Optimal phase element for generating an elliptic perfect optical vortex

We study perfect optical vortices with an elliptic shape. Like the conventional circular perfect vortices, elliptic perfect optical vortices (EPOVs) have diameters that are independent on the topological charge. A pure-phase optical element is proposed for efficient generation of such EPOV. Intensity of EPOV generated by this element is order of magnitude higher than that of the EPOV generated by the Fraunhofer diffraction of an elliptic Bessel beam. We obtain exact analytical expressions for the orbital angular momentum (OAM) of the EPOV. These expressions show that the OAM of the EPOV can be fractional and it always exceeds the OAM of the conventional circular perfect optical vortex, which equals the topological charge. EPOVs can be used for movement of microscopic particles along an ellipse with acceleration, as well as for generation of OAM-entangled photons.