An algorithm for determination of the amplitudes of reflected and transmitted waves in the case when counterpropagating waves are incident on a multilayer stepwise inhomogeneous structure

A simple algorithm is proposed for derivimg analytical expressions for the amplitudes of reflected and transmitted waves in the case when two 1D counterpropagating waves are incident on a multilayer stepwise inhomogeneous structure. Wave amplitudes are analytically expressed for structures consisting of three, four, and five layers. The proposed algorithm is applied to solve numerically the problem of wave propagation in an inhomogeneous structure where the wave number linearly changes along the structure’s length. The algorithm involves approximation of a smooth inhomogeneity by a step one. A criterion and conditions are obtained for the applicability of the step approximation for the investigation of wave propagation through inhomogeneous media with smoothly varying parameters. It is shown that the algorithm can be applied to problems on propagation of electromagnetic waves in the cases of the normal and oblique incidence.