Toward arbitrary spin-orbit flat optics via structured geometric phase gratings

Reciprocal spin-orbit coupling (SOC) via geometric phase with flat optics provides a promising platform for shaping and controlling paraxial structured light. Current devices, from the pioneering q-plates to the recent J-plates, provide only spin-dependent wavefront modulation without amplitude control. However, achieving control over all the spatial dimensions of paraxial SOC states requires spin-dependent control of corresponding complex amplitude, which remains challenging for flat optics. Here, to address this issue, we present a new type of flat-optics elements termed structured geometric phase gratings that is capable of conjugated complex-amplitude control for orthogonal input circular polarizations. By using a microstructured liquid crystal photoalignment technique, we engineered a series of flat-optics elements and experimentally showed their excellent precision in arbitrary SOC control. This principle unlocks the full-field control of paraxial structured light via flat optics, providing a promising way to develop an information exchange and processing units for general photonic SOC states, as well as extra-/intracavity mode convertors for high-precision laser beam shaping.