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