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Integral equation approach to reflection and transmission of a plane TE-wave at a (linear/nonlinear) dielectric film with spatially varying permittivity

Integral equation approach to reflection and transmission of a plane TE-wave at a... A method 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 (linear or nonlinear) dielectric film situated between two linear semi-infinite media. All three media are assumed to be lossless, nonmagnetic and isotropic. The permittivity of the film is modelled by (i) a continuously differentiable real-valued function of the transverse coordinate, and by (ii) a Kerr-nonlinearity. It is shown that the solution of the Helmholtz equation exists in the form of a uniformly convergent series (in case (i)) and in the form of a uniformly convergent sequence (in case (ii)) of iterations of the equivalent Volterra integral equation. Numerical results of the approach are presented. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Physics A: Mathematical and General IOP Publishing

Integral equation approach to reflection and transmission of a plane TE-wave at a (linear/nonlinear) dielectric film with spatially varying permittivity

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Copyright
Copyright 2004 IOP Publishing Ltd
ISSN
0305-4470
eISSN
1361-6447
DOI
10.1088/0305-4470/37/10/012
Publisher site
See Article on Publisher Site

Abstract

A method 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 (linear or nonlinear) dielectric film situated between two linear semi-infinite media. All three media are assumed to be lossless, nonmagnetic and isotropic. The permittivity of the film is modelled by (i) a continuously differentiable real-valued function of the transverse coordinate, and by (ii) a Kerr-nonlinearity. It is shown that the solution of the Helmholtz equation exists in the form of a uniformly convergent series (in case (i)) and in the form of a uniformly convergent sequence (in case (ii)) of iterations of the equivalent Volterra integral equation. Numerical results of the approach are presented.

Journal

Journal of Physics A: Mathematical and GeneralIOP Publishing

Published: Mar 12, 2004

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