  Recent advances in metasurfaces and optical nanostructures have enabled complex control of incident light with optically thin devices. However, it has thus far been unclear whether it is possible to achieve complete linear control of coherent light transmission, i.e., independent control of polarization, amplitude, and phase for both input polarization states, with just a single, thin nanostructure array. Here we prove that it is possible and propose a universal metasurface, a bilayer array of high-index elliptic cylinders, that possesses a complete degree of optical freedom with fully designable chirality and anisotropy. We mathematically show the completeness of achievable light control with corresponding Jones matrices, experimentally demonstrate new types of three-dimensional holographic schemes that were formerly impossible, and present a systematic way of realizing any input-state-sensitive vector linear optical device. Our results unlock previously inaccessible degrees of freedom in light transmission control. 
Universal metasurfaces for complete linear control of coherent light   transmission