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.
Highlights
Scattering of transverse-electric TE electromagnetic waves at a single nonlinear homogeneous, isotropic, nonmagnetic layer situated between two homogeneous, semiinfinite media has been the subject of intense theoretical and experimental investigations in recent years
The Kerr-like nonlinear dielectric film has been the focus of a number of studies 1–6
Exact analytical solutions have been obtained for the scattering of plane TE-waves with Kerr-nonlinear films 7, 8
Summary
Scattering of transverse-electric TE electromagnetic waves at a single nonlinear homogeneous, isotropic, nonmagnetic layer situated between two homogeneous, semiinfinite media has been the subject of intense theoretical and experimental investigations in recent years. Exact analytical solutions have been obtained for the scattering of plane TE-waves with Kerr-nonlinear films 7, 8. Using these solutions, we determine the phase function θ y of the electric field, and, evaluating the boundary conditions, we derive analytical expressions for reflectance, transmittance, absorptance, and phase shifts on reflection and transmission. In order to prove that the sequence 2.24 is uniformly convergent to the solution of 2.14 it suffices to check that all conditions of the Banach fixed-point theorem 12 are fulfilled
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