Achieving and manipulating ultra-long optical needles based on the generalized sinc beam

In recent years, optical needle in the focal plane, featuring an ultra-long depth of focus and no diffraction confinement over a distance along the propagation direction, has emerged as a hot research topic. In this paper, we propose a structured light beam called the generalized sinc beam (GSB). The beam enables the achievement of ultra-long optical needles through two distinct schemes: self-focusing scheme and tight-focusing scheme, respectively. The self-focusing process capitalizes on the inherent propagation characteristics of the beam, allowing it to naturally converge over an extended distance without substantial divergence, thus forming an ultra-long optical needle. Based on the abruptly self-focusing GSB, the optical needle can reach up to a length of 2.51 × 10⁵λ with λ = 532 nm being the wavelength. Meanwhile, when the GSB is tightly focused, the ultra-long optical needles are achieved, and the needle's length can reach up to 100λ. The optical needles produced by the GSBs are not only ultra-long but also flexibly controllable, which have broad application potential in various areas such as optical trapping, optical microscopy, atom optical experiments, photolithography, and so on.