Abstract

Since that time there were no investigations about refractive index modulation by incident wave in nonlinear medium and how an opportunity of reflected wave birth depends on that modulation. In this paper we study numerically^[4] this phenomenon in the case of Kerr nonlinear medium. Some results have been obtained, which show how taking into account refractive index gradient in nonlinear Schrodinger equation changes considerably the global character of beams propagating.^[1] Now the self-focusing nonlinear medium looks like a mirror (some aspects of reflection phenomenon were printed in Refs. 2, 3). The equations of this process are given by where${\text{A}}_{+}^{-}$ are complex beam amplitudes, which are given in terms of incident beam amplitude maximum value (A+₀). A_ the reflected beam amplitude, z dimensionless coordinate along which the incident optical radiation spreads, k_o the wave number of beams, n₂ $\left(|{\text{A}}_{+}^{-}{|}^{\text{2}}\right)$ the nonlinear addition to linear refractive index n_o, $\Delta \perp =\frac{{\partial }^2}{\partial {\text{x}}^2}+\frac{{\partial }^2}{\partial {\text{y}}^{2’}}\text{x,y}$ dimensionless transverse coordinates.

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