Statistics properties of a cylindrical vector partially coherent beam.

Cylindrical vector partially coherent beam is introduced as a natural extension of cylindrical vector coherent beam based on the unified theory of coherence and polarization. Analytical propagation formula for the cross-spectral density matrix of a cylindrical vector partially coherent beam passing through paraxial ABCD optical system is derived based on the generalized Collins integral formula. As an application example, the statistics properties, such as the average intensity, spreading and the degree of polarization, of a cylindrical vector partially coherent beam propagating in free space are studied in detail. It is found that the statistics properties of a cylindrical vector partially coherent beam are much different from a cylindrical vector coherent beam. Our results may find applications in connection with laser beam shaping and optical trapping.