Directionality of Gaussian array beams propagating in atmospheric turbulence

The angular spread is chosen as the characteristic parameter of beam directionality, and the directionality of Gaussian array beams propagating in atmospheric turbulence is studied. The consistency of the directionality of Gaussian array beams expressed in terms of the angular spread and the normalized far-field average intensity distribution is also examined. Closed-form expressions for the mean-squared beam width and angular spread of Gaussian array beams propagating in atmospheric turbulence are derived. It is found that for the case of coherent combination, under a certain condition array beams exist that may have the same directionality (i.e., the same angular spread) as a fully coherent Gaussian laser beam in free space and also in turbulence. However, the directionality of Gaussian array beams in terms of the angular spread is not consistent with that in terms of the normalized far-field average intensity distribution in free space, whereas they may be consistent as a result of turbulence.