Computer-algebraic study of the asymptotic method for modeling waveguide propagation of electromagnetic radiation

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Abstract

This paper formulates an asymptotic method for investigating vector electromagnetic fields of waveguide modes in the adiabatic approximation. The asymptotic method in the zero approximation is reduced to the symbolic investigation of a homogeneous system of ordinary differential equations; higher approximations correspond to inhomogeneous systems of ordinary differential equations with a similar matrix of coefficients. Using the asymptotic method, symbolic solutions in the zero and first approximations are obtained.

About the authors

D. A. Starikov

Peoples' Friendship University of Russia

Email: starikov_da@pfur.ru
ul. Miklukho-Maklaya 6, Moscow, 117198 Russia

D. V. Divakov

Peoples' Friendship University of Russia

Email: divakov_dv@pfur.ru
ul. Miklukho-Maklaya 6, Moscow, 117198 Russia

A. A. Tyutyunnik

Peoples' Friendship University of Russia

Email: tyutyunnik_aa@pfur.ru
ul. Miklukho-Maklaya 6, Moscow, 117198 Russia

References

  1. Stevenson A.F. General Theory of Electromagnetic Horns // Journal of Applied Physics. 1951. Vol. 22. No. 12. P. 1447–1460.
  2. Schelkunoff S.A. Conversion of Maxwell’s equations into generalized Telegraphist’s equa-tions // The Bell System Technical Journal. 1955. Vol. 34. No. 5. P. 995–1043.
  3. Katsenelenbaum Boris Z., del Rio L. Mercader, Pereyaslavets M.L., Ayza Mario Sorolla, and Thumm M.K.A. Theory of Nonuniform Waveguides: The cross-section method. 1998.
  4. Shevchenko V.V. Plavnye perekhody v otkrytykh volnovodakh: vvedenie v teoriyu. Sovremennye problemy fiziki (Smooth Transitions in Open Waveguides: Introduction to Theory: Modern Problems of Physics), Moscow: Nauka, 1969.
  5. Sveshnikov A.G. A substantiation of a method for computing the propagation of electromagnetic oscillations in irregular waveguides // USSR Computational Mathematics and Mathematical Physics. 1963. Vol. 3. No. 2. P. 413–429.
  6. Fedoryuk M.V. Justification of the method of cross-sections for an acoustic waveguide with inhomogeneous filling // USSR Computational Mathematics and Mathematical Physics. 1973. Vol. 13. No. 1. P. 162–173.
  7. Babich V.M., Buldyrev V.S. Asimptoticheskie metody v zadachakh difraktsii korotkikh voln. Metod etalonnykh zadach (Asymptotic Methods in Short Wave Diffraction Problems: A Method of Reference Problems), Moscow: Nauka, 1972.
  8. Adams M.J. An Introduction to Optical Waveguides. Wiley-Interscience publication. – Wiley, 1981. ISBN 9780471279693.
  9. Sevast’yanov L.A., 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. P. 576–584.
  10. 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. In: England, M., Koepf, W., Sadykov, T., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2019. Lecture Notes in Computer Science, 2019, vol. 11661. Springer, Cham. https://doi.org/10.1007/978-3-030-26831-2_8
  11. Divakov D.V., Tiutiunnik A.A. Symbolic Investigation of Eigenvectors for General Solution of a System of ODEs with a Symbolic Coefficient Matrix // Programming and Computer Software. 2021. Vol. 47. No. 1. P. 6–16.
  12. Divakov D.V., Tyutyunnik A.A., Starikov D.A. Symbolic-Numerical Implementation of the Model of Adiabatic Guided Modes for Two-Dimensional Irregular Waveguides // Programming and Computer Software. 2024. Vol. 50. No. 2. P. 147–152.
  13. Divakov D.V., Tyutyunnik A.A. Symbolic-Numerical Modeling of the Propagation of Adiabatic Waveguide Mode in a Smooth Waveguide Transition // Computational Mathematics and Mathematical Physics. 2023. Vol. 63. No. 1. P. 96–105.
  14. Tiutiunnik A.A., Divakov D.V., Lovetskiy K.P., Sevastianov A.L. Single-mode propagation of the adiabatic waveguide mode in a smooth transition between planar waveguide // Laser Physics, Photonic Technologies, and Molecular Modeling / ed. by V.L. Derbov; International Society for Optics and Photonics. – SPIE. 2022. Vol. 12193. P. 1219305.
  15. Mathematics-based software and services for education, engineering, and research. https://www.maplesoft.com/

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