Counterpropagating optical vortices in photorefractive crystals

We present a comprehensive numerical study of (2+1)D counterpropagating incoherent vortices in photorefractive crystals, in both space and time. We consider a local isotropic dynamical model with Kerr-type saturable nonlinearity, and identify the corresponding conserved quantities. We show, both analytically and numerically, that stable beam structures conserve angular momentum, as long as their stability is preserved. As soon as the beams loose stability, owing to radiation or non-elastic collisions, their angular momentum becomes non-conserved. We discover novel types of rotating beam structures that have no counterparts in the copropagating geometry. We consider the counterpropagation of more complex beam arrangements, such as regular arrays of vortices. We follow the transition from a few beam propagation behavior to the transverse pattern formation dynamics.