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

Abstract EN

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.