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The propagation of electromagnetic waves in cylindrical dielectric waveguides filled with a nonlinear medium. (Russian, English) Zbl 1114.78002

Zh. Vychisl. Mat. Mat. Fiz. 44, No. 10, 1850-1860 (2004); translation in Comput. Math. Math. Phys. 44, No. 10, 1762-1772 (2004).
Propagation of electromagnetic waves in dielectric waveguides of circular section filled with medium with Kerr-like nonlinearity is studied. The problem reduces to solving a nonlinear integral equa- tion with the kernel given by the Green’s function for the Bessel equation. The existence of propagating TE-polarized waves is proved by means of the Schauder principle and the contracting mapping method. An iteration algorithm for numerical solving of the problem is suggested, and its convergence is proved. The existence of roots of the dispersion equation – the waveguide propagation constants – is proved. Conditions for the propagation of one, two, three, or four waves are obtained, and the localization domains of the corresponding propagation constants are found. Dependences of the propagation con- stants on various parameters are numerically constructed.

MSC:

78A25 Electromagnetic theory (general)
78A50 Antennas, waveguides in optics and electromagnetic theory
35Q60 PDEs in connection with optics and electromagnetic theory