MAXWELL'S EQUATIONS WITH NONLINEAR INHOMOGENEOUS CONSTITUTIVE RELATION: GUIDED WAVES IN A FILM FILLED WITH INHOMOGENEOUS KERR MEDIUM

A transmission eigenvalue problem for nonlinear Maxwell's equations that describes propagation of monochromatic transverse electric waves in a dielectric film having cubic inhomogeneous permittivity sandwiched between two half-spaces with constant permittivities is considered. It is proved that even if the nonlinearity coefficient is small, there exist guided waves with as well as without linear counterparts. The found theoretical results predict existence of a new type of nonlinear guided waves. The paper suggest an original mathematical approach that allows one to determine asymptotic distribution of the eigenvalues and zeros of the eigenfunctions. Numerical results are given to illustrate the theoretical findings.

Automated summary

This paper considers a transmission eigenvalue problem for nonlinear Maxwell's equations, which describes the propagation of monochromatic transverse electric waves in a dielectric film with cubic inhomogeneous permittivity sandwiched between two half-spaces with constant permittivities. It is proved that guided waves exist with and without linear counterparts, even if the nonlinearity coefficient is small. The theoretical results suggest the existence of a new type of nonlinear guided waves. The paper proposes an original mathematical approach to determine the asymptotic distribution of the eigenvalues and zeros of the eigenfunctions. Numerical results are provided to illustrate the theoretical findings.