Flat-topped vortex hollow beam and its propagation properties

In this paper, a flat-topped vortex hollow beam, which is a new mathematical model for dark hollow beams, has been introduced. The propagation properties of a flat-topped vortex hollow beam of circular and elliptical symmetry are investigated. According to the Collins formula under paraxial conditions, analytical formulas of the average intensity and the effective beam radius of a flat-topped vortex hollow beam are derived. Compared with a general flat-topped hollow beam by using numerical simulation, the propagation characteristics of a flat-topped vortex hollow beam are studied in detail. The relationships between the effective beam radius and propagation distance z are also provided graphically. From the graphical outputs of the receiver plane, it is observed that a flat-topped vortex hollow beam propagating to the far field still maintains a dark hollow spot and the radius of the dark hollow spot will get gradually larger as the propagation distance is extended. Furthermore, the flat-topped vortex hollow beam carrying the orbital angular momentum can be widely applied in atomic optics.