A Transverse-Longitudinal Cross-Spectral Density Matrix of Partially Coherent Electromagnetic Beams

A transverse-longitudinal cross-spectral density matrix (TLCSDM) of partially coherent electromagnetic beams is proposed. It can extend the traditional Stokes parameters and polarization singularities from the paraxial field to the more general situation. The impact produced by the atmospheric turbulence on polarization singularities of the partially coherent electromagnetic vortex beams is analyzed with the TLCSDM.