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Zbl 1067.35122
Smirnov, Y.; Schürmann, H.W.; Shestopalov, Y.
Integral equation approach for the propagation of TE-waves in a nonlinear dielectric cylindrical waveguide. (English)
[J] J. Nonlinear Math. Phys. 11, No. 2, 256-268 (2004). ISSN 1402-9251; ISSN 1776-0852/e

Summary: We consider the propagation of TE-polarized electromagnetic waves in cylindrical dielectric waveguides of circular cross section filled with lossless, nonmagnetic, and isotropic medium exhibiting a local Kerr-type dielectric nonlinearity. We look for axially-symmetric solutions and reduce the problem to the analysis of the associated cubic-nonlinear equation. We show that the solution in the form of a TE-polarized electromagnetic wave exists and can be obtained by iterating a cubic-nonlinear integral equation. We derive the associated dispersion equation and prove that it has a root that determines this solution.

MSC 2000:: *35Q60 PDE of electromagnetic theory and optics
78A40 Waves and radiation

Keywords: Maxwell equations; nonlinear second-order ordinary differential equation; nonlinear integral equation

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