Second-order statistics of a Hermite-Gaussian correlated Schell-model beam carrying twisted phase propagation in turbulent atmosphere.

We investigate the second-order statistics of a twisted Hermite-Gaussian correlated Schell-model (THGCSM) beam propagation in turbulent atmosphere, including the spectral density, degree of coherence (DOC), root mean square (r.m.s.) beam wander and orbital angular momentum (OAM) flux density. Our results reveal that the atmospheric turbulence and the twist phase play a role in preventing the beam splitting during beam propagation. However, the two factors have opposite effects on the evolution of the DOC. The twist phase preserves the DOC profile invariant on propagation, whereas the turbulence degenerates the DOC. In addition, the influences of the beam parameters and the turbulence on the beam wander are also studied through numerical examples, which show that the beam wander can be reduced by modulating the initial parameters of the beam. Further, the behavior of the z-component OAM flux density in free space and in atmosphere is thoroughly examined. We show that the direction of the OAM flux density without the twist phase will be suddenly inversed at each point across the beam section in the turbulence. This inversion only depends on the initial beam width and the turbulence strength, and in turn, it offers an effective protocol to determine the turbulence strength by measuring the propagation distance where the direction of OAM flux density is inversed.