Sub-50-pm displacement sensing via phase-matched metasurface-prism configuration

Accurate transverse displacement measurement at the picometer scale is essential for advancing ultraprecision metrology and probing microscopic physical interactions. Here, we demonstrate a high-precision transverse displacement sensor leveraging a phase-matched Pancharatnam-Berry (PB) metasurface and trapezoidal prism configuration, which simplifies optical alignment by eliminating stringent Talbot self-imaging requirements. By synergistically matching the phase gradient of the PB metasurface with the prism geometry, we enable robust signal extraction through the photonic spin Hall effect, while a near-infrared source (λ = 1550 nm) suppresses environmental interference. Differential amplification further rejects common-mode noise from laser fluctuations and electronic drift. The system achieves a displacement resolution of 46.18 pm under quasi-static conditions (0.2-100 Hz) and 124.86 pm across the full operational bandwidth (0.2-1.25 MHz), surpassing conventional polarization-encoded schemes in both sensitivity and practicality. This work thus presents a strategy for metasurface-enhanced metrology via geometric-phase-engineered photonic architectures, with transformative potential across applications from semiconductor lithography to quantum optomechanics.