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Propagation properties of radially polarized Pearcey-Gauss vortex beams in free space

We introduce a family of the radially polarized Pearcey-Gauss vortex beam (RPPGVB). We obtain the general propagation expressions of the RPPGVB and study the intensity distribution, the phase pattern, the spin currents as well as the orbital currents when the RPPGVB propagates in the free space. The focal plane and the intensity of the focal point can be adjusted by changing the position of the vortex and the scaling factors. We also investigate how the refractive indexes of the medium and the waist size influence the propagation property.