Longitudinally Tunable Perfect Vortex Beams Via Partitioned Bijective Caustic Mapping For Independent 3D Orbital Angular Momentum Control

ABSTRACT The dynamic control of orbital angular momentum (OAM) in 3D space represents one of the central challenges in high‐capacity optical communications and multi‐particle optical tweezers. However, existing schemes are constrained by parametric coupling among topological charge, propagation trajectory, and beam size. This study proposes a partitioned mapping framework based on caustic theory. Different bijection bands at the initial plane are assigned to distinct spatial partitions in 3D space, enabling independent phase encoding on each band. This achieves longitudinally tunable 3D vortex beams propagating along preset curvilinear trajectories (e.g., power‐function trajectories). Furthermore, by introducing parametric compensation, we generate for the first time 3D perfect vortex beams, preliminarily realizing “non‐ideal decoupling” among topological charge, propagation trajectory, and beam size. Vortex beams generated through this approach exhibit average OAM purity exceeding 85% at different cross‐sectional positions. This provides a compact, single‐beam solution for optical micromanipulation and 3D OAM‐multiplexed communications.