Symmetrical localized states in three-layered structure consisting of linear layer between defocusing media separated by interfaces with nonlinear response

Abstract

The three-layered symmetric structure consisting of a linear layer sandwiched between defocusing nonlinear media was considered. The layers are separated by interfaces with nonlinear properties. The nonlinear symmetrical localized states arising in such a structure were described theoretically. The proposed model is based on the nonlinear Schrodinger equation with negative Kerr-type nonlinear term and nonlinear self-consistent potential describing the interaction of the waves and interfaces. Even and odd solutions of nonlinear Schrodinger equation correspond to the localized states of two types existing in different energy ranges. The stationary state energies as the system parameter functions are calculated in explicit form. The conditions of their existence were analyze depending on the combination of signs of nonlinear interface parameters. The localized states of the special kinds existing only for the case of interfaces, which are characterized by a strong nonlinear response, were found. The dependencies of localization energies on the amplitude of the interface oscillations were studied analytically.