Metasurfaces are composed of arrays of subwavelength nanopillars which, owing to their strong form birefringence, provide an innovative platform to realize novel polarization control. Using matrix Fourier optics, phase retrieval principles, and Jones calculus, we propose and implement a general design strategy to enable polarization holograms with user-specified polarization responses, in the far-field. We fabricate these metasurface holograms (for operation at visible wavelengths) and test them with Mueller matrix polarimetry, showing good agreement with designs. This unprecedented polarization control in the far-field should enable applications in many areas, including in digital displays, augmented and virtual reality, structured illumination, and machine vision.
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