Hsu Sen-Ming, Chang Hung-Chun
Opt Express. 2007 Nov 26;15(24):15797-811. doi: 10.1364/oe.15.015797.
A full-vectorial finite element method based eigenvalue algorithm is developed to analyze the band structures of two-dimensional (2D) photonic crystals (PCs) with arbitray 3D anisotropy for in-planewave propagations, in which the simple transverse-electric (TE) or transverse-magnetic (TM) modes may not be clearly defined. By taking all the field components into consideration simultaneously without decoupling of the wave modes in 2D PCs into TE and TM modes, a full-vectorial matrix eigenvalue equation, with the square of the wavenumber as the eigenvalue, is derived. We examine the convergence behaviors of this algorithm and analyze 2D PCs with arbitrary anisotropy using this algorithm to demonstrate its correctness and usefulness by explaining the numerical results theoretically.
开发了一种基于全矢量有限元方法的特征值算法，用于分析具有任意三维各向异性的二维光子晶体（PC）在平面波传播中的能带结构，其中简单的横向电（TE）或横向磁（TM）模式可能不明确。通过同时考虑所有场分量，而不将二维光子晶体中的波模解耦为TE和TM模式，推导了一个以波数平方为特征值的全矢量矩阵特征值方程。我们研究了该算法的收敛行为，并使用该算法分析具有任意各向异性的二维光子晶体，通过理论解释数值结果来证明其正确性和实用性。
