Transformation of the spatial statistics of a partially coherent light beam in a nonlinear medium

The self-interaction of a partially coherent multimode light beam in a cubically nonlinear medium is considered using a Monte Carlo technique. The transformation of the intensity and phase distribution statistics of the radiation is investigated. The behavior of the mean intensity, the mean-intensity fluctuation dispersion, and the coherence lengths along and across the beam is examined. The results show that the normal distribution law for the field of a broadband beam holds during self-focusing but that self-focusing of narrowband radiation is accompanied by the breakup of the beam into filaments. It is found that self-focusing in the narrowband case greatly transforms the intensity distribution but does not affect the phase distribution.