Radially polarized twisted partially coherent vortex beams.

We introduce a new type of partially coherent vector beam, named the radially polarized twisted partially coherent vortex (RPTPCV) beam. Such a beam carries the twist phase and the vortex phase simultaneously, and the initial state of polarization (SOP) is radially polarized. On the basis of the pseudo-modal expansion and fast Fourier transform algorithm, the second-order statistics such as the spectral density, the degree of polarization (DOP) and the SOP, propagation through a paraxial ABCD optical system are investigated in detail through numerical examples. The results reveal that the propagation properties of the RPTPCV beam closely depends on the handedness of the twist phase and the vortex phase. When the handedness of the two phases is same, the beam profile is easier to remain a dark hollow shape and the beam spot rotates faster during propagation, compared to the partially coherent vortex beam or the RPTPCV beam with the opposite handedness of the two phases. In addition, the same handedness of two phases resists the coherence induced de-polarization of the beam upon propagation, and the SOP is also closely related to the handedness, topological charge of the vortex phase and the twist factor of the twist phase, providing an efficient way to modulate the beam's DOP and SOP in the output plane. Moreover, we establish an experiment setup to generate the RPTPCV beam. The average spectral density and the polarization properties are examined in the experiment. The experimental results agree reasonable well with the theoretical predictions. Our results will be useful for particle manipulating, free-space optical communications, and polarization lidar systems.