The influence of phase aperture on Beam propagation factor of partially coherent flat-topped beams in a turbulent atmosphere

Analytical formula has been derived for the M2-factor of a partially coherent flat-topped (PCFT) beam truncated by a phase aperture in turbulent atmosphere based on the extended Huygens-Fresnel principle and the second-order moments of the Wigner distribution function. The M2-factor of the mentioned beams in atmospheric turbulence have been discussed precisely with numerical analysis. It can be shown that the M2-factor of a PCFT beam truncated by a phase aperture in turbulent atmosphere increases with propagation distance, and is mainly determined by the parameters of the beam, phase aperture and turbulent atmosphere. The presented results are expected to be useful in long-distance free-space optical communications.