Wave Interaction with the Defect Characterized by Nonlinearity of General Form

Abstract

Possible types of stationary states and waves in linear media separated by a nonlinear interface are analyzed. The mathematical formulation of the model is reduced to a one-dimensional boundary value problem for the nonlinear Schrödinger equation. The nonlinearity of the equation in the form of an arbitrary function of the desired field is taken into account only inside the waveguide. It is shown that there are stationary states of three types for different ranges of propagation constant values. The dispersion dependences of the propagation constant as functions of the parameters of the medium and the interface have explicitly been obtained for stationary states of all types, and conditions of their existence have been indicated. It is shown that total wave transition through the interface is possible. It has been established that the total transition of wave through the interface with nonzero parameters can occur only if the nonlinear response of the medium is taken into account.