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

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.

Guided Electromagnetic Waves Propagating in a Two-Layer Cylindrical Dielectric Waveguide with Inhomogeneous Nonlinear Permittivity

“…Results obtained in this paper together with the results given in [16] give an opportunity to consider a very intriguing phenomenon of coupled electromagnetic TE-TM wave propagation in a two-layered cylindrical waveguide. This problem will be treated in a separate paper.…”

“…It is assumed that waves propagating along the boundary of Σ depend harmonically on [1,8,16,23]. Substituting the TM waves into (3) one is convinced that the field does not depend on .…”

“…where the functions 1 , 2 are easily found. Thus the problem M (0) is a (linear) problem of Sturm-Liouville type for (16) with conditions (19).…”

“…Currently there has been significant progress in studying of polarised electromagnetic TE and TM wave propagation in waveguide structures (for a planar waveguide, see [8][9][10][11]; for a circular cylindrical waveguide, see [1,8,[12][13][14][15]; for a circular two-layered cylindrical waveguide, see [7,16]) filled with nonlinear dielectric permittivities. In particular, theorems on existence and localization of eigenvalues in some of these problems have been proved.…”

“…Most of these papers are devoted to studying of polarized waves in waveguides filled with a homogeneous nonlinear medium. From aforementioned studies only [7,13,15,16] focus on inhomogeneous nonlinear permittivity.…”