1、Articleshttps:/doi.org/10.1038/s41566-020-00750-2Harvard John A.Paulson School of Engineering and Applied Sciences,Harvard University,Cambridge,MA,USA.e-mail:capassoseas.harvard.eduPolarization refers to the vibration of light,which is conven-tionally described by the trajectory of the electric fiel

2、d vec-tor1.As a fundamental property of light,polarization has been exploited in various domains,from quantum optics and imaging to optical displays,lightmatter interaction,and sensing25.Versatile manipulation of polarization and its exact characterization are therefore two crucial sought-after goal

3、s.Conventional tools for polarization control such as polarizers and wave plates consider lights polarization as a homogeneous characteristic that is man-aged globally.This point of view of polarization has recently been disrupted with the evolution of advanced wavefront-shaping plat-forms based on

4、subwavelength-spaced arrays of optical elements(known as metasurfaces)that can manipulate lights polarization point by point across the transverse plane612.Such manipulation is commonly achieved using schemes with locally varying anisotropy,which can modify the two orthogonal polarizations of an inc

5、ident waveform independently,thus converting the incident polarization state locally to any desired output13.These schemes have been widely exploited in versatile polarization management12,polarization grat-ings6,14,15,holography9,16,polarization imaging17 and in creating opti-cal beams with structu

6、red polarization18(often dubbed cylindrical vector beams19,20),thus expanding the scope of polarization optics and its applications2125.However,these new schemes and existing polarization optics share a common limitation:they consider the polarization behav-iour only in a single plane transverse to