A reconfigurable arbitrary retarder array as complex structured matter

Tuneable retarder arrays, such as spatially patterned liquid crystal devices, have given rise to impressive photonic functionality, fuelling diverse applications ranging from microscopy and holography to encryption and communications. Presently these solutions are limited by the controllable degrees of freedom of structured matter, hindering applications that demand photonic systems with high flexibility and reconfigurable topologies. Here we demonstrate a compound modulator that implements a synthetic tuneable arbitrary retarder array as virtual pixels derived by cascading low functionality tuneable devices, realising full dynamic control of its arbitrary elliptical axis geometry, retardance value, and induced phase. Our approach offers unprecedented functionality that is user-defined and possesses high flexibility, allowing our modulator to act as a new beam generator, analyser, and corrector, opening an exciting path to tuneable topologies of light and matter.