Application of the Banach Fixed-Point Theorem to the Scattering Problem at a Nonlinear Three-Layer Structure with Absorption. (30th May 2010)

• Record Type: Journal Article
• Authors: Serov, V. S.; Schüermann, H. W.; Svetogorova, E.
• Other Names: Furi Massimo Academic Editor.
• Is Part Of: Fixed point theory and applications. Volume 2010(2010)
• Publication Date: 2010-05-30
• Subjects: Fixed point theory -- Periodicals; Mappings (Mathematics) -- Periodicals; 515.7248
• DOI: 10.1155/2010/439682
• Languages: English
• ISSNs: 1687-1812

Abstract

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.