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