Representation and Evolution of the Angular Momentum of the Light

A compact formalism for representing the angular momentum modes in paraxial optics is considered. The evolution of both spin and orbital components of angular momentum is described within such representation. A thorough analysis of the effect of reflection is carried out, and different kinds of reflective interfaces are analyzed. A general method for building the matrices representing the transformations of the spin and orbital angular momenta is introduced and applied to some meaningful examples concerning wave plates, mirrors, and prisms.