电磁波导的半解析辛分析  

SYMPLECTIC SEMI-ANALYTICAL METHOD FOR ELECTRO-MAGNETIC WAVE GUIDE

作　　者：钟万勰[1] 

机构地区：[1]大连理工大学工程力学研究所,大连116023

出　　处：《力学学报》2003年第4期401-410,共10页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家重点基础研究基金(G1999032805)~~

摘　　要：根据电磁波导的Hamilton体系,辛几何可用于任意各向异性材料,而且便于处理不同区段的界面条件,横向的电场和磁场构成了对偶向量。基于Hamilton变分原理用半解析法进行横向离散应当保持体系的辛结构。离散后可以运用应用力学的有效算法,求解其辛本征值问题。每段波导可以引入两端Riccati矩阵,用精细积分法求解其方程组。Based on the Hamilton formulation for electro-magnetic wave-guides, the symplectic formulation can be applied to arbitrary an isotropic material, and also easier for treating interface conditions between different materials. The transverse electric and magnetic components are dual vectors to each other. The semi-analytical transverse discretisation under the variational principle for Hamilton system should keep its symplectic structure unchanged. Thereafter, the effective algorithms in applied mechanics can be invoked. The compensation terms are proposed to treat the discontinuity along the interfaces between adjacent elements for solving the so-called variational crime problem. Then effective algorithms in applied mechanics can be transplanted to solve the symplectic eigenvalue problem. For each wave-guide segment, the two-end Riccati matrices are introduced and the precise integration algorithm can be invoked to solve the respective equations.

关 键 词：电磁波导 半解析法 辛分析 横向离散 本征值 对偶向量 各向异性材料 哈密顿体系 应用力学 

分 类 号：O441[理学—电磁学] O39[理学—物理]