Optical vortices in self-focusing Kerr nonlinear media

In this work we numerically compare the interaction of optical vortices (OVs) in self-defocusing and self-focusing Kerr nonlinear media. We find that the basic scenarios (attraction/repulsion, translation/rotation vs. background) in the interaction of two and three vortices with equal and alternative topological charges (TCs) are the same in both media. However, the vortex dynamics under self-focusing conditions is influenced by the reshaping of the surrounding part of the background. Square structure of OVs with alternating TCs is found to be stable with respect to the vortex positions in self-focusing media. This elementary cell is successfully generalized in a large square array of OVs with alternative TCs which brings ordering in the multiple filamentation of the background beam in self-focusing conditions.