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Application of the Banach Fixed-Point Theorem to the Scattering Problem at a Nonlinear Three-Layer Structure with Absorption

Abstract

A method based on the Banach fixed-point theorem is proposed for obtaining certain solutions (TE-polarized electromagnetic waves) of the Helmholtz equation describing the reflection and transmission of a plane monochromatic wave at a nonlinear lossy dielectric film situated between two lossless linear semiinfinite media. All three media are assumed to be nonmagnetic and isotropic. The permittivity of the film is modelled by a continuously differentiable function of the transverse coordinate with a saturating Kerr nonlinearity. It is shown that the solution of the Helmholtz equation exists in form of a uniformly convergent sequence of iterations of the equivalent Volterra integral equation. Numerical results are presented.

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Correspondence to VS Serov.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Serov, V., Schüermann, H. & Svetogorova, E. Application of the Banach Fixed-Point Theorem to the Scattering Problem at a Nonlinear Three-Layer Structure with Absorption. Fixed Point Theory Appl 2010, 439682 (2010). https://doi.org/10.1155/2010/439682

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  • DOI: https://doi.org/10.1155/2010/439682

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