Pancharatnam-Berry Phase Engineering from Spin Duality to Spin Selectivity for Optical Vortex Generation

Pancharatnam-Berry (PB) metasurfaces provide a compact platform for spin-dependent wavefront manipulation, yet conventional birefringent designs generally allow both incident spin states to access the geometric phase. Here, we establish a unified Jones-matrix framework for PB-phase generation in reflective half-wave-plate-like (HWP-like), quarter-wave-plate-like (QWP-like), and non-Hermitian chiral-exceptional-point (chiral-EP) metasurfaces. The analysis shows that the rotation-induced PB phase appears in the off-diagonal channels of the reflection matrix expressed in a fixed laboratory-frame circular basis, while the local scattering response determines the accessibility of these channels. The HWP-like metasurface generates conjugate vortices under opposite circularly polarized incidences. The QWP-like metasurface produces a PB-modulated vortex together with an orthogonally polarized background without rotation-induced PB phase. Near a chiral EP, one off-diagonal channel remains finite while the opposite conversion channel is strongly suppressed, enabling incident-spin-selective optical-vortex generation. These results provide a unified description of birefringent and non-Hermitian PB metasurfaces and introduce spin-channel selectivity as an additional degree of freedom for geometric-phase wavefront control.