On the solvability of the problem of electromagnetic wave diffraction by a layer filled with a nonlinear medium

The problem of diffraction of a polarized electromagnetic wave by a layer filled with a nonlinear medium is considered. The layer is located between two half-spaces with constant permittivities. Two widely used types of nonlinearities: saturation nonlinearity and Kerr nonlinearity are considered. It is proved that the results on the solvability of the problems in these cases are qualitatively different: in the case of saturation nonlinearity, there are conditions under which the diffraction problem has a unique solution and, in the case of Kerr nonlinearity, the diffraction problem always has an infinite set of solutions. Analytical and numerical methods for solving this kind of problems are developed. Numerical results are presented.