LAUSR

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.