Topological transition of Pancharatnam–Berry phase in a nonlocal twisted bilayer metasurface

The Pancharatnam-Berry (PB) phase principle has been extensively utilized in the design of polarization-dependent, ultrathin, phase-gradient metasurfaces, where the PB phase shift is determined by twice the change in orientation angle of individual building blocks. Here, we reveal a topological transition in the phase-orientation dependence within a nonlocal bilayer metasurface, where a fourfold dependence emerges as the building blocks are tightly arranged. Additionally, we demonstrate that the Moiré pattern inherent to the bilayer metasurface provides a tunable mechanism for driving this topological transition, enabling the modulation of both deflection angle and topological charge of the transmitted field. Our findings not only offer a refined understanding of the PB phase principle in linear optical systems but also introduce twist angle as a novel degree of freedom for designing tunable PB phase devices.