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A numerical method for the computation of electromagnetic modes in optical fibres
Author(s) -
Joly Patrick,
Poirier Christine
Publication year - 1999
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19990325)22:5<389::aid-mma31>3.0.co;2-e
Subject(s) - mathematics , computation , numerical analysis , optical fiber , mathematical analysis , algorithm , optics , physics
In this article, we propose a new numerical method for the computation of electromagnetic modes in an optical fibre. The main difficulty lies in the fact that we have to solve an eigenvalue problem posed in ℝ 2 . We reduce the problem to a disc with the help of the introduction of non‐local boundary operators that can be expressed in terms of Fourier series. Particular attention is drawn to the free divergence condition. Finally, our method is reduced to the resolution of a series of fixed point equations related to the eigenvalues of some self‐adjoint operators with compact resolvent. Copyright © 1999 John Wiley & Sons, Ltd.