Instability of speckle patterns in random media with noninstantaneous Kerr nonlinearity

The onset of instability of a multiple-scattering speckle pattern in a random medium with Kerr nonlinearity is significantly affected by the noninstantaneous character of the nonlinear medium's response. The fundamental time scale of the spontaneous speckle dynamics beyond the instability threshold is set by the larger of times TD and tau(NL), where TD is the time required for the multiply scattered waves to propagate through the random sample and tau(NL) is the relaxation time of the nonlinearity. The inertial nature of the nonlinearity should complicate the experimental observation of the instability phenomenon.