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Solutions to the Helmholtz equation for TE-guided waves in a three-layer structure with Kerr-type nonlinearity. (English) Zbl 1038.78016
Summary: We study certain solutions (TE-polarized electromagnetic waves) of the Helmholtz equation on the line describing waves propagating in a nonlinear three-layer structure consisting of a film surrounded by semi-infinite media. All three media are assumed to be lossless, nonmagnetic, isotropic and exhibiting a local Kerr-type dielectric nonlinearity. The linear component of the permittivity is modelled by a continuous real-valued function of the transverse coordinate. We show that the solution of the Helmholtz equation in the form of a TE-polarized electromagnetic wave exists and can be obtained by iterating the equivalent Volterra equation. The associated dispersion equation has a simple root (if the semi-infinite media are linear and if the nonlinearity parameter of the film is sufficiently small) that uniquely determines this solution.
78A60Lasers, masers, optical bistability, nonlinear optics
35C05Solutions of PDE in closed form
35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
45D05Volterra integral equations
78A48optics in special media