Nan T, Zhao H, Guo JY et al. Generation of structured light beams with polarization variation along arbitrary spatial trajectories using tri-layer metasurfaces. Opto-Electron Sci 3, 230052 (2024).

Polarization plays a crucial role in structured light beams. Besides polarization manipulation on a single transverse plane, controlling polarization along the propagation direction in longitudinal structured light beams is also an important dimension. However, existing research mainly focuses on the light propagation along the optical axis. Exploring the manipulation of polarization along arbitrary trajectories in space, as opposed to only the optical axis, presents a fascinating prospect. Designing the phase modulation function in the input plane, which consists of a series of expanding circular rings with moving centers, conical beams generated from these moving circular rings on the input plane converge to form the trajectory curve. Simultaneously, polarization control at each point on the predetermined transmission trajectory can be achieved by controlling the amplitude and phase difference of two orthogonal polarized components corresponding to the moving circular rings. The concept for longitudinally varying polarization in arbitrary trajectory structured light beams provides a workable way to continuously control the properties of non-axially transmitted spatially structured light beams and creates new opportunities for the development of customized spatially structured light beams. This technique has potential applications in optical encryption, particle manipulation, and biomedical imaging.