Digitalized Geometric Phases for Parallel Optical Spin and Orbital Angular Momentum Encoding

Geometric phases have attracted considerable attention in recent years, due to their capability of arbitrary beam shaping in a most efficient and compact way, while traditional geometric phases are usually limited to handling single-structured beams and lack the capability of parallel manipulation. Here, we propose a digitalized geometric phase enabling parallel optical spin and orbital angular momentum encoding. The concept is demonstrated in inhomogeneous anisotropic media by imprinting a particularly designed binary phase into a space-variant geometric phase. We theoretically analyze its spin orbit interaction of light and experimentally created higher-order Poincare sphere beam lattices, the order number and symmetry of which can be flexibly manipulated. Special lattices of cylindrical vector beams and orbital angular momentum modes with square and hexagonal symmetry are presented. This work discloses a new insight in programming geometric phases for tailoring the optical field and inspires various photonics applications.