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.
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REFERENCES
Sevastianov, L.A. and Egorov, A.A., Theoretical analysis of the waveguide propagation of electromagnetic waves in dielectric smoothly irregular integrated structures, Optics and Spectroscopy, 2008, vol. 105, no. 4, pp. 576–584.
Egorov, A.A. and Sevastianov, L.A., Structure of modes of a smoothly irregular integrated optical four-layer three-dimensional waveguide, Quantum Electronics, 2009, vol. 39, no. 6, pp. 566–574.
Egorov, A.A., Lovetskiy, K.P., Sevastianov, A.L., and Sevastianov, L.A., Simulation of guided modes (eigenmodes) and synthesis of a thin-film generalized waveguide Luneburg lens in the zero-order vector approximation, Quantum Electronics, 2010, vol. 40, no. 9, pp. 830–836.
Babich, V.M. and Buldyrev, V.S., Asimptotic Methods in Short-Wave Diffraction Problems. Method of Reference Problems, Moscow: Nauka, 1972.
Divakov, D.V. and Sevastianov, A.L., The implementation of the symbolic-numerical method for finding the adiabatic waveguide modes of integrated optical waveguides in CAS Maple, Lect. Notes Comp. Sci., 2019, vol. 11661, pp. 107–121.
Adams, M.J., An Introduction to Optical Waveguides, New York: Wiley, 1981.
Mathematics-Based Software and Services for Education, Engineering, and Research. https://www.maplesoft.com/
Divakov, D.V. and Tyutyunnik, A.A., Symbolic investigation of the spectral characteristics of guided modes in smoothly irregular waveguides, Program. Comput. Software, 2022, vol. 48, no. 2, pp. 80–89.
Kuznetsov, E.B. and Shalashilin, V.I., Solution of differential-algebraic equations using the parameter continuation method, Differ. Uravn., 1999, vol. 35, no. 3, pp. 379–387.
Divakov, D.V. and Tyutyunnik, A.A., Symbolic-numerical modeling of adiabatic waveguide mode in a smooth waveguide transition, Comput. Math. Math. Phys., 2023, vol. 63, no. 1, pp. 95–105.
Funding
This work was supported by the RUDN University Strategic Academic Leadership Program, project no. 021934-0-000.
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Translated by E. Chernokozhin
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Divakov, D.V., Tyutyunnik, A.A. & Starikov, D.A. Symbolic-Numerical Implementation of the Model of Adiabatic Guided Modes for Two-Dimensional Irregular Waveguides. Program Comput Soft 50, 147–152 (2024). https://doi.org/10.1134/S0361768824020063
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DOI: https://doi.org/10.1134/S0361768824020063