三角晶格光子晶體缺陷態之研究

Abstract

本研究是利用平面波展開法(plane wave expansion method)以及超晶格(Supercell)的概念，來計算二維光子晶體(photonic crystal)中的缺陷態(defect state)。研究的對象是具有缺陷的三角晶格光子晶體，我們以上述方法計算了光子能帶結構、能態密度及場分佈，並探討缺陷態能階與缺陷的半徑及介電係數之關係。這項研究除了有助於分析由缺陷構成的共振腔，未來推廣至包含離面傳遞的計算後，也能應用於空心光子晶體光纖的研究上。

We employed the plane-wave expansion method and the concept of supercell to study the defect state in two dimension photonic crystal of hexagonal lattice. The defect is defined by a different radius or dielectric constant in an otherwise perfect photonic crystal. We calculated the band structures to see how the defect modes evolve with these parameters. The density of states was also worked out to estimate the corresponding Q factor, which can also be perceived in the localized field distribution. These approaches can be easily adapted to systems containing an arbitrary defect. They can be used to analyze the photonic crystal fiber after being extended to the off-plane calculations in the future.