The Gaussian lenses give birth to optical vortices in laser beams

It is shown theoretically that Gaussian-like lenses initiate birth, evolution and annihilation of the phase singularities in coherent beams with initially smooth wavefront. The stigmatic lens originates circular edge dislocation, which disappears immediately. The astigmatic Gaussian lenses give birth to quadrupoles of opposite single-charged optical vortices. The optical vortices move in space along a closed trajectory, the more stretched the greater is the lens astigmatism. The developed model gives the complete scenario of the optical singularities origin and evolution, and describes naturally all experimentally observed features for known light-induced Gaussian-like nonlinear lenses.