Light localization near an interface between media with an exponential permittivity profile and a sharply vanishing Kerr nonlinearity with an increasing light intensity

New peculiarities of light localization near the interface between media with an exponential profile of the dielectric permittivity and with a sharp suppression of the Kerr nonlinear response in a near-surface layer formed with an increasing light intensity are described theoretically. Two signs of nonlinear response corresponding to self-focusing and defocusing nonlinear media are considered. Exact solutions to stationary wave equation with dielectric permittivity consisting of spatial-dependent and intensity-dependent parts satisfying the boundary conditions at the medium interface and the near-surface layer boundary are found. The effect of the optical and geometric parameters on the transverse distribution of the light intensity and the features of the lightwave localization is analyzed. It is found that light localization length decreases with a decrease in the wavelength of excited radiation but the maximum of intensity remains unchanged. The wave intensity enlarges with an increase in the effective refractive index and in the threshold intensity. The near-surface domain width where a nonlinear response is suppressed enlarges with increasing the effective refractive index, the threshold intensity, and the Kerr nonlinearity coefficient. It reduces with increasing values of the parameters of the exponential graded-index layer. It is shown that the largest portion of the lightwave power is concentrated in the near-surface domain with suppressed nonlinear response, which plays the role of the main waveguide layer. It is found that the optical parameters of the exponential graded-index layer affect the redistribution of the wave energy between the contacting areas of the waveguide structure.