Propagation dynamics of partially coherent crescent-like optical beams in free space and turbulent atmosphere.

We introduce theoretically and realize experimentally a class of random, wide-sense stationary optical beams with uniform correlations which, on propagation in free space, produce a crescent-like intensity distribution with the maximum at an off-axis position. The crescent's position of maximum intensity accelerates transversally at intermediate distances, and then exhibits a constant lateral shift further from the axis in the far zone of the source. We also show that on propagation in the isotropic turbulent atmosphere, the crescent beam shifts away from the axis as well, but slower than in free space, with rate depending on the strength of turbulence. 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.