M 2-factors of a non-circular partially coherent flat-topped beam

Based on the extended Huygens-Fresnel integral and the second-order moments of the Wigner distribution function, analytical formulae for the propagation factors (known as M (2)-factors) of a non-circular (i.e., rectangular or elliptical) partially coherent flat-topped beam in turbulent atmosphere are derived. The properties of the M (2)-factors of a non-circular partially coherent flat-topped beam in turbulent atmosphere and in free space are studied numerically and comparatively. It is found that the evolution properties of the M (2)-factors are mainly determined by the parameters of the beam and the turbulent atmosphere. The relative M (2)-factors of a non-circular partially coherent flat-topped beam can be smaller than a circular partially coherent flat-topped beam and a Gaussian Schell-model beam, particularly at long propagation ranges in turbulent atmosphere. Our results will be useful in long-distance free-space optical communications.