Propagation Characteristics of Aberrated Partially Coherent Flat-topped Beam in Turbulent Atmosphere

In this paper, we investigate the characteristics of a partially coherent flat-topped (PCFT) beam through turbulent atmosphere. The analytical expressions for the spectral density and the beam width of the astigmatic PCFT beams with circular symmetry propagating in turbulent atmosphere are derived. It is shown that the spectral density and beam width of these beams in turbulent atmosphere are heavily influenced by the astigmatism coefficient, as well as by the order of flatness. Also, analytical formulas for beam width of aberrated PCFT beams propagated through turbulent atmosphere are derived, which show that higher order aberrated PCFT beams are more spread, but aberrated PCFT beams are not affected by correlation length. We also compute the effective width of the spectral degree of coherence for aberrated PCFT beams, which evidently show that aberrated beams with higher astigmatism coefficient are more influenced in turbulent atmosphere.