Modulation Instability of Spatially Incoherent Light Beams and Pattern Formation in Incoherent Wave Systems

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Abstract : Modulation Instability (MI) is a universal process that appears in most nonlinear wave systems in nature. Because of MI, small amplitude and phase perturbations (from noise) grow rapidly under the combined effects of nonlinearity and diffraction (or dispersion, in the temporal domain). As a result, a broad optical beam or a quasi-continuous wave pulse disintegrates during propagation, leading to filamentation or to break-up into pulse trains. Modulation instability is largely considered as a precursor of solitons, because the filaments (or pulse trains) that emerge from the MI process are actually trains of almost ideal solitons. Over the years, MI has been systematically investigated in connection with numerous nonlinear processes. Yet, it was always believed that MI is inherently a coherent process and thus it can only appear in nonlinear systems with a perfect degree of spatial/temporal coherence. Recently, the authors theoretically demonstrated that MI can also exist in relation with partially incoherent wave-packets or beams. They have made the first experimental observation of incoherent MI. They have shown that in a nonlinear partially coherent system patterns can form spontaneously (from noise) when the nonlinearity exceeds the threshold, and a periodic train of one-dimensional filaments emerges. At a higher value of nonlinearity, the incoherent 1D filaments display a two-dimensional instability and break up into self-ordered arrays of light spots. The ability to suppress MI has led to new families of solitons that have no counterpart whatsoever in the coherent regime. The discovery of incoherent MI actually reflects on many other nonlinear systems beyond optics: it implies that patterns can form spontaneously (from noise) in nonlinear many-body systems involving weakly-correlated particles, such as atomic gases at temperatures near Bose-Einstein-Condensation temperatures and electrons in semiconductors at the vicinity of the quantum Hall regime.