Numerical Modeling of Optical Fibers Using the Finite Element Method and an Exact Non-reflecting Boundary Condition-Reference-Cited by-同舟云学术

Numerical Modeling of Optical Fibers Using the Finite Element Method and an Exact Non-reflecting Boundary Condition

Published:2017-11-17 Issue:4 Volume:18 Page:581-601
ISSN:1609-9389
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Dautov Rafail Z.¹,Karchevskii Evgenii M.²

Affiliation:

1. Department of Numerical Mathematics , Kazan Federal University , 18 Kremliovskaya street , Kazan 42008 , Russia

2. Department of Applied Mathematics , Kazan Federal University , 18 Kremliovskaya street , Kazan 42008 , Russia

Abstract

Abstract The original problem for eigenwaves of weakly guiding optical fibers formulated on the plane is reduced to a convenient for numerical solution linear parametric eigenvalue problem posed in a disk. The study of the solvability of this problem is based on the spectral theory of compact self-adjoint operators. Properties of dispersion curves are investigated for the new formulation of the problem. An efficient numerical method based on FEM approximations is developed. Error estimates for approximate solutions are derived. The rate of convergence for the presented algorithm is investigated numerically.

Funder

Russian Foundation for Basic Research

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

Reference37 articles.

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