Customizable Fully Structured Vector Trajectory Beams in the Focal Plane via a Single-Layer Metasurface

As a class of structured light exhibiting unique spatial configurations, trajectory beams (TBs) feature the characteristic parameters of the light field, also referred to as the degrees of freedom (DoFs) of the light field, distributed along predefined trajectories. However, achieving TBs in which multiple DoFs are completely decoupled remains a significant challenge. Here, we demonstrate the generation of customizable fully structured vector trajectory beams (VTBs) in the focal plane using a single-layer metasurface designed via computer-generated holography. The controllable DoFs encompass the trajectory shape and the distributions of amplitude, phase, and polarization along the predefined trajectory. The generated TBs surpass existing methods in the number of controllable DoFs. More significantly, by shifting the key principle of the design from angular-variant topological phases to spatial trajectory, they surpass conventional vortex beams based on the prior principle, including their more advanced derivatives. The demonstrated ability to independently control multiple DoFs holds great promise in enhancing the channel capacity in optical communication.