Unified matrix representation for spin and orbital angular momentum in partially coherent beams

A matrix representation is introduced for stationary beamlike light fields that allows for simultaneous treatment of the orbital angular momentum (OAM) and the second-order state of spatial coherence. This coherence-OAM matrix is a counterpart of the 2 ×2 beam coherence-polarization matrix in a Cartesian polarization basis or coherence-spin angular momentum (SAM) matrix in a circular polarization basis. The general properties of the coherence-OAM matrix are discussed and then the coherence-SAM-OAM matrix is introduced as a unifying entity for treating beams with any coherence, spin, and orbital angular momentum states.