Two Iterative Methods for Solving a Volumetric Singular Equation for a Nonlinear Diffraction Problem in a Semi-infinite Rectangular Waveguide

The goal of this study is to construct a nonlinear electromagnetic field inside a waveguide. We assume that a body is located in a semi-infinite rectangular waveguide and that an electromagnetic field propagates inside the body. Iterative algorithms based on solving a volumetric nonlinear singular integral equation are proposed and described. Numerical results are presented. The boundary value problem for the system of Maxwell’s equations is reduced to a volumetric singular integral equation. An iterative method for creating a nonlinear medium inside the body with a dielectric structure is constructed. The problem is solved numerically. The size of the matrix obtained in the calculation is about 15 000 elements. The internal convergence of the iterative methods are demonstrated. The curves illustrating the field distribution inside the nonlinear body are plotted. A numerical method for finding wavenumbers that make it possible to create a nonlinear field is proposed and implemented.