Hamilton体系辛半解析法及在非均匀电磁波导中的应用

力学中的Hamilton体系需用对偶变量来描述，而电磁场正好有电场和磁场这一对对偶变量．尝试将力学中的Hamilton体系理论应用于电磁波导的分析，以横向电场和磁场作为对偶变量，将电磁波导的基本方程导向辛几何的形式．基于Hamilton变分原理， 导出横向离散的半解析系统方程， 保持体系的辛结构．以非均匀波导为例， 求解了方程的辛本征值问题， 计算结果与解析解相当吻合．

Hamiltonian Symplectic Semi-Analytical Method and Its Application in Inhomogeneous Electromagnetic Waveguides

Dual vectors are applied in Hamilton system of applied mechanics. Electric and magnetic field vectors are the dual vectors in electromagnetic field. The Hamilton system method is introduced into the analysis of electromagnetism waveguide with inhomogeneous materials. The transverse electric and magnetic fields are regarded as the dual. The basic equations are solved in Hamilton system and symplectic geometry. With the Hamilton variational principle, the symplectic semi-analytical equations are derived and preserve their symplectic structures. The given numerical example demonstrates the solution of LSE mode in a dielectric waveguide.