光子晶體之缺陷計算與研究

Abstract

利用K.P理論推導光子在光子晶體之現象，我們發現由於周期性介電物質排列造成入射光具有準粒子特性，也因為光子晶體之儲能效應，光子在光子晶體中具有靜止質量。缺陷的產生使得光子晶體具有束縛位能井，其位能深度和準光子靜止質量以及缺陷介電常數有著正相關，此光子晶體性質和量子力學中電子束縛態相似：在一維系統中無論位能井多窄束縛態仍存在;值得注意的是此性質但卻無法用一般共振腔能解釋。 藉由模糊邊界法，和利用Dyson方程式計算Green函數，我們提供一個很有效率的方法去計算光子晶體中的缺陷態以及錯位問題，此方法大量節省記憶體容量以及CPU處理時間，讓我們可由較少平面波數展開卻有精確計算結果。這是第一次藉由Dyson方程式來計算光子晶體的缺陷態，並得到良好的計算結果和實驗的比較。

Using the k.p theory to study photons in a photonic crystal (PC), we found the incident photon excites a quasi-particle (QP) of photon from the periodic background field. This QP contains an inertial mass, which is due to energy-storing mechanism occurring in the photonic crystals. The defect in photonic crystal will introduce an attractive potential that is linearly proportional to the product of the inertial mass and the normalized dielectric defect. It is similar to quantum mechanics that the trapping of QP can successfully explain the trapping effect in defects, which cannot be explained by microcavity theory. By smoothing the sharp varying dielectric constant and using the Green’s function with Dyson’s equation method, we construct an efficient method to calculate the disorder and defect problem in 2D photonic crystals. For the first time, we successful apply the Dyson’s equation to solve the defect modes in photonic crystal.