Partially coherent radially polarized beam with an off-axis vortex

In this paper, we propose a generalized kind of partially coherent vector beams with an off-axis vortex, named partially coherent radially polarized (PCRP) off-axis vortex beam for considering such a case in which laser beam passes through a spiral phase plate (SPP) but slightly deviates from the vortex core due to the experimental misoperation. The influences of such off-axis vortex phase on the focusing properties of the PCRP off-axis vortex beam after passing through a thin lens are theoretically investigated in detailed. It is found that the intensity pattern of the PCRP off-axis vortex beam possesses an additional dark core corresponding to the off-axis position of vortex core in the source plane, while it rotates gradually up to an angle of pi/2 with respect to the initial displacement vectors as propagation distance increases for high spatial coherence, being qualitatively different from that of the on-axis vortex beam. However, such unique characteristics of the PCRP off-axis vortex beam will disappear in the case of a very low coherence. In addition, the vortex-induced changes of polarization start from its off-axis vortex core, which will be useful for the detection of a phase object as well as its vortex position in the application of optical detection technology. More importantly, our results show that, besides the topological charge and coherence length, the off-axis parameters of vortex phase play a great role in modulating the propagation properties, which provides an additional degree of freedom for focus shaping.