Continuous three-dimensional varifocal of vortex beams with twisted metasurfaces

Vortex beams with helical phase wavefronts and doughnut-shaped intensity profiles hold great promise for optical trapping, imaging, and quantum communication. However, dynamic control over their steering and focusing remains challenging with existing static generation methods. Here, we demonstrate a dynamic and compact moiré metasurfaces that enables full three-dimensional (3D) control over vortex beams. The paradigm incorporates a numerical unit cell model and an off-axis angular spectrum algorithm based on the generalized Snell’s law of refraction in full space. The beam’s transverse position and longitudinal focal length can be simultaneously controlled by integrating phase elements such as gratings, lenses, and spiral phase plates. This scheme offers a 12× large axial zoom range from 7.42 mm to 85.45 mm and a lateral steering capability of up to ±48 mm. The device exhibits an average side-mode suppression ratio of 27.3 and maintains a constant full width at half maximum over a 50° deflection range, preserving beam quality and directional stability during dynamic steering. This lightweight vortex beams solution may open new ways for dynamic beam shaping in super-resolution imaging, free-space communication, and biophotonics.