Scattering by a two‐dimensional doped photonic crystal presenting an optical Kerr effect

Pierre Godard (Faculté de Saint‐Jérôme, Institut Fresnel, Aix‐Marseille Université, Marseille, France)
Frédéric Zolla (Faculté de Saint‐Jérôme, Institut Fresnel, Aix‐Marseille Université, Marseille, France)
André Nicolet (Faculté de Saint‐Jérôme, Institut Fresnel, Aix‐Marseille Université, Marseille, France)

Abstract

Purpose

The purpose of this paper is to discuss two‐dimensional electromagnetic diffraction by a finite set of parallel nonlinear rods (optical Kerr effect). To point out the versatility of this approach, a nonlinear (Kerr‐effect) finite crystal is considered.

Design/methodology/approach

In this paper, a new route for obtaining the scattered field by nonlinear obstacles is proposed. The basic idea consists in simulating the real incident field (e.g. plane waves) by a virtual field emitted by an appropriate antenna, located in a meshed domain, and encompassing or lying above the obstacles. This latest problem is then solved by a finite element method that is well suited to take into account the material inhomogeneities due to the nonlinearity of the permittivity.

Findings

The transmission through a finite Kerr crystal doped by a microcavity is given and a resonant wavelength is obtained. At this resonant wavelength, it is shown that the nonlinearity has a large influence on the behaviour of the electromagnetic wave.

Originality/value

Introducing the concept of virtual antenna, the paper proposes a rigorous treatment of the scattering of an electromagnetic wave by a bounded nonlinear obstacle of arbitrary shape.

Keywords

Citation

Godard, P., Zolla, F. and Nicolet, A. (2009), "Scattering by a two‐dimensional doped photonic crystal presenting an optical Kerr effect", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 28 No. 3, pp. 656-667. https://doi.org/10.1108/03321640910940918

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Publisher

:

Emerald Group Publishing Limited

Copyright © 2009, Emerald Group Publishing Limited

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