徵模態場分佈和區域光子能態密度，以做為未來研究主動光能隙系統如光子晶體發光二極體等發光性質的依據。

In this thesis, we employed the plane-wave expansion method to study the density of states (DOS) and the distribution of eigenmodes for two dimensional photonic crystals. The DOS is close related to the transmission spectrum and other optical properties of photonic crystals. The distribution of eigenmodes is not only helpful in analyzing the formation of band gaps but is also essential, together with DOS, in the calculation of the local density of states. According to Purcell effect, the radiation pattern of active medium can be altered by the change of the cavity as well as the location of the medium. Therefore the local density of states is crucial in determining the location to insert active medium in the photonic crystal and it is closely related to the spontaneous emission decay rate of active medium in the photonic crystal. We have calculated the distributions of eigenmodes and LDOS of certain energy states which may be of interest in further application. We plan to incorporate these investigations to study the light-emitting properties active photonic band-gap systems such as photonic-crystal light emitting diodes.

第一章 導論 1
1.1光子晶體簡介 1
1.2光子晶體之應用 3
1.3 章節概述 9
第二章 理論基礎與計算方法 10
2.1光子能帶結構原理 10
2.2能帶結構與自發輻射 16
第三章 二維光子晶體之本徵模態 22
3.1 正方晶格 22
3.1.1 由圓柱所組成之正方晶格 22
3.1.2 由方柱所組成之正方晶格 26
3.1.3 完全能隙 30
3.2三角晶格 35
3.3 蜂巢晶格 39
3.4 群論對於本徵模態之分析 42
第四章 二維光子晶體之能態密度 55
4.1.1 正方晶格 55
4.1.2 三角晶格 61
4.1.3 蜂巢晶格 63
4.2光子能態密度與本徵模態之對稱性 65
4.3局部光子能態密度 67
4.3.1正方晶格 67
4.3.2 三角晶格 70
4.3.3 蜂巢晶格 72
第五章 結語 74
參考文獻 76
附錄一:圓柱組成之正方晶格本徵模態分佈Fortran90程式碼 78
附錄二:圓柱組成之三角晶格能態密度分佈Fortran90程式碼 85
附錄三:圓柱組成之正方晶格局部能態密度分佈Fortran90程式碼 91
附錄四:圓柱組成之三角晶格局部能態密度分佈Fortran90程式碼 99

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