  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.
