Email this article Symbolic-numerical implementation of the model of adiabatic guided modes for two-dimensional irregular waveguides
- Authors: Divakov D.V.1, Tyutyunnik А.А.1, Starikov D.А.1
-
Affiliations:
- RUDN University
- Issue: No 2 (2024)
- Pages: 45-50
- Section: КОМПЬЮТЕРНАЯ АЛГЕБРА
- URL: https://journals.rcsi.science/0132-3474/article/view/262642
- DOI: https://doi.org/10.31857/S0132347424020066
- EDN: https://elibrary.ru/ROVQMP
- ID: 262642
Cite item
Open Access
Access granted
Subscription Access
Abstract
In this work, a symbolic-numerical solution of Maxwell’s equations is constructed, describing the guided modes of a two-dimensional smoothly irregular waveguide in the zeroth approximation of the model of adiabatic waveguide modes. The system of linear algebraic equations obtained in this approximation is solved symbolically. The dispersion relation is solved numerically using the parameter continuation method.
About the authors
D. V. Divakov
RUDN University
Author for correspondence.
Email: divakov_dv@pfur.ru
Russian Federation, 6 Miklukho-Maklaya St, Moscow, 117198
А. А. Tyutyunnik
RUDN University
Email: tyutyunnik_aa@pfur.ru
Russian Federation, 6 Miklukho-Maklaya St, Moscow, 117198
D. А. Starikov
RUDN University
Email: starikov_da@pfur.ru
Russian Federation, 6 Miklukho-Maklaya St, Moscow, 117198
References
- Sevastianov L.A., Egorov A.A. Theoretical analysis of the waveguide propagation of electromagnetic waves in dielectric smoothlyirregular integrated structures // Optics and Spectroscopy. 2008. V. 105. № 4. P. 576–584.
- Egorov A.A., Sevastianov L.A. Structure of modes of a smoothly irregular integrated optical four-layer three-dimensional waveguide // Quantum Electronics. 2009. V. 39. № 6. P. 566–574.
- Egorov A.A., Lovetskiy K.P., Sevastianov A.L., Sevastianov L.A. Simulation of guided modes (eigenmodes) and synthesis of a thin-film generalised waveguide Luneburg lens in the zero-order vector approximation // Quantum Electronics. 2010. V. 40. № 9. P. 830–836.
- Babich V.M., Buldyrev V.S. Asimptotic Methods in Short-Wave Diffraction Problems. Method of Reference Problems, Moscow: Nauka, 1972.
- Divakov D.V., Sevastianov A.L. The Implementation of the Symbolic-Numerical Method for Finding the Adiabatic Waveguide Modes of Integrated Optical Waveguides in CAS Maple // Lecture Notes in Computer Science. 2019. V. 11661. P. 107–121.
- Adams M.J. An Introduction to Optical Waveguides. Wiley, New York (1981).
- Mathematics-based software and services for education, engineering, and research https://www.maplesoft.com/
- Divakov D.V., Tyutyunnik A.A. Symbolic investigation of the spectral characteristics of guided modes in smoothly irregular waveguides // Program. Comput. Software. 2022. V. 48. № 2. P. 80–89.
- Kuznetsov E.B., Shalashilin V.I. Solution of differential-algebraic equations using the parameter continuation method // Differ. Uravn. 1999. V. 35. № 3. P. 379–387.
- Divakov D.V., Tyutyunnik A.A. Symbolic-numerical modeling of adiabatic waveguide mode in a smooth waveguide transition // Comput. Math. Math. Phys. 2023. V. 63. № 1. P. 95–105.
