Quantitative orbital angular momentum measurement of perfect vortex beams

Perfect (optical) vortices (PVs) have the mooted ability to encode orbital angular momentum (OAM) onto the field within a well-defined annular ring. Although this makes the near-field radial profile independent of OAM, the far-field radial profile nevertheless scales with OAM, forming a Bessel structure. As yet, the quantitative measurement of the OAM of PVs has been elusive, with current detection protocols opting for more qualitative procedures using interference or mode sorters. Here, we show that the OAM content of a PV can be measured quantitatively using optical modal decomposition: an already widely utilized technique for decomposing an arbitrary light field into a set of basis functions. We outline the theory and confirm it by experiment with holograms written to spatial light modulators, highlighting the care required for accurate decomposition of the OAM content. Our work will be of interest to the large community who seek to use such structured light fields in various applications, including optical trapping and tweezing, and optical communications.