Beam coherence-polarization matrix

We present an approach for describing the properties of a quasi-monochromatic, beam-like field that is both partially polarized and partially coherent from the spatial standpoint. It is based on the use of a single 2 x 2 matrix, called the beam coherence-polarization matrix, whose elements have the form of mutual intensities. This approach, which can be viewed as an approximate form of Wolf's general tensorial theory of coherence, appears to be very simple, yet it is able to cover significant aspects of the beam behaviour that would not be accounted for by a scalar theory or by a local polarization matrix approach. A peculiar interference law applying to mutual intensities is derived. We show through simple examples how this approach leads to distinguish fields that would appear identical in a scalar treatment or in a local polarization matrix description. Hints for extensions are given.