Surface Waves at the Interface of a Photorefractive Crystal and a Medium with Positive Kerr Nonlinearity
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Surface Waves at the Interface of a Photorefractive Crystal and a Medium with Positive Kerr Nonlinearity S. E. Savotchenko* Belgorod State Technological University named after V.G. Shukhov, Belgorod, Russia *e-mail: [email protected] Received October 19, 2019; revised October 19, 2019; accepted October 25, 2019
Abstract—The types of nonlinear surface waves with extraordinary polarization arising at the interface between a photorefractive crystal and a medium with positive Kerr nonlinearity are described. It has been shown that nonlinear surface waves of two types with an asymmetric profile can exist in such a system. Waves of the first type damp when moving away from the interface into the depth of the photorefractive and Kerr crystals without oscillations, while waves of the second type damp into the depth of a photorefractive crystal with oscillations. Dispersion relations have been obtained and the conditions for the existence of all described types of waves have been written depending on the optical characteristics of the crystals. Keywords: media interface, photorefractive crystal, optical nonlinear medium, nonlinear surface waves DOI: 10.1134/S1063783420060268
1. INTRODUCTION There are a lot of theoretical works devoted to the description of surface electromagnetic waves (plasmons, polaritons) at the boundaries of various media [1–7]. Of particular importance are studies of the properties of surface waves in various nonlinear optical media such as photorefractive crystals [8–11] and media with a Kerr effect [12]. However, poorly understood are the features of the propagation of nonlinear surface waves at the boundaries of media in which nonlinear effects are due to various processes of the charges density redistribution and the field induced by them. Therefore, many practically important aspects require detailed analysis. In particular, these include the laws governing the formation of nonlinear surface waves with an asymmetric profile arising near the boundaries between photorefractive crystals and other nonlinear optical media. In most existing theoretical works, the localization of the electromagnetic field excitations near interfaces of media with the same forms of nonlinearity and physical nature is treated. The most common case is the contact between two media with Kerr nonlinearity [13–18], or an interface of the linear and nonlinear media [19–22]. In this paper, we propose a theoretical description of new types of nonlinear localized states corresponding to surface waves at the boundary of two optical media with nonlinear forms of various physical nature. Obviously, such surface waves will have an asymmetric profile relative to the interface.
2. MODEL FORMULATION Consider the contact of a uniaxial photorefractive crystal with a diffusion process of nonlinearity formation and a uniaxial crystal with Kerr nonlinearity (hereinafter, for brevity, it is called a Kerr crystal) in the absence of an applied external field. The interface between crystals is assumed to be so thin that the optical effec
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