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The double-ring perfect vortex beam (DR-PVB) is generated through the superposition of two concentric perfect vortex beams (PVB). In this paper, we first study the intensity and phase distribution of the DR-PVB in the source plane. Secondly, utilizing the Huygens-Fresnel principle and the Collins formula, we obtain the intensity distribution of the DR-PVB after being focused by an ABCD optical system that includes a focusing lens. The results indicate that the intensity distribution of the focused beam is consistent with the interference pattern of two Bessel Gaussian beams. Furthermore, the number of spots in the focused intensity distribution is a multiple of the absolute value of the difference in the topological charges of the two PVBs. On the other hand, the overall size of the light beam can be adjusted by changing the lens's focal length. Thirdly, we analyze the optical radiation force exerted by the focused DR-PVB on Rayleigh particles with different refractive indices, silica and bubble, respectively. The results show that the focused DR-PVB can capture both high and low refractive index particles in the water. In addition, by comparing the focused DR-PVB under different radius combinations, we found that changing the beam radius will also change the light intensity distribution, which will lead to a change in the position and quantity of the captured particles. This result provides us with a new idea for adjusting the capture of particles in future experiments. Finally, we analyzed the gradient forces, scattering, and Brownian forces acting on the particles in the x, y, and z directions, respectively. Based on our analysis, we established the condition for stable particle capture, where the gradient force must overcome the effects of Brownian motion and scattering forces. From this, we determined the theoretical size range of particles that can be captured by the focused DR-PVB. Compared with other beams, such as Airy beams and Bessel beams, focused DR-PVB can be modulated by changing the topological charges of the two PVBs, which enables the possibility of capturing multiple particles. The results of this paper have potential application value in the field of optical manipulation.
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