Instability of speckle patterns in random media with noninstantaneous Kerr nonlinearity

Onset of the 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 response. The fundamental time scale of the spontaneous speckle dynamics beyond the instability threshold is set by the largest of times $T_{\mathrm{D}}$ and $\tau_{\mathrm{NL}}$, where $T_{\mathrm{D}}$ is the time required for the multiple-scattered waves to propagate through the random sample and $\tau_{\mathrm{NL}}$ is the relaxation time of the nonlinearity. Inertial nature of the nonlinearity should complicate the experimental observation of the instability phenomenon.