Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)4366810.22363/2658-4670-2024-32-4-395-405EQOGQJModeling and SimulationМатематическое моделированиеResearch ArticleOn the problem of normal modes of a waveguideЗадача о нормальных модах волноводаhttps://orcid.org/0000-0002-5691-733157212346588GLS-3788-2022KroytorOleg K.КройторО. К.

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

kroytor_ok@pfur.ruhttps://orcid.org/0000-0001-6541-66036602318510P-8123-2016MalykhMikhail D.МалыхМ. Д.

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

malykh_md@pfur.ruhttps://orcid.org/0000-0002-1856-46438783969400B-8497-2016SevastianovLeonid A.СевастьяновЛ. А.

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

sevastianov_la@pfur.ruRUDN UniversityРоссийский университет дружбы народовJoint Institute for Nuclear ResearchОбъединённый институт ядерных исследований15122024324VOL 32, NO4 (2024)ТОМ 32, №4 (2024)39540505042025Copyright ©; 2024, Kroytor O.K., Malykh M.D., Sevastianov L.A.Copyright ©; 2024, Кройтор О.К., Малых М.Д., Севастьянов Л.А.2024Kroytor O.K., Malykh M.D., Sevastianov L.A.Кройтор О.К., Малых М.Д., Севастьянов Л.А.https://creativecommons.org/licenses/by-nc/4.0https://journals.rudn.ru/miph/article/view/43668

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.

Рассмотрены различные подходы к вычислению нормальных мод закрытого волновода. Дан обзор литературы, проведено сравнение двух формулировок этой задачи. Показано, что использование самосопряжённой постановки задачи о нормальных модах волновода исключает возникновение артефактов, связанных с появлением малой мнимой добавки у собственных значений. Представлена реализация этого подхода для волновода прямоугольного сечения с прямоугольными вставками в системе компьютерной алгебры Sage и протестирована на гибридных модах слоистых волноводов. Тесты показали, что наша программа прекрасно справляется с вычислением точек дисперсионной кривой, отвечающих гибридным модам волновода.

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