Jones and Stokes–Mueller analogous calculi for OAM-transforming optics

We introduce a matrix-based approach for characterization of local interactions of optical beams with devices that result in changes of their orbital angular momentum (OAM) content. For deterministic interactions, a method similar to the Jones calculus is developed, while for interactions involving random beams and/or devices, its generalization based on the coherence-OAM matrix is suggested. Applications of the new, to the best of our knowledge, calculus to a spiral plate, a trigonometric grating, and a diffuser are considered. An alternative formulation similar to the Stokes-Mueller calculus is also outlined.