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Accurate Full-Vectorial Finite Element Method Combined with Exact Non-Reflecting Boundary Condition for Computing Guided Waves in Optical Fibers

  • Rafail Z. Dautov and Evgenii M. Karchevskii EMAIL logo
Published/Copyright: June 23, 2021

Abstract

The vector electromagnetic problem for eigenwaves of optical fibers, originally formulated on the whole plane, is equivalently reduced to a linear parametric eigenvalue problem posed in a circle, convenient for numerical solution. The study of the solvability of this problem is based on the spectral theory of compact self-adjoint operators. Asymptotic properties of the dispersion curves and their smoothness are investigated for the new formulation of the problem. A numerical method based on finite element approximations combined with an exact non-reflecting boundary condition is developed. Error estimates for approximating eigenvalues and eigenfunctions are derived.

MSC 2010: 65N30; 65N25; 65Z05

Funding statement: This paper has been supported by the Kazan Federal University Strategic Academic Leadership Program.

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Received: 2020-10-09
Revised: 2021-06-04
Accepted: 2021-06-05
Published Online: 2021-06-23
Published in Print: 2022-01-01

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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