Statistical properties of a partially coherent radially polarized beam propagating through an astigmatic optical system

In a recent publication (Wang et al., Appl. Phys. Lett. 100 (2012) 051108), we reported experimental generation of a partially coherent radially polarized (RP) beam. In this paper, based on the unified theory of coherence and polarization, we derive the analytical expressions for the elements of the cross-spectral density matrix of a partially coherent RP beam propagating through an astigmatic optical system. As an application example, we study numerically the effect of astigmatism of the optical system on the focusing properties of a partially coherent RP beam. Our results show that the astigmatism of the optical system can be used for modulating the statistical properties of a focused partially coherent RP beam, which will be useful for beam shaping and particle trapping.