Abstract
In this paper, we analyzed the influence of on-axis and off-axis vortex on the intensity distribution of the linearly polarized auto-focusing Bessel-Gaussian vortex beam (LABGVB). By comparing its tight-focusing properties with that of the linearly polarized circular Airy beam, it is found that when transmitted in the tight-focusing system, the LABGVB not only generates multiple focusing, but also allows the focal points to be located away from the geometric focus of the high numerical aperture (HNA) lens. In addition, changing the focal length of the HNA lens not only causes the splitting and merging of the focal points, but also results in different control effects on the depth of focus and the distance between focal points due to different focusing times. In particular, the LABGVB can not only form multiple optical bottles for particle capture in the focusing region, but also exhibit two different distributions of the spin density vectors along the optical axis after choosing the appropriate scale factor and main ring radius, one being a circular line and the other being a helical line.
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