Pupil-Plane Inversion Symmetry Governs the Photonic Spin Hall Effect for Optical Manipulation

Abstract

Reconfigurable optical manipulation requires controlled switching between conservative confinement and nonconservative transport. However, achieving both functions often relies on digital wavefront shaping or nanofabricated photonic elements. Here, we establish pupil-plane inversion symmetry as a selection rule for controlling photonic spin Hall responses and optical-force landscapes in focused cylindrical vector beams using passive fractional sector masks. Decomposing the mask transmission into inversion-paired and inversion-breaking components shows that the longitudinal spin angular momentum density and transverse energy flow arise from interference between these two symmetry channels. Inversion-asymmetric transmission permits focal-plane spin-dependent momentum circulation, whereas inversion-symmetric transmission restores its cancellation. Electric-dipole and Maxwell-stress-tensor calculations map these regimes onto vortical nonconservative forces and conservative parallel-trapping landscapes. Gold-particle trajectories provide particle-level observations consistent with the calculated mechanical responses, showing opposite rotation directions at conjugate trapping sites and static parallel confinement under inversion-symmetric masks. Thus, pupil-plane inversion symmetry provides a practical design principle for tailoring photonic spin Hall responses and reconfigurable optical manipulation.