Data di Pubblicazione:
2004
Citazione:
Wave propagation in a 3-D optical waveguide / O. Alexandrov, G. Ciraolo. - In: MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. - ISSN 0218-2025. - 2004-06(2004).
Abstract:
In this paper we study the problem of electromagnetic wave propagation in a
3-D optical fiber. The goal is to obtain a solution for the time-harmonic
field caused by a source in a cylindrically symmetric waveguide. The
geometry of the problem, corresponding to an open waveguide, makes the
problem challenging. To solve it, we construct a transform theory which
is a nontrivial generalization of a method for solving a 2-D version of
this problem given by Magnanini and Santosa.
The extension to 3-D is made complicated by the fact that the resulting
eigenvalue problem defining the transform kernel is singular both at the
origin and at infinity. The singularities require the investigation of
the behavior of the solutions of the eigenvalue problem. Moreover, the
derivation of the transform formulas needed to solve the wave
propagation problem involves nontrivial calculations.
The paper provides a complete description on how to construct the
solution to the wave propagation problem in a 3-D optical waveguide with
cylindrical symmetry. A follow-up article will study the particular
cases of a step-index fiber and of a coaxial waveguide. In those cases
we will obtain concrete formulas for the field and numerical
examples.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Equazioni alle derivate parziali; equazione di Helmholtz; guide d'onda
Elenco autori:
O. Alexandrov, G. Ciraolo
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