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

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

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 line...

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Main Authors: V. S. Serov, H. W. Schüermann, E. Svetogorova
Format: Article
Language:English
Published: SpringerOpen 2010-01-01
Series:Fixed Point Theory and Applications
Online Access:http://dx.doi.org/10.1155/2010/439682
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spelling doaj-1f97c45c57da42c581fa0948c6d3a5762020-11-24T22:09:47ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122010-01-01201010.1155/2010/439682Application of the Banach Fixed-Point Theorem to the Scattering Problem at a Nonlinear Three-Layer Structure with AbsorptionV. S. SerovH. W. SchüermannE. SvetogorovaA 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. http://dx.doi.org/10.1155/2010/439682
collection DOAJ
language English
format Article
sources DOAJ
author V. S. Serov
H. W. Schüermann
E. Svetogorova
spellingShingle V. S. Serov
H. W. Schüermann
E. Svetogorova
Application of the Banach Fixed-Point Theorem to the Scattering Problem at a Nonlinear Three-Layer Structure with Absorption
Fixed Point Theory and Applications
author_facet V. S. Serov
H. W. Schüermann
E. Svetogorova
author_sort V. S. Serov
title Application of the Banach Fixed-Point Theorem to the Scattering Problem at a Nonlinear Three-Layer Structure with Absorption
title_short Application of the Banach Fixed-Point Theorem to the Scattering Problem at a Nonlinear Three-Layer Structure with Absorption
title_full Application of the Banach Fixed-Point Theorem to the Scattering Problem at a Nonlinear Three-Layer Structure with Absorption
title_fullStr Application of the Banach Fixed-Point Theorem to the Scattering Problem at a Nonlinear Three-Layer Structure with Absorption
title_full_unstemmed Application of the Banach Fixed-Point Theorem to the Scattering Problem at a Nonlinear Three-Layer Structure with Absorption
title_sort application of the banach fixed-point theorem to the scattering problem at a nonlinear three-layer structure with absorption
publisher SpringerOpen
series Fixed Point Theory and Applications
issn 1687-1820
1687-1812
publishDate 2010-01-01
description 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.
url http://dx.doi.org/10.1155/2010/439682
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AT hwschamp252ermann applicationofthebanachfixedpointtheoremtothescatteringproblematanonlinearthreelayerstructurewithabsorption
AT esvetogorova applicationofthebanachfixedpointtheoremtothescatteringproblematanonlinearthreelayerstructurewithabsorption
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