Noncanonical Perfect Vortex Beams Enabled Via Nonuniformly Varying Phase Gradient

A method is proposed for generating noncanonical perfect vortex beams (PVBs) based on a theory deduced from the definition of topological charge. Varying the phase gradient of the light field in the region of the decomposed integral provides arbitrary control over the nonuniform phase distribution in the transverse plane. To correct the distorted beam shape, the traditional "perfect" method of controlling the global amplitude distribution is modified and used to adjust the local beam diameter and produce what are known as noncanonical scalar PVBs. Moreover, noncanonical vector PVBs with tunable azimuthal polarization can be obtained by combining two orthogonal circularly polarized scalar PVBs. The results of experiments and numerical simulations show that the structure of the inhomogeneous phase and polarization can be tuned arbitrarily.