Pattern formation of spatiotemporal modulation instability of incoherent light and its phase transition

Summary form only given. In self-focusing nonlinear media, modulation instability (MI) causes the uniform light beam to break up into periodic patterns since the noise, carried by the light, of certain spatial frequency gets amplified by the interplay between the diffraction and the self-focusing effect. Thus, when the light source is incoherent, the nonlinear effect must be above some threshold for MI to develop as incoherent light diffracts more. The observation of incoherent MI has been done in noninstantaneous nonlinear media because it is preferred the nonlinearity not to respond to the very quick intensity fluctuation of incoherent light. Recently, we observe that the MI patterns of coherent light actually comes from time-varying random noise rather than from a static noise. The evidence is that the MI patterns of coherent light can move, and the moving rate depends on the response time of the material´s nonlinearity. We then suspect similar spatiotemporal MI of incoherent light can also happen. Indeed, we observe the spatiotemporal MI of incoherent light, and even to our surprise, we observe that the MI patterns change from one periodicity to another periodicity abruptly at certain critical nonlinearity strength or spatial coherence of the light, indicating a first order phase transition.