A numerical method for solving the problem of TE-polarized waves’ propagation in a multilayer inhomogeneous circular waveguide filled with a metamaterial 

Ekaterina D. Derevyanchuk, Candidate of physical and mathematical sciences, associate professor of the sub-department of mathematics and supercomputer modeling, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: mmm@pnzgu.ru
Andrey O. Lapich, Master’s degree student, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: mmm@pnzgu.ru
Maksim O. Snegur, Postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: snegur.max15@gmail.com 

519.622 

10.21685/2072-3040-2021-1-8 

Background. The purpose of this work is to numerical study the problem of TEelectromagnetic waves’ propagation in a multilayer regular waveguide structure with metamaterial layers.
Material and methods. The problem boils down to solving the eigenvalue problem for a system of ordinary differential equations. To achieve a numerical solution, the parameter shooting method is used.
Results. A numerical method is implemented to solve the problem of an electromagnetic wave’s propagation in a multilayer waveguide. Numerical results were obtained.
Conclusions. The applied method is excellent for finding an approximate solution to the problem of propagation of electromagnetic waves in the structure of a waveguide. 

propagation problem of electromagnetic waves, Maxwell's equations, TE-waves, differential equations, multilayer waveguide, metamaterial, shooting method 

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