The R-index: A universal metric for evaluating OAM content and mode purity in optical fields

Despite its pivotal role in optical manipulation, high-capacity communications, and quantum information, a general measure of orbital angular momentum (OAM) in structured light remains elusive. In optical fields, where multiple vortices coexist, the local nature of vortex OAM and the absence of a common rotation axis make the total OAM of the field difficult to quantify. Here, we introduce the R-index, a metric that captures the intrinsic OAM content of any structured optical field, from pure Laguerre-Gaussian modes to arbitrary multi-vortex superpositions. Not only does this metric quantify the total OAM, it also assesses field purity, providing insight into the fidelity and robustness of the OAM generation. By unifying OAM characterization into a single figure of merit, the R-index enables direct comparison across diverse beam profiles and facilitates the identification of optimal configurations for both foundational studies and applied technologies.