New patterns of the light intensity distribution localized near the interface between the crystal with a hyperbolic index profile layer and the crystal with the nonlinearity emergence with an increasing light intensity

¹ Russian Sergo Ordzhonikidze State Geological Prospecting University, Miklukho-Maklaya St., 23, 117997, Moscow, Russia
² Moscow Technical University of Communications and Informatics, Aviamotornaya St., 8a, 111024, Moscow, Russia

^* Corresponding author: savotchenkose@mail.ru

Received: 23 November 2024
Accepted: 4 September 2025

Abstract

The nonlinear wave propagation along interface between a hyperbolic graded-index crystal and a nonlinear crystal where the Kerr nonlinear response emerges when the light intensity exceeds its threshold value is considered. New model of such contacting crystals basing on the wave equation with the nonlinear and inhomogeneous dielectric constant is formulated. New exact analytical solutions describing the surface waves and waveguide modes in both cases of the positive and negative nonlinearity signs corresponding to a self-focusing and defocusing nonlinear response emergence respectively are found. It is found that the maximum of the light intensity can be located in both nonlinear and the hyperbolic graded-index crystals in the case of a self-focusing nonlinearity emergence in dependence of the values of the system parameters. However, the light intensity maximum is always located in the graded-index crystal in the case of a defocusing nonlinearity emergence. The localization width of the light flux decreases with an increase in the effective refractive index in the both cases of nonlinearity signs. The waveguide modes characterized by several intensity maxima distributed in a hyperbolic graded-index crystal can be excited (in addition to the surface waves characterized by a single intensity maximum localized near the interface). The hyperbolic profile parameters can be considered the most effective parameters controlling the light intensity transverse distribution and an excitation of the high-order waveguide modes.