Work

Coupled Electromagnetic Wave Propagation in A Waveguide With Nonlinear Permittivity: Nonlinear Perturbation Approach And Existence of Nonlinearizable Solutions

Year: 2025

Type: article

Abstract: ABSTRACT We study propagation of a sum of two electromagnetic waves of the same frequency in a plane shielded waveguide with anisotropic nonlinear permittivity. Since the permittivity is nonlinear, then the sum of waves forms a coupled nonlinear wave. The main problem is to prove that the waveguide supports coupled nonlinear guided waves. The problem is formulated for Maxwell's equations and then is reduced to a specific type of nonlinear eigenvalue problems. Existence of the guided waves is proved using a nonlinear perturbation approach. Using this approach it is proved existence of solutions without linear counterparts. We also present numerical results that, on the one hand, illustrate the theoretical findings and, on the other hand, show that there are solutions that cannot be found using the developed approach.

Source: Studies in Applied Mathematics

DOI: 10.1111/sapm.70152

Authors: Valeria Martynova, Dmitry Valovik

Institution: Penza State University

Language: English

Topic: Nonlinear Photonic Systems

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: bronze

Funder: Russian Science Foundation

Award: G5243794380