Solving the propagation of electromagnetic wave in a simple two-dimensional inhomogeneous media based on symplectic geometric theory

A new symplectic geometrical high-frequency approximation method for solving the propagation of electromagnetic waves in the two-dimensional inhomogeneous media is presented in this paper. The propagating caustic problem of electromagnetic wave is translated into non-caustic problem by the coordinate transform on the symplectic space. The high-frequency approximation solution that includes the caustic region is obtained with the method combining the geometrical optics. The drawback that the solution in the caustic region can't be obtained with geometrical optics is overcome by this method. The results are compared with those obtained by finite elements method; it proves to be satisfactory.