Generation and manipulation of multiple multidimensional perfect Poincaré beams enabled by a single-layer all-dielectric geometric metasurface

Perfect Poincar beams (PPBs) are highly esteemed for their topological charge-independent radius and intensity profile.However, the generation and manipulation of PPBs typically involve two-dimensional planes perpendicular to the optical axis, hindering broader usability.Here, leveraging a single-layer all-dielectric geometric metasurface platform, we numerically showcase the generation and manipulation of multiple multidimensional PPBs.Multiple dimensions of PPBs, involving orbital angular momentum (OAM), polarization state, and three-dimensional (3D) spatial propagation, can be manipulated independently via tailoring topological charges assigned to two orthogonal perfect vortex beam (PVB) components, varying initial phase difference and amplitude ratios between two orthogonal PVB components, and strategizing 3D propagation trajectories.To demonstrate the feasibility of the recipe, two metasurfaces are designed: one is for generating an array of PPBs with tailored polarization states along cylindrical helical trajectories, and the other is for creating dual arrays of PPBs with personalized OAM and polarization eigenstates across two misaligned focal planes.As a proof-of-concept illustration, we showcase an optical information encryption scheme through a single metasurface encoding personalized polarization states and OAM in parallel channels of multiple PPBs.This work endeavors to establish an ultra-compact platform for generating and manipulating multiple PPBs, potentially advancing their applications in optical encryption, particle manipulation, and quantum optics.