Symbolic-numerical implementation of the model of adiabatic guided modes for two-dimensional irregular waveguides

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Resumo

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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Sobre autores

D. Divakov

RUDN University

Autor responsável pela correspondência
Email: divakov_dv@pfur.ru
Rússia, 6 Miklukho-Maklaya St, Moscow, 117198

А. Tyutyunnik

RUDN University

Email: tyutyunnik_aa@pfur.ru
Rússia, 6 Miklukho-Maklaya St, Moscow, 117198

D. Starikov

RUDN University

Email: starikov_da@pfur.ru
Rússia, 6 Miklukho-Maklaya St, Moscow, 117198

Bibliografia

  1. 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.
  2. 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.
  3. 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.
  4. Babich V.M., Buldyrev V.S. Asimptotic Methods in Short-Wave Diffraction Problems. Method of Reference Problems, Moscow: Nauka, 1972.
  5. 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.
  6. Adams M.J. An Introduction to Optical Waveguides. Wiley, New York (1981).
  7. Mathematics-based software and services for education, engineering, and research https://www.maplesoft.com/
  8. 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.
  9. 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.
  10. 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.

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2. Fig. 1. Geometry of a two-dimensional smoothly irregular waveguide transition between two regular waveguides.

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3. Рис. 2. The values of ohoj (ohoj j (z)), j = 1..4 for Z áho [0, L].

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4. Fig 3. Values J (Yj (z)), j = 1..4 for z E [0, L].

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5. Fig. 4. Residuals dj(z), j = 1..4 for z e [0,L] with abserr and relerr values equal to 10-10.

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6. Fig. 5. Residuals dj(z), j = 1..4 for z e [0,L] with abserr and relerr values equal to 10-12.

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