Propagation formulae and characteristics of partially coherent laser beams in nonlinear media

Analytical propagation formulae of partially coherent beams (PCBs) in nonlinear media are derived. It is proven that the ABCD law is valid if a new complex beam parameter is adopted, which presents a simple method to study the propagation of PCBs through an optical system in nonlinear media. In self-focusing media, the spatial coherence for the beam spreading case is better than that for the beam self-focusing case, when the propagation distance is longer than the inversion coherence distance. An optimal beam will necessarily involve a trade-off between collimation and spatial coherence when PCBs propagate in self-focusing media.