Analytic Studies on the Helmholtz Spatial Solitons in Power-Law Optical Materials

Abstract

In order to describe refraction phenomena, the propagation of a spatial soliton in power-law optical materials is considered. Hereby, we work on the behavior of solitons described by a generalized nonlinear Helmholtz equation in the power-law optical materials. Via the Hirota method, analytic one- and two-soliton solutions are obtained. We study the spatial solitons in two adjoining power-law materials with dissimilar medium coefficients. Based on the choice of the Heaviside function in the equation, we distinguish the two different optical materials. One-soliton dynamics with different choices of the nonlinear and linear refractive properties along the propagation direction of the carrier wave are discussed. In the first medium, with an increase of the inverse width, the soliton will be amplified. In the second medium, the soliton amplitude will increase when the linear refractive property increases, or the nonlinear refractive property decreases. Asymptotic analysis is carried out on the two-soliton solutions. Through a graphic and asymptotic analysis, we find that there exist elastic and inelastic collisions between two solitons, as well as soliton fusion.