多重散射法在光子晶體與其表面模態之應用

Apply multiple-scattering method to photonic crystals and their surface modes

吳俊平(Jun-Ping Wu)

指導教授 ： 李瑞光

國立清華大學/電機資訊學院/光電工程研究所/碩士(2007年)

摘要

本篇論文主要是研究如何以多重散射法來計算二維光子晶體的特性。
本論文總共分為三個部分，第一部分包括光子晶體的簡介和光子晶體的數值計算。第二部分介紹在本文中所用的數值方法，將多重散射法作詳細的推論。
多重散射法是一種非常直接且方便的數值方法，多重散射法主要的缺點是他被限制在處理每些特殊的結構。二維必須是圓柱體，三維必須是球體。
最後，我們使用多重散射法來計算一些例子。包括:兩個相同圓柱體在E-polarized light下的散射圖、分析有限二維光子晶體排列的穿透頻譜、ㄧ個缺陷和兩個缺陷光子晶體排列的穿透頻譜和其共振模態。
利用平面波展開法，我們計算出二維光子晶體六角形排列的光子能帶結構。和由多重散射法求出的穿透頻譜在強烈衰減的頻率範圍跟平面波展開法求出的光子能隙相符。

關鍵字

光子晶體 ； 多重散射法

並列摘要

The main purpose of this thesis is to employ the multiple scattering method to calculate the propertys of two-dimensional photonic crystals. The thesis has divided into three parts, the first part includes the introduction of photonic crystal and numerical computation of photonic crystal. The second part we have introduction of numerical computation in this thesis,we will deduce multiple scattering method more detail. The multiple scattering method is very convenient and directly numerical method,but it has main disadvantage which limit to special geometry. 2D must be cylindric,3D must be spheric. Finally,we use multiple scattering method to calculate some example. Include : scattering diagram of a set of two identical dielectric circular cylinders、analysis transmission spectra of finite 2-D photonic crystals、transmission
spectra of 2D photonic crystals with one defect and two defects and their resonant mode. By using plane-wave method, we calculate the band structure of two-dimensional photonic crystals in a hexagonal array with dielectric rods. And use multiple scattering method to calculate transmission spectra, a strong attenuation of the transmitted wave is seen in the frequency range that accords well the photonic band gap obtained by the plane-wave method.

並列關鍵字

photonic crystals ； multiple scattering method

參考文獻

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