Propagation characteristics of partially coherent flat-topped beams propagating through inhomogeneous atmospheric turbulence.

M²-factor and root-mean-square (rms) angular width of partially coherent flat-topped (PCFT) beams propagating through inhomogeneous atmospheric turbulence are studied based on the extended Huygens-Fresnel principle and the Wigner distribution function (WDF). It is shown that the effect of turbulence on the PCFT beams can be neglected as the vertical height increases, which is different from the homogeneous turbulence. Analytical formulae of the M²-factor and rms angular width of PCFT beams have been given. The saturation propagation distances (SPDs) increase with increasing zenith angle. It can be seen that the SPDs of the M²-factor and rms angular width of PCFT beams propagating through inhomogeneous atmospheric turbulence are about 30 km and 0.5 km, respectively, when the zenith angle is π/4. It can be found that the M²-factor increases with increasing beam order and zenith angle, and with decreasing waist width, inner scale, wavelength, and transverse coherence length. The rms angular width increases with increasing beam order, wavelength, and zenith angle, and decreasing waist width, inner scale, and transverse coherence length.