基于Hamilton体系的辛半解析法在各向异性电磁波导中的应用

力学中的Hamilton体系使用对偶变量来描述问题，而电磁场正好有电场和磁场这一对对偶变量。本文将力学中的Hamilton体系应用到电磁波导问题。根据电磁波导的Hamilton体系理论，辛几何可用于任意各向异性材料。将横向的电场和磁场构成对偶向量，基于Hamilton变分原理做半解析横向离散，并保持结构辛体系。本文以各向异性材料电磁波导为例，求解了问题的辛本征值，得到了镜像线的色散曲线。

Hamiltonian symplectic semi-analytical method and its application in anisotropic electromagnetic waveguide

Dual vectors are applied in Hamilton system of applied mechanics.Electric and magnetic field vectors are the dual vectors in electromagnetism.In this paper,the Hamilton system method is introduced into the analysis of electromagnetic waveguide problem.Applying the Hamilton system theory in electromagnetic field,symplectic geometry can be used in various anisotropic materials.The transverse electric and magnetic fields compose of the dual.With the Hamilton variational principle,the symplectic semi-analytical equations are derived and preserve their symplectic structures.The numerical example of anisotropic electromagnetic waveguide is given.The symplectic eigenvalues are derived.The dispersion curve of image is obtained.