Solvability of the boundary value problem associated with the wave diffraction by a layer filled with a Kerr-type nonlinear medium

TL;DR

This paper develops analytical and numerical methods to solve the boundary value problem for wave diffraction by a nonlinear Kerr medium layer, establishing conditions for unique solvability.

Contribution

It introduces a novel approach to analyze wave diffraction in Kerr media by reducing the problem to a nonlinear integral equation and deriving solvability conditions.

Findings

Established unique solvability conditions using the contraction principle.

Reduced the diffraction problem to a nonlinear integral equation.

Developed iterative solution techniques for the boundary value problem.

Abstract

The diffraction of a plane wave by a transversely inhomogeneous isotropic nonmagnetic linearly polarized dielectric layer filled with a Kerr-type nonlinear medium is considered. The analytical and numerical solution techniques are developed. The diffraction problem is reduced to a singular boundary value problem for a semilinear second-order ordinary differential equation with a cubic nonlinearity and then to a cubic-nonlinear integral equation of the second kind and to a system of nonlinear operator equations of the second kind solved using iterations. Sufficient conditions of the unique solvability are obtained using the contraction principle.