Coherence Poincaré sphere of partially polarized optical beams

Abstract

A Poincar\'e sphere representation of electromagnetic spectral two-point spatial coherence was recently introduced for fully polarized light beams. In this work, we employ the singular-value decomposition of the cross-spectral density matrix and establish a rigorous interpretation for the formalism in the context of partial polarization. At a single point, the construction reduces to the traditional polarization Poincar\'e sphere, which therefore can be regarded as a limiting case of the coherence sphere. The formalism is illustrated with paraxial blackbody radiation and Gaussian Schell-model beams. We expect our results will find use in understanding the coherence-polarization state of optical beams in situations dealing with random light.