Exploiting hidden singularity on the surface of the Poincar\'e sphere

The classical Pancharatnam-Berry phase, a variant of the geometric phase, arises purely from the modulation of the polarization state of a light beam. Due to its dependence on polarization changes, it cannot be effectively utilized for wavefront shaping in systems that require maintaining a constant (co-polarized) polarization state. Here, we present a novel topologically protected phase modulation mechanism capable of achieving anti-symmetric full 2{π} phase shifts with near-unity efficiency for two orthogonal co-polarized channels. Compatible with -- but distinct from- - the dynamic phase, this approach exploits phase circulation around a hidden singularity on the surface of the Poincar\'e sphere. We validate this concept in the microwave regime through the implementation of multi-layer metasurfaces. This new phase modulation mechanism expands the design toolbox of flat optics for light modulation beyond conventional techniques.