Arbitrary, direct and deterministic manipulation of vector beams via electrically-tuned q-plates

Vectorial vortex light beams, also referred to as spirally polarized beams, are of particular interest since they can be exploited in several applications ranging from quantum communication to spectroscopy and microscopy. In particular, symmetric pairs of vector beams define two-dimensional spaces which are described as "hybrid Poincaré spheres" (HPS). While generation of vortex beams has been demonstrated by various techniques, their manipulation, in particular in order to obtain transformations describing curves entirely contained on a given HPS, is quite challenging, as it requires a simultaneous action on both polarization and orbital angular momentum degrees of freedom. Here, we demonstrate experimentally this kind of manipulation by exploiting electrically-tuned q-plates: an arbitrary transformation on the HPS can be obtained, by controlling two parameters of the q-plate, namely the initial optic axis orientation α0 and the uniform birefringent phase retardation δ. Upon varying such parameters, one can determine both the rotation axis and the rotation angle on the HPS, obtaining the desired state manipulation with high fidelity.