Analysis to beam quality of partially coherent flat-topped vortex beams propagating through atmospheric turbulence

Based on the extended Huygens-Fresnel principle and the second-order moments of the Wigner distribution function (WDF), the analytical formula for the propagation factor (M2-factor) of partially coherent flat-topped vortex beams propagating through atmospheric turbulence are derived, and used to analyze beam quality of partially coherent flat-topped vortex beams propagating through atmospheric turbulence. It is shown that the smaller the structure constant and the correlation length are, the bigger the inner scale of turbulence, the beam order and the wave length are, the smaller the normalized propagation factor is, and the better the beam quality of partially coherent flat-topped vortex beams in atmospheric turbulence is. The partially coherent flat-topped vortex beams is less affected by atmospheric turbulence than that of partially coherent flat-topped beams under certain condition, and will be useful in atmospheric optical communications.