Restoration scale in nonequilibrium optical vortex fields

The evolution of the number of vortices in an artificial vortex field is investigated using numerical simulations. These vortex fields are artificial in the sense that vortices with the same topological charge are separated from vortices with the opposite topological charge and placed in the same region or cell. It is found that the number of vortices in such a field increases during propagation until equilibrium is reached where the vortex field behaves like a random wave field: the topological charges of neighboring vortices are anticorrelated and the vortex density is determined by the coherence area. The restoration scale---i.e., the propagation distance necessary to achieve equilibrium---is found to be inversely proportional to both the wavelength and initial vortex density and a logarithmic function of the topological charge of a cell.