# On a dispersion curve of a waveguide filled with inhomogeneous substance

**Authors:**Kroytor O.K.^{1}, Malykh M.D.^{1}^{,2}-
**Affiliations:**- Peoples’ Friendship University of Russia (RUDN University)
- Joint Institute for Nuclear Research

**Issue:**Vol 30, No 4 (2022)**Pages:**330-341**Section:**Articles**URL:**https://journals.rudn.ru/miph/article/view/33014**DOI:**https://doi.org/10.22363/2658-4670-2022-30-4-330-341

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## Abstract

The paper discusses the relationship between the modes traveling along the axis of the waveguide and the standing modes of a cylindrical resonator, and shows how this relationship can be explored using the Sage computer algebra system. In this paper, we study this connection and, on its basis, describe a new method for constructing the dispersion curve of a waveguide with an optically inhomogeneous filling. The aim of our work was to find out what computer algebra systems can give when calculating the points of the waveguide dispersion curve. Our method for constructing the dispersion curve of a waveguide with optically inhomogeneous filling differs from those proposed earlier in that it reduces this problem to calculating the eigenvalues of a self-adjoint matrix, i.e., a well-studied problem. The use of a selfadjoint matrix eliminates the occurrence of artifacts associated with the appearance of a small imaginary addition to the eigenvalues. We have composed a program in the Sage computer algebra system that implements this method for a rectangular waveguide with rectangular inserts and tested it on SLE modes. The obtained results showed that the program successfully copes with the calculation of the points of the dispersion curve corresponding to the hybrid modes of the waveguide, and the points found fit the analytical curve with graphical accuracy even when with a small number of basis elements taken into account.

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1. Introduction In classical electrodynamics, there are two related spectral problems - the problem of the normal modes of the waveguide and the problem of eigenmodes of the resonator. Recall their formulations. Let## About the authors

### Oleg K. Kroytor

Peoples’ Friendship University of Russia (RUDN University)
Email: kroytor-ok@rudn.ru

ORCID iD: 0000-0002-5691-7331

Senior lecturer of Department of Applied Probability and Informatics

6, Miklukho-Maklaya St., Moscow, 117198, Russian Federation### Mikhail D. Malykh

Peoples’ Friendship University of Russia (RUDN University); Joint Institute for Nuclear Research
**Author for correspondence.**

Email: malykh-md@rudn.ru

ORCID iD: 0000-0001-6541-6603

Doctor of Physical and Mathematical Sciences, Assistant Professor of Department of Applied Probability and Informatics

6, Miklukho-Maklaya St., Moscow, 117198, Russian Federation; 6, Joliot-Curie St., Dubna, Moscow Region, 141980, Russian Federation## References

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