Two-dimensional diffraction on a cylinder induced by a laser beam in a nonlinear gradient medium

A wave theory was developed and a numerical simulation performed of the diffractive flow of a signal wave around a negative inhomogeneity induced by a cylindrical pump beam in nonlinear medium while keeping both waves in the potential well. It was shown that a broad pump beam reflects a narrow signal beam. A nonlinear waveguide (a dark soliton) is described as well. These phenomena can be observed in Bose-Einstein condensate (BEC) and in a gradient waveguide.