Numerical Simulation of the Planar waveguide

The paper is devoted to the analysis of the TE-wave propagation in a planar waveguide with variable permittivity. The setting is reduced to a transmission eigenvalue problem for an ordinary differential equation where the spectral parameter is the wave propagation constant. For the computation of eigen-values the shooting method is applied in the form specifically developed for this class of problems. The method allows one to calculate propagating, evanescent, and complex surface and leaky waves. A variety of numerical results illustrating the method is presented.