{"title":"Two Iterative Methods for Solving a Volumetric Singular Equation for a Nonlinear Diffraction Problem in a Semi-infinite Rectangular Waveguide","authors":"A. O. Lapich, M. Yu. Medvedik","doi":"10.1134/s1063784224700622","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>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.</p>","PeriodicalId":783,"journal":{"name":"Technical Physics","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Technical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1134/s1063784224700622","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"PHYSICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
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.
期刊介绍：
Technical Physics is a journal that contains practical information on all aspects of applied physics, especially instrumentation and measurement techniques. Particular emphasis is put on plasma physics and related fields such as studies of charged particles in electromagnetic fields, synchrotron radiation, electron and ion beams, gas lasers and discharges. Other journal topics are the properties of condensed matter, including semiconductors, superconductors, gases, liquids, and different materials.
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