Symbolic-Numerical Modeling of the Propagation of Adiabatic Waveguide Mode in a Smooth Waveguide Transition

D. V. Divakov; Диваков Д. В.; A. A. Tyutyunnik; Тютюнник А. А.

doi:10.31857/S0044466923010076

Symbolic-Numerical Modeling of the Propagation of Adiabatic Waveguide Mode in a Smooth Waveguide Transition

Authors: Divakov D.V.¹, Tyutyunnik A.A.²
Affiliations:
1. Peoples’ Friendship University of Russia (RUDN University)
2. Joint Institute for Nuclear Research
Issue: Vol 63, No 1 (2023)
Pages: 112-122
Section: Partial Differential Equations
URL: https://freezetech.ru/0044-4669/article/view/664909
DOI: https://doi.org/10.31857/S0044466923010076
EDN: https://elibrary.ru/LKQVIF
ID: 664909

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Abstract

In this work, the model of adiabatic waveguide modes is studied by means of computer algebra. Within the model, the solution of the system of Maxwell’s equations is reduced to a form expressed via the solution of a system of four ordinary differential equations and two algebraic equations for six components of the electromagnetic field. In the case of multilayer waveguides, by means of a computer algebra system, the equations are reduced to a homogeneous system of linear algebraic equations, which is studied symbolically. The condition for non-trivial solvability of the system defines a dispersion relation, which is solved by the symbolic-numerical method, while the system is solved symbolically. The paper presents solutions that describe adiabatic waveguide modes in the zeroth approximation, taking into account the small slope of the interface of the waveguide layer, which are qualitatively different from solutions that do not take into account this slope.

Keywords

symbolic solution of linear equations, symbolic solution of differential equations, adiabatic waveguide modes, guided modes, smoothly irregular waveguide

About the authors

D. V. Divakov

Peoples’ Friendship University of Russia (RUDN University)

Email: divakov-dv@rudn.ru
117198, Moscow, Russia

A. A. Tyutyunnik

Joint Institute for Nuclear Research

Author for correspondence.
Email: tyutyunnik-aa@rudn.ru
141980, Dubna, Moscow oblast, Russia

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