Local Estimation of Orbital and Spin Angular Momentum Mode Numbers

At radio frequencies, previous works by Mohammadi et al. derived from quantum mechanics state that the spin angular momentum (SAM), orbital angular momentum (OAM), and their sum [the total angular momentum (TAM)] can be estimated locally without ambiguity. In this letter, we highlight an inconsistency in this method when adding an SAM with an OAM. The latter cannot be estimated for a nonzero SAM. From optical currents, we propose a more general method. It is based on the Poynting expansion into spin and orbital components to estimate the OAM regardless of the SAM value.