Second-order statistical properties of a J0-correlated Schell-model beam in a turbulent atmosphere

Abstract We derive the analytical expressions for the second-order moments of the Wigner distribution function of a J0-correlated Schell-model (JCSM) beam propagating in a turbulent atmosphere. With the help of the second-order moments, we explore the second-order statistical properties (i.e., the M2-factor, the effective radius of curvature and the Rayleigh range) of a JCSM beam propagating in a turbulent atmosphere for different turbulence parameters and beam parameters. It is found that the statistical properties of the JCSM beam are closely related to the initial beam parameters and turbulence parameters, and we can mitigate the negative effect of the turbulence by choosing suitable initial beam parameters. Our results will be useful for long distance free-space optical communications.