On the problem of normal modes of a waveguide

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Abstract

Various approaches to calculating normal modes of a closed waveguide are considered. A review of the literature was given, a comparison of the two formulations of this problem was made. It is shown that using a self-adjoint formulation of the problem of normal waveguide modes eliminates the occurrence of artifacts associated with the appearance of a small imaginary additive to the eigenvalues. The implementation of this approach for a rectangular waveguide with rectangular inserts in the Sage computer algebra system is presented and tested on hybrid modes of layered waveguides. The tests showed that our program copes well with calculating the points of the dispersion curve corresponding to the hybrid modes of the waveguide.

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1. Introduction In classical electrodynamics there are two related spectral problems, the problem of normal modes of a waveguide and the problem of eigenmodes of a resonator [1, 2]. The first of these problems in the vector case turned out to be surprisingly difficult, its solution requiring the use of very subtle theorems from the field of functional analysis. 2. Scalar model Let
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About the authors

Oleg K. Kroytor

RUDN University

Email: kroytor_ok@pfur.ru
ORCID iD: 0000-0002-5691-7331
Scopus Author ID: 57212346588
ResearcherId: GLS-3788-2022

Candidate of Physical and Mathematical Sciences, Employee of the department of Mathematical Modeling and Artificial Intelligence

6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation

Mikhail D. Malykh

RUDN University; Joint Institute for Nuclear Research

Email: malykh_md@pfur.ru
ORCID iD: 0000-0001-6541-6603
Scopus Author ID: 6602318510
ResearcherId: P-8123-2016

Doctor of Physical and Mathematical Sciences, Head of the department of Mathematical Modeling and Artificial Intelligence of RUDN University, research fellow of MLIT JINR

6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation; 6 Joliot-Curie St, Dubna, 141980, Russian Federation

Leonid A. Sevastianov

RUDN University; Joint Institute for Nuclear Research

Author for correspondence.
Email: sevastianov_la@pfur.ru
ORCID iD: 0000-0002-1856-4643
Scopus Author ID: 8783969400
ResearcherId: B-8497-2016

Doctor of Physical and Mathematical Sciences, Professor of the department of Mathematical Modeling and Artificial Intelligence of RUDN University, research fellow of LTPh JINR

6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation; 6 Joliot-Curie St, Dubna, 141980, Russian Federation

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Copyright (c) 2024 Kroytor O.K., Malykh M.D., Sevastianov L.A.

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