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Integral equation approach for the propagation of TE-waves in a nonlinear dielectric cylindrical waveguide. (English) Zbl 1067.35122
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:
35Q60PDEs in connection with optics and electromagnetic theory
78A40Waves and radiation (optics)