Cheng Xiao-liang, Yang Jing
J Opt Soc Am A Opt Image Sci Vis. 2013 Nov 1;30(11):2314-9. doi: 10.1364/JOSAA.30.002314.
This paper is devoted to a numerical algorithm for the maximization of band gaps in two-dimensional photonic crystals in square lattices. We first apply the finite element method to solve the eigenvalue problem, then use the piecewise constant level set (PCLS) method to maximize the band gaps. The PCLS method is very powerful for representing and modeling regions of different structures. Extremely large gaps are realized with gallium arsenide material, for transverse magnetic field (TM), transverse electric field (TE), and for complete band gaps. When the mean gap frequency is below 1, the biggest gap is about 0.2922 for the TE.
本文致力于一种用于最大化方形晶格二维光子晶体带隙的数值算法。我们首先应用有限元方法来求解特征值问题，然后使用分段常数水平集（PCLS）方法来最大化带隙。PCLS方法在表示和建模不同结构区域方面非常强大。对于横向磁场（TM）、横向电场（TE）以及完全带隙，使用砷化镓材料实现了极大的带隙。当平均带隙频率低于1时，对于TE模式，最大带隙约为0.2922。
