Weibull-type speckle distributions as a result of saturation in stimulated scattering processes

During the propagation of an optically smoothed laser beam through a warm plasma the speckle field pattern and the corresponding speckle intensity distribution are modified in time and along the laser propagation direction. It is shown here that the laser–plasma interaction can change the character of speckle statistics from an initially exponential-type limit law to a Weibull-type law. The Weibull distribution is characterized by a power-law-type behavior in a limited interval of the random variable, which is, in the present case, the speckle intensity. The properties of the speckle distributions are studied using methods of extremal and order statistics. The scattering instability process (here stimulated Brillouin forward scattering) causing the change in speckle statistics has an onset behavior associated with a “critical gain” value, as pointed out in work by Rose and DuBois (1993b). The saturation of the instability process as a function of intensity explains the limited interval of the Weibull-type speckle distribution. The differences in the type of the speckle statistics are analyzed by using “excess over threshold” methods relying on the generalized Pareto distribution, which clearly brings to evidence the transition from an exponential type distribution to the Weibull-type distribution as a function of the instability gain value, that is, from the regime below critical gain to values above the critical gain.