Propagation of partially coherent radially polarized beam in free space

Based on the propagation law of the 2×2 cross-spectral density matrix and the unified theory of coherence and polarization of partially coherent beams, the transmission characteristics of partially coherent radially polarized beams (PCRPB) have been investigated in the paper. It is shown that the intensity distribution, the degree of polarization (DOP) and the Stokes parameters will change after propagation through the free space. The doughnut beam spot of the partially coherent radially polarized beam becomes a solid beam, which is related to the propagation length and the coherence length. In addition, the degree of polarization and Stokes parameters in the propagation both relate to the propagation length and coherence length. With the increase of the propagation length, the modulus values of Stokes parameters S 1 and S 2 will decrease, the rate of the distribution of the DOP with radius will decrease. In a certain propagation length, with the increase of the coherence length, the modulus values of Stokes parameters S 1 and S 2 will increase, and their distribution will close to the axis, the rate of the distribution of the DOP with radius will increase.