Second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere

The multi-Gaussian Schell-model (MGSM) beam was introduced recently [Opt. Lett. 37, 2970 (2012); J. Opt. Soc. Am. A 29, 2159 (2012)]. In this paper, we derive analytical expressions for the second-order moments of the Wigner distribution function of a MGSM beam in a turbulent atmosphere based on the extended Huygens–Fresnel integral. With the help of the derived formulae, the evolution properties of the propagation factor and the effective radius of curvature of a MGSM beam in a turbulent atmosphere are studied in detail. Our results show that a MGSM beam is affected less by the atmospheric turbulence than a GSM beam, which will be useful in long-distance free-space optical communications.

► Analytical expressions for the second-order moments of a multi-Gaussian Schell-model beam in a turbulent atmosphere are derived.
► Evolution properties of the propagation factor and the effective radius of curvature are demonstrated.
► A multi-Gaussian Schell-model beam is affected less by turbulence than a Gaussian Schell-model beam.