We set forth a method to analyze the orbital angular momentum of a light field. Instead of using the canonical formalism for the conjugate pair angle-angular momentum, we model this latter variable by the superposition of two independent harmonic osc
illators along two orthogonal axes. By describing each oscillator by a standard Wigner function, we derive, via a consistent change of variables, a comprehensive picture of the orbital angular momentum. We compare with previous approaches and show how this method works in some relevant examples.
We advocate for a simple multipole expansion of the polarization density matrix. The resulting multipoles are used to construct bona fide quasiprobability distributions that appear as a sum of successive moments of the Stokes variables; the first one
corresponding to the classical picture on the Poincare sphere. We employ the particular case of the $Q$ function to formulate a whole hierarchy of measures that properly assess higher-order polarization correlations.
We discuss different proposals for the degree of polarization of quantum fields. The simplest approach, namely making a direct analogy with the classical description via the Stokes operators, is known to produce unsatisfactory results. Still, we argu
e that these operators and their properties should be basic for any measure of polarization. We compare alternative quantum degrees and put forth that they order various states differently. This is to be expected, since, despite being rooted in the Stokes operators, each of these measures only captures certain characteristics. Therefore, it is likely that several quantum degrees of polarization will coexist, each one having its specific domain of usefulness.
Quantum light depolarization is handled through a master equation obtained by coupling dispersively the field to a randomly distributed atomic reservoir. This master equation is solved by transforming it into a quasiprobability distribution in phase
space and the quasiclassical limit is investigated.
