Propagation properties of partially coherent quasi-rectangular beams in a turbulent atmosphere

A class of random, wide-sense stationary optical beams with uniform correlations, named the partially coherent quasi-rectangular beam, is introduced theoretically. Based on the extended Huygens-Fresnel principle, the analytical expressions for the cross-spectral density (CSD), effective radius of curvature, and beam wander of the beam in the non-Kolmogorov turbulence are derived. It is found that the position of maximum intensity of the partially coherent quasi-rectangular beams shifts farther from the axis at intermediate distance, the shift in the turbulence is depressed compared to that in free space. As the effective radius of curvature decreases from infinity to a constant with the increase of the coherence length, it always takes a higher value than that in free-space propagation when the other parameters are fixed. In addition, the beam wander can be reduced by picking a relative small initial beam width, short coherence length, or long wavelength. These results are of importance for optical systems operating through long-range turbulent channels in which a beam must have a range-dependent tilt, e.g. on travelling around an obstacle on the axis.