Application of the Banach Fixed-Point Theorem to the Scattering Problem at a Nonlinear Three-Layer Structure with Absorption
|Serov, V. S.
Schueermann, H. W.
|DIELECTRIC FILM; ELECTROMAGNETIC-WAVES; Mathematics; Mathematics, Applied; OPTICAL-RESPONSE; PLANE TE-WAVE; REFLECTION; TRANSMISSION
|HINDAWI PUBLISHING CORPORATION
|FIXED POINT THEORY AND APPLICATIONS
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.
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