Локализация возбуждений вблизи тонкого дефектного слоя с нелинейными свойствами, разделяющего линейный и нелинейный кристаллы

Abstract

It is shown that the localized and quasi-local stationary states exist near a thin defect layer with nonlinear properties separating a linear medium from a non-linear medium of Kerr type. Localized states are characterized by a monotonically decreasing field amplitude on both sides of the interface. Quasi-local states are described by a field in the form of a standing wave in a linear medium and monotonously decreasing in a nonlinear medium. The contacts with nonlinear self-focusing and defocusing media are analyzed. The mathematical formulation of the proposed model is a system of linear and nonlinear Schrödinger equations with a potential that is nonlinear with respect to the field and which simulates a thin defect layer with nonlinear properties. Dispersion relations determining the energy of local and quasi-local states are obtained. The expressions for energies were obtained explicitly in limiting cases and the conditions for their existence were indicated.