Surface waves propagating along an interface between media with an exponential spatial profile of the dielectric function and an abruptly appearance of a self-focusing nonlinear response in a near-surface layer at the strong light intensity.

Surface waves propagating along the planar interface between an exponentially graded-index medium and the non-Kerr-type nonlinear medium are described analytically. Equations describing the stationary transverse electric wave propagation containing two-component spatially and intensity dependent dielectric function are formulated. The proposed model describes an appearance at the finite distances from the interface a self-focusing nonlinear response when the electric field amplitude exceeds the critical value. New features of the localization of surface wave depending on the optical and geometric parameters of the system are specified analytically. An increase in the frequency adduces to an increase in the field penetration depth in the nonlinear medium and to a reducing the penetration depth in the exponentially graded-index medium. The thickness of the formed near-surface layer with a nonlinear response is about two light localization lengths along the interface. This thickness reduces with an increase in the system parameter. Its maximum at the critical value of the effective refractive index is observed and explicit equation determining this maximum is obtained. Explicit equation of the time-average total power flow conserving along the medium interface is calculated. The main part of the energy flux of the surface wave is concentrated in the near-surface layer in a wide range of values of the system parameters. [ABSTRACT FROM AUTHOR]