Light localization in a linearly graded-index substrate covered by intensity dependent nonlinear self-focusing cladding

Abstract

The new features of the light localization along the graded-index substrate covered by the cladding characterized by a self-focusing nonlinearity are described theoretically. In the model of nonlinearity the dielectric function in substrate depends linearly on the distance from the cover-substrate interface. The optical characteristics of Kerr type positive nonlinear response in the cover is changed abruptly with an increasing light intensity. The light intensity distribution in across interface direction described by exact solution to nonlinear wave equation is calculated and analyzed. It is found that increasing the width of the graded-index layer leads to a shift in the position of the maximum intensity. The intensity maximum appears in the graded-index substrate after the effective refractive index reaches the critical value. The thickness of nonlinear near-surface layer, which is formed after the light intensity reaches the critical value, monotonically decreases with increasing width of the graded-index layer. The possibility of realizing a multimode regime of the light propagation, which can be realized with an increasing width of the graded-index layer and it is characterized by a deep penetration of the light field into the substrate, is derived. The possibility of control the distribution of the light power between the cover and substrate by change in the effective refractive index and the width of the graded-index layer is described.

Surface waves propagating along the interface between a parabolic graded-index medium and a self-focusing nonlinear medium: exact analytical solution

“…We find also the exact analytical solutions describing the surface waves propagating along the contact between the linearly graded-index layer and crystal with the layer, in which the Kerr nonlinear response appears with increasing the electric field [61]. In addition, we describe theoretically light localization in a linearly graded-index substrate covered by intensity dependent nonlinear self-focusing cladding [62].…”

New features of the surface wave propagation along an exponentially graded-index layer and nonlinear substrate with generalized Kerr-type nonlinear response

“…In this paper, we continue research aimed at finding exact analytical solutions that describe new types of nonlinear surface waves traveling along the contact of graded-index and nonlinear media. Our previous papers [41,42] devoted to the waves propagating along the linearly graded-index layer covered by nonlinear medium with a sharp change in the value of the Kerr nonlinearity coefficient in dependence of the wave amplitude. Here we present new surface waves travelling along the interface between a medium with the same type of the Kerr nonlinearity generalization (proposed in [43]) and an exponentially graded-index layer [23,24].…”