光子晶体中平面波展开法的新观点
A novel view of plane wave expansion method in photonic crystals
摘要：
提出了一种基于简单平面波展开的方法，可以方便地求解真空与半无限大光子晶体的界面问题。该方法的目的是找到完整的一套所有的本征函数，传播或倏逝，在一个固定的频率的翻译运营商$\{{\bf T_R} \}$。利用这些本征函数及其本征值，可以确定透射波和反射波。介绍了二维光子晶体的两种应用。第一种是确定真空-光子晶体界面法线方向的选择规则，以在带隙频率下获得最大的衰减效果。第二个是计算光从真空入射到半无限大光子晶体的透射率和反射率。作为一个例子，我们重新计算了K. Sakoda等人的结果与他们的一致。
英文摘要：
We propose a method derived from the simple plane wave expansion that can easily solve the interface problem between vacuum and a semi-infinite photonic crystal. The method is designed to find the complete set of all the eigenfunctions, propagating or evanescent, of the translation operators $\{{\bf T_R} \}$, at a fixed frequency. With these eigenfunctions and their eigenvalues, the transmitted and reflected waves can be determined. Two kinds of applications are presented for 2D photonic crystals. The first is a selection rule for determine the normal direction of the vacuum-photonic crystal interface to achieve the highest attenuation effect at a gap frequency. The second is to calculate the transmittance and reflectance for a light incident from vacuum to an semi-infinite photonic crystal. As an example we recalculate a system studied previously by K. Sakoda et al. and get results in agreement with theirs.
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