变截面电磁波导的辛分析

电磁波导的求解可将基本方程导向Hamilton体系、辛几何的形式。横向的电场和磁场构成了对偶向量。辛体系便于处理不同介质波导的界面连接条件。正则对偶方程、分离变量法、Hamilton算子矩阵本征值问题、共轭辛正交归一关系、本征解的展开定理等整套理论，可以适用于多种波导的课题，有利于不同截面的波导连接、以及与共振腔的连接等。本文分析了两段不同材料不同截面对接的平面波导作为例题，表明辛体系用于波导的分析是有力的。

Symplectic Analysis for Electro-magnetic Wave Guide with Varied Cross Sections

The solution of electro-magnetic wave-guide problems can be derived to Hamilton system form and using symplectic mathematics. The transverse electric and magnetic vector components compose the dual vectors of Hamilton system formulation. One of the merit of symplectic system is easier for treating interface conditions between wave-guide segments with different materials connected longitudinally. The whole set of methodology, which includes method of separation of variables, the eigen-problem for Hamilton operator matrix, the adjoint symplectic ortho-normality relationship and the eigen-function expansion method, etc. , can be used to various wave guide problems. The problem of connection of two wave-guide segments with different materials and staged cross sections is solved for demonstration.