电子学报 ›› 2015, Vol. 43 ›› Issue (10): 1898-1903.DOI: 10.3969/j.issn.0372-2112.2015.10.003

• 学术论文 • 上一篇    下一篇

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

杨红卫, 王改页, 黄翠莺, 孟珊珊   

  1. 北京工业大学应用数理学院, 北京 100124
  • 收稿日期:2014-03-28 修回日期:2015-02-06 出版日期:2015-10-25 发布日期:2015-10-25
  • 作者简介:杨红卫 女,1967年8月出生于北京市.现为北京工业大学应用数理学院副教授、硕士生导师.主要研究方向为计算物理学.E-mail:yanghongwei@bjut.edu.cn王改页 女,1989年10月出生于河北省邯郸市,研究生.主要研究方向为计算电磁学.E-mail:wanggy@emails.bjut.edu.cn

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

YANG Hong-wei, WANG Gai-ye, HUANG Cui-ying, MENG Shan-shan   

  1. College of Applied Sciences, Beijing University of Technology, Beijing 100124, China
  • Received:2014-03-28 Revised:2015-02-06 Online:2015-10-25 Published:2015-10-25

摘要:

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.

关键词: 各向异性, 光子带隙(PBG), 谱单元, 精细积分法

Abstract:

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.

Key words: anisotropic, photonic band-gap (PBG), spectral element method, precise integration method

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