基于半解析谱元法的各向异性介质PBG结构传输特性的研究

将精细积分方法与谱单元法结合,对含有各向异性介质的波导介质层光子带隙(PBG)结构的传输特性进行了研究.从矢量波动方程相对应的单变量变分形式出发,对含有各向异性介质波导横截面采用谱单元进行离散,引入对偶变量,将单变量变分原理导入到哈密顿体系,利用精细积分法求出出口刚度矩阵.数值算例将半解析谱元法与常规有限元法、半解析有限元法进行了比较,表明本文方法具有高精度、高效率的特点,而且计算精度随着谱单元阶数的增加呈指数增长.

Research on Transmission Characteristics of an Anisotropic Dielectric PBG Structures Based on Semianalytical Spectral Element Method

Precise integration method combined with the spectral element is used to simulate and analyze the stop-band characteristic of anisotropic dielectric layer photonic band-gap (PBG) structures in waveguide.From the variational principle based on single variable corresponding to the vector wave equation, 2-D spectral elements are employed to discretize the cross section of the layered structure, which contains anisotropic dielectric.Introducing the dual-variables, the variational principle is cast into the Hamiltonian system, and then the high precision integration method is utilized to perform the stiff matrices.Compared with conventional finite element method and semianalytical finite element method, numerical results demonstrate that the semianalytical spectral element method is more accurate and efficient for anisotropic PBG structures analysis, and it can achieve spectral accuracy with the increase of interpolation degrees of basis functions.