Nonlinear interface waves in a trilayered optical structure with different layer characteristics and internal self-focusing

A model of a trilayered optical structure, the plane-parallel boundary of which possesses its own nonlinear properties, is considered. The inner layer with a finite thickness is an optically transparent medium with Kerr self-focusing nonlinearity, which is in contact with linear half-spaces from the outer surface that are characterized by refractive indices independent of the electric field strength amplitude. Refractive indices in the layer interfaces within infinitely small thicknesses are approximated by the dependence that includes Dirac's delta function. It is shown that the mathematical formulation of the model boils down to a nonlinear Schrödinger equation with a nonlinear self-consistent potential. It is established that two types of nonlinear localized waves of the electric field strength perturbations can propagate along the layers in the considered trilayered structure. Dispersion relations of the interface waves that allow one to determine the propagation constant and decrements of their spatial attenuation in linear half-spaces as a function of the system parameters are derived. Conditions for localization of a luminous flux along the layer interfaces are analyzed in relation to the sign of the layer parameters. It is shown that the characteristic distance of the field localization linearly depends on the interface nonlinear response parameter. It is established that the characteristic localization distance is shortened in the case of a positive nonlinear response in comparison with the localization length when interfaces do not interact with the field and lengthened in the case of a negative nonlinear response.