Parametric frequency conversion of optical vortices

Summary form only given. It is demonstrated that walk-off essentially changes the dynamics of optical vortex interaction in sum-frequency mixing in nonlinear crystals. The walk-off breaks the interaction symmetry and various phenomena of vortex interaction may be observed. They include the decay of higher order vortex into singly charged vortices, particle-like interaction of vortices as pulling and pushing, an appearance of the pairs of vortices having opposite topological charges in the case of fundamental wave depletion.