SOLVING THE DIRECT AND INVERSE DIFFRACTION
PROBLEMS ON FLAT OBJECTS WITH DIFFERENT TYPES OF FIELD NONLINEARITY 

Andrey O. Lapich, Assistant of the sub-department of mathematics and supercomputer modeling, Penza State University (40 Krasnaya street, Penza, Russia) lapich.a@yandex.ru

Background. The aim of the work is to solve the inverse problem of diffraction on flat objects. Materials and methods. The initial problem is reduced to solving an integral equation. This equation will be solved numerically. When solving the inverse problem, an up-to-date two-step method is used. Various types of field nonlinearity are used to simulate a nonlinear process. Results. Graphical images illustrating the value of the dielectric constant inside the body for the initial problem and the reconstructed values are presented. Graphs of convergence of the iterative process of injection of a nonlinear field are shown. The results are compared for different parameter values. Conclusions. A numerical method for solving the problem is proposed and implemented, and comparative results are obtained.

inverse problem, integral equation, boundary value problem, numerical method, two-step method, Kerr nonlinearity, saturation nonlinearity, Galerkin method

Lapich A.O. Solving the direct and inverse diffraction problems on flat objects with different types of field nonlinearity. Modeli, sistemy, seti v ekonomike, tekhnike, prirode i obshchestve = Models, systems, networks in economics, technology, nature and society. 2024;(3):138–146. (In Russ.). doi: 10.21685/2227-8486-2024-3-12