电磁波导的半解析辛分析

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．

SYMPLECTIC SEMI-ANALYTICAL METHOD FOR ELECTRO-MAGNETIC WAVE GUIDE

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.