Experimental evidence of dynamical propagation for solitary waves in ultra slow stochastic non-local Kerr medium

We perform a statistical analysis of the optical solitary wave propagation in an ultra-slow stochastic non-local focusing Kerr medium such as liquid crystals. Our experimental results show that the localized beam trajectory presents a dynamical random walk whose beam position versus the propagation distance z depicts two different kind of evolutions A power law is found for the beam position standard deviation during the first stage of propagation. It obeys approximately z³/² up to ten times the power threshold for solitary wave generation.