Nonlinear waves in a waveguide with a linear spatial profile of the refractive index and a near-surface layer with disappearing nonlinearity

We consider the planar contact of the layer with a linear spatial profile of the refractive index and the medium where the nonlinear Kerr-type response disappears in the near-surface layer with an increment in the light intensity. We use special form of dielectric function which depends on spatial coordinate in the layer with a linear index profile and on electric field amplitude in nonlinear medium. We derive exact solutions to formulated equations in the cases of positive and negative values of the Kerr nonlinearity coefficient corresponding to self-focusing and defocusing nonlinear responses respectively, which disappear with enhancing light intensity. We obtain that a varying in the value of the effective refractive index and the width of the layer with a linear index profile leads to the possibility of adjusting the intensity level of the light field in the transverse direction in different areas of the waveguide structure. The width of formed near-surface layer increases with enhancing the effective refractive index the fixed values of the critical field and the width of the layer with a linear profile of the refractive index. We show the evolution of the appearance of high-order modes with an increase in the width of the layer with a linear index profile depending on the effective refractive index. We calculate the power flows, the analysis of which shows the possibility of control the level of energy carried by the surface waves along the waveguide at different distances from the contact surface.