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)2518210.22363/2658-4670-2020-28-4-361-377ArticlesСтатьиResearch ArticleSingle-mode propagation of adiabatic guided modes in smoothly irregular integral optical waveguidesОдномодовый режим распространения адиабатических волноводных мод плавно-нерегулярных интегрально-оптических волноводовSevastianovAnton L.СевастьяновА. Л.

Candidate of Physical and Mathematical Sciences, assistant professor of Department of Applied Probability and Informatics

sevastianov-al@rudn.ruPeoples’ Friendship University of Russia (RUDN University)Российский университет дружбы народов15122020284VOL 28, NO4 (2020)ТОМ 28, №4 (2020)36137709122020Copyright ©; 2020, Sevastianov A.L.Copyright ©; 2020, Севастьянов А.Л.2020Sevastianov A.L.Севастьянов А.Л.http://creativecommons.org/licenses/by/4.0https://journals.rudn.ru/miph/article/view/25182

This paper investigates the waveguide propagation of polarized electromagnetic radiation in a thin-film integral optical waveguide. To describe this propagation, the adiabatic approximation of solutions of Maxwell’s equations is used. The construction of a reduced model for adiabatic waveguide modes that retains all the properties of the corresponding approximate solutions of the Maxwell system of equations was carried out by the author in a previous publication in DCM & ACS, 2020, No 3. In this work, for a special case when the geometry of the waveguide and the electromagnetic field are invariant in the transverse direction. In this case, there are separate nontrivial TEand TM-polarized solutions of this reduced model. The paper describes the parametrically dependent on longitudinal coordinates solutions of problems for eigenvalues and eigenfunctions - adiabatic waveguide TE and TM polarizations. In this work, we present a statement of the problem of finding solutions to the model of adiabatic waveguide modes that describe the stationary propagation of electromagnetic radiation. The paper presents solutions for the single-mode propagation of TE and TM polarized adiabatic waveguide waves.

В работе представлено исследование волноводного распространения поляризованного электромагнитного излучения в тонкоплёночном интегральнооптическом волноводе. Для описания этого распространения используется адиабатическое приближение решений уравнений Максвелла. Построение редуцированной модели для адиабатических волноводных мод, сохраняющей все свойства соответствующих приближённых решений системы уравнений Максвелла, было проведено автором в предыдущей публикации в DCM&ACS, 2020, № 3. В настоящей работе исследование проведено для частного случая, когда геометрия волновода и электромагнитное поле инвариантны в поперечном направлении. В этих условиях существуют раздельные нетривиальные ТЕи ТМ-поляризованные решения указанной редуцированной модели. В работе описываются параметрически зависящие от продольных координат решения задач на собственные значения и собственные функции - адиабатические волноводные ТЕи ТМ-поляризации. В работе приводится постановка задачи отыскания решений модели адиабатических волноводных мод, описывающих стационарное распространение электромагнитного излучения. Представлены решения для одномодового распространения ТЕи ТМ-поляризованных адиабатических волноводных волн.

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