Nonlinear Double-Layer Bragg Waveguide: Analytical and Numerical Approaches to Investigate Waveguiding Problem. (22nd January 2014)

• Record Type: Journal Article
• Authors: Smirnov, Yury G.; Smol'kin, Eugenii Yu.; Valovik, Dmitry V.
• Other Names: Simos Theodore E. Academic Editor.
• Is Part Of: Advances in numerical analysis. Volume 2014(2014)
• Publication Date: 2014-01-22
• Subjects: Numerical analysis -- Periodicals; Numerical analysis; Periodicals; Electronic journals; 518
• DOI: 10.1155/2014/231498
• Languages: English
• ISSNs: 1687-9562

Abstract

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.