Nonlocality and fluctuations near the optical analog of a sonic horizon

We consider the behavior of fluctuations near the sonic horizon and the role of the nonlocality of interaction (nonlinearity) on their regularization. The nonlocality dominates if its characteristic length scale is larger than the regularization length. The influence of nonlocality may be important in the current experiments on the transonic flow in Kerr nonlinear media. Experimental conditions, under which the observation of straddled fluctuations can be observed, are discussed.

Figure 1

A sketch of an all-optical Laval nozzle demonstrating the relative length scales which determine the window in real space where straddled fluctuations may be generated in an experiment. $\sigma$ is the nonlocality length (typically 1 mm); $l_r$ is the regularization length, determined by the nonlinear length and the acceleration rate (typically a few tenths of a mm); $\alpha$ is the acceleration rate (typically $\ge 1{\text{mm}}^{-1}$); $\nu$ is the characteristic “frequency” of the fluctuations, and should be such that $1/\nu$ be of the order of the size of the experimental test cell (a few centimeters).