Schürmann, H. W.; Serov, V. S.; Shestopalov, Yu. V. Solutions to the Helmholtz equation for TE-guided waves in a three-layer structure with Kerr-type nonlinearity. (English) Zbl 1038.78016 J. Phys. A, Math. Gen. 35, No. 50, 10789-10801 (2002). 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. Cited in 6 Documents MSC: 78A60 Lasers, masers, optical bistability, nonlinear optics 35C05 Solutions to PDEs in closed form 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 45D05 Volterra integral equations 78A48 Composite media; random media in optics and electromagnetic theory Keywords:Volterra equation PDFBibTeX XMLCite \textit{H. W. Schürmann} et al., J. Phys. A, Math. Gen. 35, No. 50, 10789--10801 (2002; Zbl 1038.78016) Full Text: DOI