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.
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