Calculation of the normal modes of closed waveguides

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Abstract

The aim of the work is the development of numerical methods for solving waveguiding problems of the theory of waveguides, as well as their implementation in the form of software packages focused on a wide range of practical problems from the classical issues of microwave transmission to the design of optical waveguides and sensors. At the same time, we strive for ease of implementation of the developed methods in computer algebra systems (Maple, Sage) or in software oriented to the finite element method (FreeFem++). The work uses the representation of electromagnetic fields in a waveguide using four potentials. These potentials do not reduce the number of sought functions, but even in the case when the dielectric permittivity and magnetic permeability are described by discontinuous functions, they turn out to be quite smooth functions. A simple check of the operability of programs by calculating the normal modes of a hollow waveguide is made. It is shown that the relative error in the calculation of the first 10 normal modes does not exceed 4%. These results indicate the efficiency of the method proposed in this article.

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About the authors

Mikhail D. Malykh

Peoples’ Friendship University of Russia (RUDN University)

Email: malykh-md@rudn.ru
Doctor of Physical and Mathematical Sciences, Assistant Professor of Department of Applied Probability and Informatics 6, Miklukho-Maklaya St., Moscow 117198, Russian Federation

Dmitriy V. Divakov

Peoples’ Friendship University of Russia (RUDN University)

Email: divakov-dv@rudn.ru
Candidate of Physical and Mathematical Sciences, Assistant of Department of Applied Probability and Informatics 6, Miklukho-Maklaya St., Moscow 117198, Russian Federation

Alexandre A. Egorov

A. M. Prokhorov General Physics Institute Russian Academy of Sciences

Email: yegorov@kapella.gpi.ru
Doctor of Physical and Mathematical Sciences, Chief Researcher of Department of Oscillations 38, Vavilov St., Moscow 119991, Russian Federation

Yaroslav Yu. Kuziv

Peoples’ Friendship University of Russia (RUDN University)

Email: yaroslav.kuziw@yandex.ru
PhD student of Department of Applied Probability and Informatics 6, Miklukho-Maklaya St., Moscow 117198, Russian Federation

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Copyright (c) 2020 Malykh M.D., Divakov D.V., Egorov A.A., Kuziv Y.Y.

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