Propagation of radial Airy array beams through atmospheric turbulence

Expressions for the average intensity of both phase-locked and non-phase-locked Airy array beams propagating through atmospheric turbulence are derived based on the extended Huygens-Fresnel principle. The evolution of the average intensity distribution of both phase-locked and non-phase-locked Airy array beams during propagation in atmospheric turbulence is examined by numerical examples and is compared with that in free space. It is found that both phase-locked and non-phase-locked Airy array beams can have the “self-focusing” capability which is impacted by the beamlet-combination type, turbulence strength and Airy-beamlet parameters. It is also shown that when the atmospheric turbulence is strong enough, the differences between the propagation properties of phase-locked Airy array beams and those of non-phase-locked ones become unobservable; this is different from the free-space propagation cases. The obtained results are helpful for understanding the propagation properties of Airy array beams in atmospheric turbulence and hence useful for practical applications.