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Topologically structured matter, such as metasurfaces and metamaterials, have given rise to impressive photonic functionality, fuelling diverse applications from microscopy and holography to encryption and communication. Presently these solutions are limited by their largely static nature and preset functionality, hindering applications that demand dynamic photonic systems with reconfigurable topologies. Here we demonstrate a universal optical modulator that implements topologically tuneable structured matter as virtual pixels derived from cascading low functionality tuneable devices, altering the paradigm of phase and amplitude control to encompass arbitrary spatially varying retarders in a synthetic structured matter device. Our approach opens unprecedented functionality that is user-defined with high flexibility, allowing our synthetic structured matter to act as an information carrier, beam generator, analyser, and corrector, opening an exciting path to tuneable topologies of light and matter.

How light and matter interact has been a fundamental question for centuries and is still actively researched today, given renewed importance in the context of structured matter and structured light (1, 2). Unprecedented control of structured matter includes the creation of artificial atoms through metasurfaces and metamaterials, finding diverse applications in the control of light through linear (3) nonlinear (4), and quantum (5) enhancements. Topologically structured matter has emerged from condensed matter physics to imprint itself in the photonic domain, giving rise to topologically structured light fields (6) with textures in the polarisation and phase for …