Second-Order Statistics of Partially Coherent Beams with Laguerre Non-Uniform Coherence Properties under Turbulence

We use the extended Huygens-Fresnel integral to analyze the propagation properties of a class of partially coherent beams with Laguerre non-uniform coherence properties (called Laguerre non-uniformly correlated beams) in free space and in a turbulent atmosphere. We focus on how different initial beam orders and coherence lengths affect the propagation behavior of the beams, such as the evolution of intensity, degree of coherence, propagation factor, and beam wander. Our results show that non-uniform coherence properties play a role in resisting the degrading effects of turbulence. Furthermore, adjusting the initial beam parameter of the non-uniform coherence structure, i.e., increasing the beam order and decreasing the coherence, can further improve the turbulence resistance of the beams. Our results have potential applications in free-space optical communications.