Modulation instability and pattern formation in spatially incoherent lightbeams

We report on the experimental observation of modulation instability of part ially spatially incoherent light beams in noninstantaneous nonlinear media and show that in such systems patterns can form spontaneously from noise. I ncoherent modulation instability occurs above a specific threshold that dep ends on the coherence properties (correlation distance) of the wave packet and leads to a periodic train of one-dimensional filaments. At a higher val ue of nonlinearity, the incoherent one-dimensional filaments display a two- dimensional instability and break up into self-ordered arrays of light spot s. This discovery of incoherent pattern formation reflects on many other no nlinear systems beyond optics. It implies that patterns can form spontaneou sly (from noise) in diverse nonlinear many-body systems involving weakly co rrelated particles, such as atomic gases at (or near) Bose-Einstein condens ation temperatures and electrons in semiconductors at the vicinity of the q uantum Hall regime.