Nonlinear transmission eigenvalue problem describing TE wave propagation in two-layered cylindrical dielectric waveguides. (Russian, English) Zbl 1299.78015

Zh. Vychisl. Mat. Mat. Fiz. 53, No. 7, 1150-1161 (2013); translation in Comput. Math. Math. Phys. 53, No. 7, 973-983 (2013).
Summary: The paper is concerned with propagation of surface TE waves in a circular nonhomogeneous two-layered dielectric waveguide filled with a Kerr nonlinear medium. The problem is reduced to the analysis of a nonlinear integral equation with a kernel in the form of a Green’s function. The existence of propagating TE waves is proved using the contraction mapping method. For the numerical solution of the problem, two methods are proposed: an iterative algorithm (whose convergence is proved) and a method based on solving an auxiliary Cauchy problem (the shooting method). The existence of roots of the dispersion equation (propagation constants of the waveguide) is proved. Conditions under which \(k\) waves can propagate are obtained, and regions of localization of the corresponding propagation constants are found.


78A50 Antennas, waveguides in optics and electromagnetic theory
45G05 Singular nonlinear integral equations
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