Secondary modulation instability in partially coherent beams

Due to modulation instability partially incoherent optical beams break up into stripe filaments in noninstantaneous media at a first threshold. We numerically and experimentally report on the formation of two-dimensional filaments at a secondary threshold, if increasing the nonlinearity further, which is due to material anisotropy. Particularly, we investigate the dependence of this secondary modulation instability on the coherence properties of the beam, using a photorefractive nonlinearity. From the measurement of modulation contrast in two dimensions and additionally using a Fourier method we quantitatively derive experimental thresholds for first and secondary onset of modulation instability and study how both onsets relate to the coherence properties of the beam.