平板光子晶體之全方向反射特性

Abstract

本文主要在探討平板光子晶體之全方向反射特性,首先對光子晶體的概念和理論作基本的介紹,並針對平板光子晶體,利用轉移矩陣法,以不同結構參數,不同入射角等情形來探討反射頻譜和帶隙結構圖,而帶隙結構圖又可分為通帶和禁帶,由分析結果顯示,當結構週期數夠多時,反射頻譜中反射率為1的頻率範圍,會對應到帶隙結構圖中的禁帶頻率範圍。在特定的參數條件下,平板光子晶體會有全方向反射產生,首先利用帶隙結構圖,討論結構厚度在四分之ㄧ波長時所求得的全方向能隙,並利用數值分析之數值解和近似解析解來分別探討全方向能隙的頻寬,邊界和中心頻率。而不同的結構厚度,全方向能隙的大小也會不同,其最大值也不一定發生在厚度為四分之ㄧ波長時，因此由改變厚度比例，找到全方向能隙之最大值，探討最大值的頻寬、中心頻率、和所對應的厚度, 並改變折射率之參數來觀察全方向能隙特性的趨勢，以便於設計發生全方向能隙時所需要的結構參數。

In this thesis, the properties of omnidirectional reflection of planar photonic crystals are investigated. At first, we introduce the concept theories of photonic crystals, and then discuss transfer matrix method with the characteristics of reflectance spactra and band structures by changing the parameters of planar photonic crystals and incident angle. The band structures can be divided into allow band and forbidden band. The analysis showed that if the number of periods is high enough, the frequency range of reflectance equaling to one of reflectance spectrum corresponded to the forbidden band of band structure. Under centain parameters, the planar photonic crystals will produce the omnidirectional reflection. It could be investigated the omnidirectional band gap by the bandstructure at the thickness of structure in quarter-wave wavelength. We can find the gapwidth, boundary, and center frequency of omnidirectional band gap by using approximate analytic solution and numerical solution. When the thickness of structure changes, the size of omnidirectional band gap follows, also the maximum does not certainly occur at the thickness in quarter-wave wavelength. Therefore, we can change the thickness ratio to find the maximum gapwidth of omnidirectional band gap and investigate the maixmum gapwidth, central frequency as well as the corresponding thickness. Furthermore we change the refractive index of parameters to observe the trend of the characteristics of omnidirectional band gap so that we can confine the parameters of structure that meets the condition of omnidirectional band gap.