Probability density of field and intensity fluctuations of structured light in a turbulent atmosphere

Abstract

Distributions of the probability density of fluctuations of the intensity and real and imaginary parts of the complex field amplitude of the Laguerre–Gaussian laser beam propagating through a turbulent atmosphere, provided that the beam scintillation index takes values larger than unity, are studied. The calculations are performed through numerical simulation and with application of an analytical approach based on the expansion of the probability distribution density of the wave field into the Edgeworth series. The comparison of the results of numerical and analytical calculations has demonstrated that the probability density distribution of intensity fluctuations of the laser beam is resistant to small variations in parameters of the probability density distribution of fluctuations of the real and imaginary parts of the wave field. In addition, the earlier formulated statement that the normalized probability density of intensity fluctuations of a laser beam at any point of the space occupied by this beam is determined by the value of the scintillation index and does not depend directly on the turbulent propagation conditions is confirmed. It is shown that the probability density of intensity fluctuations constructed with the Edgeworth approximation of the probability density of field fluctuations is in good agreement with the results of numerical simulation and the fractional exponential distribution for the values of the scintillation index ranging from 1.0 to 1.6.