Gaussian Lenses Initiate Optical Vortices in LaserBeams During Self-action in Kerr-like Medium

It is shown that Gaussian lenses initiate closed line of dislocations in coherent beamswith initially smooth wavefront. The stigmatic lenses originate the circle line of edge dislocation,situated on the beam cross-section. In the case of astigmatic Gaussian lens this closed curve getsout from the plane and a quadruple of alternate single-charged optical vortices is born andannihilates in the beam cross-section. The distribution of topological charge signs in the quadruplealong z axis is defined by focusing or defocusing type of Gaussian lens. The model ofGaussian lenses explains self-action of fundamental mode laser beams transmitted by Kerr-likemedia. Two methods were used for study of optical singularities appearance: the geometricaloptics analysis for rapid qualitative location and numerical modeling of Kirchhoff-Fresnel integralfor exact solution.