Propagation of partially coherent controllable dark hollow beams with various symmetries in turbulent atmosphere

Normalized intensity distribution, the complex degree of coherence and power in the bucket for partially coherent controllable dark hollow beams (DHBs) with various symmetries propagating in atmospheric turbulence are derived using tensor method and investigated in detail. Analytical results show that, after sufficient propagation distance, partially coherent DHBs with various symmetries eventually become circular Gaussian beam (without dark hollow) in turbulent atmosphere, which is different from its propagation properties in free space. The partially coherent DHBs return to a circular Gaussian beam rapidly for stronger turbulence, higher coherence, lower beam order, smaller p or smaller beam waist width. Another interesting observation is that the profile of the complex degree of coherence attains a similar profile to that of the average intensity of the related beam propagating in a turbulent atmosphere. Besides the laser power focusablity of DHBs are better than that of Gaussian beam propagating in turbulent atmosphere.