Transverse Electric Guided Wave Propagation in a Plane Waveguide with Kerr Nonlinearity and Perturbed Inhomogeneity in the Permittivity Function

Abstract

The paper focuses on the problem of transverse electric wave propagation in a plane-shielded waveguide filled with a nonhomogeneous and nonlinear (Kerr) medium. The nonlinear part of the permittivity is characterized by the Kerr law in the focusing regime, while its linear part is a constant that is perturbed by a small continuous function. Such perturbation can be considered to be an attempt to take into account the inevitable presence of impurities in the medium, causing slight deviations in the dielectric permittivity. In the paper, the existence of solutions to the considered problem is proved, including solutions with and without linear counterparts. Some numerical results are presented as well.