Universal tail of the probability density function of the intensity of light propagating in a turbulent medium

We examine the probability of the appearance of high values of the intensity I of a light beam at its propagation in the turbulent atmosphere. Starting from the functional integral representation of averages over turbulent fluctuations, we find the saddle-point configuration in the functional space corresponding to the high values of I. The saddle-point configuration determines the tail of the probability density function (PDF) of I characterized by a stretched exponent and determines the high moments of I. By investigating fluctuations of the refraction index on top of the saddle-point configuration, we establish the applicability conditions for the approach, which are different for the cases of weak and strong scintillations.