Orbital mode structure of random vectorial light beams

A characterization of a structured, stationary light beam having any distributions of polarization and orbital angular momentum states is proposed via the second-order correlation of its polarization-orbitalization tensor recently introduced for treating harmonic, vectorial light beams. We show that the tensor correlation can be decomposed into pure and completely mixed states in its polarization projection and into pure, partially mixed, and completely mixed states in its orbitalization projection. We also illustrate the behavior of the polarization and orbitalization metrics, derived from these correlations, by numerical examples.