The far-field directionality of partially coherent flat-topped beams propagating through atmospheric turbulence

The far-field directionality of partially coherent flat-topped beams propagating through atmospheric turbulence is studied. The closed-form expressions for the mean squared beam width and angular spread of partially coherent flat-topped beams propagating through atmospheric turbulence are derived. It is shown that two partially coherent flat-topped beams may generate the same angular spread, and there exist equivalent partially coherent flat-topped beams which may have the same far-field directionality as a fully coherent Gaussian beam in free space and also in atmospheric turbulence. The far-field directionality of Gaussian Schell-model (GSM) beams in atmospheric turbulence is treated as a special case of partially coherent flat-topped beams. The theoretical results are illustrated by numerical examples and interpreted physically.