Propagation of various dark hollow beams through an optical system in turbulent atmosphere

The propagation of a dark hollow beam (DHB) of circular, elliptical or rectangular symmetry through aligned and misaligned ABCD optical systems in turbulent atmosphere is investigated. Analytical propagation formulae for the average intensities of various DHBs are derived based on the extended Huygens–Fresnel integral. As a numerical example, the focusing properties of various DHBs in turbulent atmosphere are studied. It is found that the focusing properties of various DHBs in turbulent atmosphere are much different from their focusing properties in free space.