Nonlinear focusing and defocusing of partially coherent spatial beams.

We consider the propagation of a partially coherent spatial beam in both self-focusing and self-defocusing nonlinear media. Using a Gaussian-Schell model, we derive an equation governing the width of highly incoherent beams as they propagate in both types of media and confirm its validity by using numerical simulations. Experiments performed in a biased photorefractive crystal match the predicted scaling.