Propagation properties of partially coherent flat-topped beams through turbulent atmosphere

Propagation of partially coherent flat-topped beams (PCFT) through turbulent atmosphere was studied with the help of generalized Huygens-Fresnel integral and the matrix optics. The analytic expression for the cross-spectral density matrix of partially coherent flat-topped beam was derived. Through analyzing the properties of the cross-spectral density and the degree of coherence of PCFT in turbulent atmosphere, the dependence of sensitivity of PCFT to turbulence on propagating distance and beam order number N was investigated. The results show that a PCFT beam with larger propagating distance and lower beam order is more affected by atmospheric turbulence, while the dependence of PCFT order N, coherence properties itself and propagating distance on the spectral degree of coherence becomes weaker due to the existence of atmospheric turbulence.