Focusing field of the radial vector beams with multi-vortex phases

Based on vector diffraction theory, which was described originally by Richards and Wolf, we calculate the focusing fields of the radial vector beams loading two, three and four vortex phases. The calculations and simulations show that one, two and three optical dark-holes could be generated in the focusing field by a high numerical aperture for the two, three and four vortex phases, respectively. In addition, the distances between the optical dark-holes are positively correlated with the distances between vortex phases. Based on this study, the generation of the optical dark-hole and the manipulation of the dark-hole's distance may be used in the capture and manipulation of multiple particles.