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

<p>Abstract</p> <p>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 fi...

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Main Authors: Sch&#252;ermann HW, Svetogorova E, Serov VS
Format: Article
Language:English
Published: SpringerOpen 2010-01-01
Series:Fixed Point Theory and Applications
Online Access:http://www.fixedpointtheoryandapplications.com/content/2010/439682
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spelling doaj-ccf8666060bc4f8c8165b5a6f1ac39b22020-11-25T01:55:00ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122010-01-0120101439682Application of the Banach Fixed-Point Theorem to the Scattering Problem at a Nonlinear Three-Layer Structure with AbsorptionSch&#252;ermann HWSvetogorova ESerov VS<p>Abstract</p> <p>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.</p>http://www.fixedpointtheoryandapplications.com/content/2010/439682
collection DOAJ
language English
format Article
sources DOAJ
author Sch&#252;ermann HW
Svetogorova E
Serov VS
spellingShingle Sch&#252;ermann HW
Svetogorova E
Serov VS
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 Sch&#252;ermann HW
Svetogorova E
Serov VS
author_sort Sch&#252;ermann HW
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 <p>Abstract</p> <p>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.</p>
url http://www.fixedpointtheoryandapplications.com/content/2010/439682
work_keys_str_mv AT sch252ermannhw applicationofthebanachfixedpointtheoremtothescatteringproblematanonlinearthreelayerstructurewithabsorption
AT svetogorovae applicationofthebanachfixedpointtheoremtothescatteringproblematanonlinearthreelayerstructurewithabsorption
AT serovvs applicationofthebanachfixedpointtheoremtothescatteringproblematanonlinearthreelayerstructurewithabsorption
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