Nonlinear mixing of optical vortices

We present optical vortex beams interaction via degenerate two-wave mixing in liquid crystal light-valve, LCLV. The LCLV is made by combining a transparent photosensitive substrate with a nematic liquid crystal and displays a large Kerr-like effect. Being characterized by a large transverse size and spatial homogeneity, the LCLV allows performing nonlinear mixing experiments with several vortex beams and testing the interaction of different topological charges. We show that the wave-mixing occurring in the LCLV leads to the exchange of topological charge between vortex and to a cascaded generation of vortex beams. A mean-field model is developed and is shown to account for the charge selection rules observed after the mixing process. Fractional charges are demonstrated to participate to the wave-mixing in a robust way, following the same charge selection rules as for integer charges.