An analogy between optical turbulence and activator-inhibitor dynamics

The propagation of laser beams through madia with cubic nonlinear polarization is part of a wide range of practical applications. The processes that are involved are at the limit of extreme (cuasi-singular) concentration of intensity and the transversal modulational instability, the saturation and defocusing effect of the plasma generated through avalanche and multi-photon (MPI) ionization are competing leading to a complicated pattern of intensity in the transversal plane. This regime has been named \textquotedblleft optical turbulence\textquotedblright and it has been studied in experiments and numerical simulations. Led by the similarity of the portraits we have investigated the possibility that the mechanism that underlies the creation of the complex pattern of the intensity field is the manifestation of the dynamics \textit{activator-inhibitor}. In a previous work we have considered a unique connection, the \textit{complex Landau-Ginzburg equation}, a common ground for the nonlinear Schrodinger equation (optical propagation) and reaction-diffusion systems (activator-inhibitor). The present work is a continuation of this investigation. We start from the exact integrability of the elementary self-focusing propagation (\textit{gas Chaplygin with anomalous polytropic}) and show that the analytical model for the intensity can be extended on physical basis to include the potential barrier separating two states of equilibria and the drive due to competing Kerr and MPI nonlinearities. We underline the variational structure and calculate the width of a branch of the cluster of high intensity (when it is saturated at a finite value). Our result is smaller but satisfactorily in the range of the experimental observations.