Elliptic perfect optical vortices

We generalize the concept of perfect optical vortices, studying the elliptic perfect optical vortices (EPOVs), which also have diameters independent on the topological charge. A pure-phase diffractive 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. It is also higher than that of the EPOV, generated approximately by an elliptical axicon. We obtain exact analytical expressions for the orbital angular momentum (OAM) density and for the total OAM of the EPOV. These expressions show that the normalized OAM of the EPOV is fractional and it always exceeds the OAM of the conventional circular perfect optical vortex, which equals the topological charge. It allows continuous controlling of the OAM by changing the ellipticity. We show analytically that the OAM density is maximal on the smaller side of the EPOV and is minimal on its larger side. The ratio between the maximal and minimal OAM density equals the squared ratio between the ellipse diameters. Using the proposed element, EPOVs of several topological charges are generated experimentally using a spatial light modulator. We experimentally confirm the independence of their size on the topological charge, which is determined interferometrically. Such EPOVs can be used for movement of microscopic particles along an ellipse with acceleration, as well as for generation of OAM-entangled photons.