Nonlinear Surface Waves near the Interface between a Graded-Index Layer and a Medium with the Sign of the Kerr Nonlinearity Varying Depending on the Electric Field

We consider the contact of a medium in which the refractive index linearly decreases depending on the distance to a nonlinear medium, where the sign of the Kerr nonlinearity can change abruptly when the electric-field strength reaches a threshold value. It is established that surface waves of three types can propagate along such a contact, depending on the sign of the nonlinearity and the range of values of the effective refractive index. Explicit analytical expressions are obtained for the distribution of the electric-field strength in the transverse direction with respect to the contact plane, which are exact solutions of the formulated nonlinear equations. It is shown that the formation of electric-field distributions corresponding to waveguide modes with several intensity maxima is possible in the layer with a refractive-index gradient.