We predict theoretically and generate in a photorefractive crystal two-dimensional self-trapped periodic waves of different symmetries, including vortex lattices-patterns of phase dislocations with internal energy flows. We demonstrate that these nonlinear waves exist even with anisotropic nonlocal nonlinearity when the optically-induced periodic refractive index becomes highly anisotropic, and it depends on the orientation of the two-dimensional lattice relative to the crystallographic c-axis.
