The order statistics of intense speckles or “laser hot spots” are studied in the context of the so-called “optically smoothed” light beams of laser-matter interaction. We investigate theoretically and by means of numerical simulations the distribution function for the k-th most intense speckle maxima in the upper tail speckle distribution. From these distributions for each order k, a distribution function for the intense speckles as a function of their peak intensity can be established, which allows to compute their impact on nonlinear processes, like parametric instabilities. This is done for the example of stimulated Brillouin scattering, using the so-called independent hot spot model, for which the backscatter reactivity level is computed, which proves to be in very good agreements with numerical simulations. This result is of great interest for nonlinear processes, like instabilities, where extreme speckles play an important role.
