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Symbolic-Numeric Study of Geometric Properties of Adiabatic Waveguide Modes

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Computer Algebra in Scientific Computing (CASC 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12291))

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Abstract

The eikonal equation links wave optics to ray optics. In the present work, we show that the eikonal equation is also valid for an approximate description of the phase of vector fields describing guided-wave propagation in inhomogeneous waveguide structures in the adiabatic approximation. The main result of the work was obtained using the model of adiabatic waveguide modes. Highly analytical solution procedure makes it possible to obtain symbolic or symbolic-numerical expressions for vector fields of guided modes. Making use of advanced computer algebra systems, we describe fundamental properties of adiabatic modes in symbolic form. Numerical results are also obtained by means of computer algebra systems.

The contribution of D.V. Divakov (investigation – obtaining numerical results) and A.A. Tiutiunnik (investigation – obtaining symbolic results) is supported by the Russian Science Foundation (grant no. 20-11-20257). The contribution of A.L. Sevastianov is conceptualization, formal analysis and writing.

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Acknowledgments

The authors are grateful to Konstantin Lovetskiy for providing numerical data of the designed Luneburg lens, based on which all numerical calculations were carried out. The authors are grateful to Leonid Sevastianov for useful discussions and assistance provided in writing this article.

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Authors and Affiliations

  1. Department of Applied Probability and Informatics, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, 117198, Russia

    Dmitriy V. Divakov, Anastasiia A. Tiutiunnik & Anton L. Sevastianov

Authors
  1. Dmitriy V. Divakov
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  2. Anastasiia A. Tiutiunnik
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  3. Anton L. Sevastianov
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Corresponding author

Correspondence to Dmitriy V. Divakov .

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Editors and Affiliations

  1. University of Lille, Villeneuve d’Ascq, France

    François Boulier

  2. Coventry University, Coventry, UK

    Matthew England

  3. Plekhanov Russian University of Economics, Moscow, Russia

    Timur M. Sadykov

  4. Institute of Theoretical and Applied Mechanics, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Divakov, D.V., Tiutiunnik, A.A., Sevastianov, A.L. (2020). Symbolic-Numeric Study of Geometric Properties of Adiabatic Waveguide Modes. In: Boulier, F., England, M., Sadykov, T.M., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2020. Lecture Notes in Computer Science(), vol 12291. Springer, Cham. https://doi.org/10.1007/978-3-030-60026-6_13

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  • DOI: https://doi.org/10.1007/978-3-030-60026-6_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-60025-9

  • Online ISBN: 978-3-030-60026-6

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