Partially polarized Gaussian Schell-model beams

We consider a class of beams that are both partially polarized and partiall y coherent from the spatial standpoint. They are characterized by a correla tion matrix whose elements have the same form as the mutual intensity of a Gaussian Schell-model beam. We focus our attention on those beams that woul d appear identical to ordinary Gaussian Schell-model beams in a scalar trea tment. After establishing some inequalities that limit the choice of the ma trix parameters, we study the main effects of propagation. Starting from th e source plane, in which the beam is assumed to be uniformly polarized, we find that in the course of propagation the degree of polarization generally becomes non-uniform across a typical section of the beam. Furthermore, we find that the intensity distribution at the output of an arbitrarily orient ed linear polarizer is Gaussian shaped at the source plane whereas it can b e quite different at other planes.