Coherence–orbital angular momentum matrix of Schell-model sources

The coherence-orbital angular momentum (COAM) matrix characterizes the second-order field correlations in stationary sources or fields, at a pair of spiral modes with the same or different topological charges, say l and m, and at a pair of radial positions. In this Letter, we reveal the general properties of the COAM matrix for the broad class of the Schell-model sources with circularly symmetric spectral densities. Our results imply that the structure of the COAM matrix is intimately related to the symmetries of the degree of coherence (DOC). In particular, the COAM matrix is diagonal if the DOC is real-valued and rotationally symmetric; otherwise, it may acquire non-zero off diagonal elements. In particular, if the real part of the DOC has Cartesian symmetry, the COAM matrix's elements with the even/odd index difference |l - m| contain information about the real/imaginary part of the DOC. A potential application of our results is envisioned for extracting the rotation angle of the DOC of light (or an object transparency) through measuring of the off-axis COAM matrix elements.