Highly-accurate manipulation of focal length for circular Airy beams

The existing excitation models for circular Airy beams suffer from focal length deviation, which reduces the positioning accuracy of the focal point. Using the principle of Fresnel diffraction, this study investigates the influence of phase aperture diffraction on the focal point of circular Airy beams and establishes a precise focal length control model for inversely solving the phase distribution from the beam focus. On this basis, we design a circular Airy beam with a 10 cm focal length and employ a metasurface to experimentally generate such a beam. The angular spectrum simulation and experimental results demonstrate that the actual focal positions are at 10.034 cm and 10.04 cm, corresponding to deviations of 0.34% and 0.4% from the ideal 10 cm focal length, respectively. In contrast, the existing excitation model yields a focal length of 9.5530 cm, a 4.47% deviation from the ideal value. Therefore, the proposed model significantly improves the focusing accuracy of circular Airy beams. This study is expected to facilitate applications of circular Airy beams in ultra-high-precision laser structuring, laser medicine, microscopic imaging and particle manipulation.