Abstract
We formulate a new conceptual approach for one-shot complete polarization state measurement with nanostructured metasurfaces applicable to classical light and multiphoton quantum states by drawing on the principles of generalized quantum measurements based on positive operator-valued measures. Accurate polarization reconstruction from a combination of photon counts or correlations from several diffraction orders is robust with respect to even strong fabrication inaccuracies, requiring only a single classical calibration of the metasurface transmission. Furthermore, this approach operates with a single metagrating without interleaving, allowing for a reduction in metasurface size while preserving high transmission efficiency and output beam quality. We theoretically obtained original metasurface designs, fabricated the metasurface from amorphous silicon nanostructures deposited on glass, and experimentally confirmed accurate polarization reconstruction of laser beams. We also anticipate robust operation under changes in environmental conditions, opening new possibilities for space-based imaging and satellite optics.