New interface waves propagating along the contact between the media with a hyperbolic profile of the dielectric function and a step-change in the Kerr nonlinearity coefficients

New types of nonlinear interface waves propagating along a planar interface between a hyperbolic gradient medium and nonlinear medium characterized by a step-wise change in the Kerr nonlinearity coefficients under the electric field influence are obtained. The influence of the waveguide system parameters on the spatial profiles of the field distribution in the direction transverse to the interface is analyzed in detail. The height of the peak intensity of waves in the case of self-focusing nonlinearity increases, and that of waves in the case of defocusing nonlinearity decreases with an increase in the effective refractive index. The maximum intensity of the wave field in a self-focusing medium can be located in the nonlinear near-interface layer, and the peak can move to the hyperbolic gradient medium with an increase in the characteristic distance of the hyperbolic profile, however, the maximum intensity of the wave field in a defocusing medium can always be located in the hyperbolic gradient medium. The influence of the waveguide system parameters on the control of the width of the formed near-interface layer for the waves of the two types under consideration differs significantly. Comparative analysis of the relative intensities and relative power flows shows that their behavior is identical depending on the control parameters of the waveguide system at a qualitative level. The largest share of energy flow is concentrated in the nonlinear near-interface layer in the case of self-focusing nonlinearity and it is concentrated in the hyperbolic gradient medium in the case of defocusing nonlinearity.