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Advances in Numerical Analysis
Volume 2014 (2014), Article ID 231498, 11 pages
http://dx.doi.org/10.1155/2014/231498
Research Article

Nonlinear Double-Layer Bragg Waveguide: Analytical and Numerical Approaches to Investigate Waveguiding Problem

Department of Mathematics and Supercomputing, Penza State University, Krasnaya Street 40, Penza 440026, Russia

Received 30 June 2013; Accepted 14 November 2013; Published 22 January 2014

Academic Editor: Theodore E. Simos

Copyright © 2014 Yury G. Smirnov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The paper is concerned with propagation of surface TE waves in a circular nonhomogeneous two-layered dielectric waveguide filled with nonlinear medium. The problem is reduced to the analysis of a nonlinear integral equation with a kernel in the form of the Green function. The existence of propagating TE waves for chosen nonlinearity (the Kerr law) is proved using the contraction mapping method. Conditions under which k waves can propagate are obtained, and intervals of localization of the corresponding propagation constants are found. For numerical solution of the problem, a method based on solving an auxiliary Cauchy problem (the shooting method) is proposed. In numerical experiment, two types of nonlinearities are considered and compared: the Kerr nonlinearity and nonlinearity with saturation. New propagation regime is found.