We investigate a family of radially polarized Pearcey–Gauss vortex beams (RPPGVBs), obtain the general propagation expressions of an RPPGVB, and study the intensity distribution, phase pattern, spin currents as well as the orbital currents when the RPPGVB propagates in 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 waist size influences the propagation properties.

We study the propagation of the radially polarized Airy vortex beams (RPAiVBs) in a chiral medium analytically. The RPAiVBs split into the left circular polarization of the RPAiVBs (LCPRPAiVBs) and the right circular polarization of the RPAiVBs (RCPRPAiVBs). We mainly discuss the effects of the vortex and the chiral parameter on the propagation properties of the RPAiVBs, involving the intensity distributions and the radiation forces. It is shown that with the chiral parameter increasing, the intensity focusing position of the RCPRPAiVBs is further from  z = 0 Zr , while that of the LCPRPAiVBs is opposite. Besides, the maximum radiation forces of the RCPRPAiVBs are stronger than those of the LCPRPAiVBs. It is significant that we can control the acceleration, the intensity focusing position, and the radiation forces of the RPAiVBs by varying the vortex order and the chiral parameter.

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