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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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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