Focusing and tight-focusing properties of radially polarized Bessel-Gaussian power-exponent-phase vortex beams

In this paper, the focusing and tight-focusing properties of radially polarized (RP) Bessel-Gaussian (BG) rotationally-symmetric power-exponent-phase vortex beam (RPVBs) were investigated theoretically and experimentally. Based on the theory of vector beam, the propagation and tight-focusing models were derived to reveal the focusing and tight-focusing properties of the RP-BG-RPVBs by numerical simulation. Then, the experimental setup was established to validate that the RP-BG-RPVBs presented the fan-shaped and polycyclic intensity distribution, which possessed the features of RP beams, BG beams, and RPVBs, similarly. Thus, for normal focusing, the RP-BG-RPVBs would turn into a ring at the focal plane, of which the ring radius is almost constant and independent of the topological charge. Meanwhile, for the tight-focus, there are a secondary ring and several dark cores around the central spot due to the longitudinal component of the tightly focused RP-BG-RPVBs, of which the petal number is also equal to the topological charge. These remarkable properties of the RP-BG-RPVBs may have potential applications in optical trapping of multiple particles and laser fabrication of chiral microstructures.