Free Space Realization of the Symmetrical Tunable Auto-Focusing Lommel Gaussian Vortex Beam

An auto-focusing beam with adjustable symmetry is proposed numerically and experimentally. The initial field of the auto-focusing Lommel Gaussian vortex beam (ALoGVB) consists of the Lommel function and the Gaussian term. When the asymmetry factor epsilon of the beam approaches zero, the ALoGVB will degenerate into a circular Bessel Gaussian vortex beam (CBGVB). Compared with the CBGVB, the ALoGVB is more diverse. The shape, symmetry, normalized focusing intensity, and focus distance of the ALoGVB can be controlled by flexibly adjusting the asymmetry factor epsilon and the topological charge n. In addition, the effect of off-axis vortices on the propagating characteristics of the beam is also discussed. The experiment is in good agreement with the numerical simulation. The results could be beneficial for potential applications in optical trapping or micromachining.