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

Fixexd point theory and applications

VS Serov¹  HW Schü²  E Svetogorova³  ermann⁴ 

[1] Department of Mathematical Sciences, University of Oulu, Oulu, Finland;Department of Physics, University of Osnabrück, Germany;ck, Osnabrü

关键词: Integral Equation;    Electromagnetic Wave;    Differential Geometry;    Differentiable Function;    Computational Biology;   

DOI  :  10.1155/2010/439682

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY