Speckle Instability: Coherent Effects in Nonlinear Disordered Media

We numerically investigate the properties of speckle patterns formed by nonlinear point scatterers. We show that, in the weak localization regime, dynamical instability appears, eventually leading to chaotic behavior of the system. Analyzing the statistical properties of the instability thresholds for different values of the system size and disorder strength, a scaling law is emphasized. The later is found to also govern the smallest decay rate of the associated linear system, i.e., the "best'' cavity realized by the scatterers, putting thus forward the crucial importance of interference effects. This is also underlined by the fact that coherent backscattering is still observed even in the chaotic regime.