Moments of intensity distribution of super-Gauss beam in turbulent atmosphere

Abstract

Moment of intensity distribution is one of the most important parameters in studying the propagation of a beam in turbulent atmosphere. With the help of Wigner transform and the expansion of mutual coherence function (MCF) of turbulence, a relation between the moment of intensity distribution and the moment of power spectrum of refractive index fluctuations is found. The study shows that the jth-order moment of beam intensity distribution is only affected by the moment of power spectrum of refractive index fluctuations which order is not larger than j. Meanwhile, the expressions for the moment of beam intensity distribution, in which order is not larger than the fourth order are given. As a special case, the moments of the super-Gaussian beam (SGB) in turbulence are studied. The evolution of the kurtosis parameters of SGB under different condition is investigated in detail.