Paraxial and tightly focused behaviour of the double ring perfect optical vortex

In this paper we compare the intensity distributions in the paraxial and tightly focused regimes corresponding to a double ring perfect optical vortex (DR-POV). Using the scalar diffraction theory and the Richards-Wolf formalism, the fields in the back focal plane of a low and high (tight focusing) NA lens are calculated. In the paraxial case we experimentally observed a DR-POV whose rings enclose a dark zone thanks to the destructive interference introduced by a π phase shift. In the tightly focused regime, however, the numerical simulations showed that the intensity near the focus is influenced by the input field polarization and it is not intuitive. In both cases we found that the dark region subtended between the rings has a minimal width that is inversely proportional to the pupil radius of the system, reaching 0.42λ for the radially polarized DR-POV. For the tightly focused case, we calculated the optical forces in the transversal and longitudinal coordinates exerted on a metallic particle. As a result, it is theoretically demonstrated that the circularly polarized DR-POV can trap Au metallic particles in 3D using a light wavelength close to its resonance.