Birth, evolution and annihilation of phase singularities in the propagation of a laser beam passed through a self-focusing strontium barium niobate crystal

We report the first observations and the mechanism of natural nucleation, propagation and annihilation of optical vortices in a laser beam with initially smooth Gaussian wave front passed through self-focusing photorefractive strontium barium niobate crystal. Wave-front distortions due to the formation of thermal-induced nonlinear lens lead to the origin of phase singularities. Pairs of opposite topological charge screw wave-front dislocations nucleate and annihilate through a formation of limited edge dislocations. In a free-space propagation the alternating sign vortices array nested in the beam has the form of quadruple.