Fig. 1. Waveplate metasurface. (a) Schematic diagram of a half-waveplate metasurface in a free background, capable of polarization conversion and anomalous reflection in orthogonally polarized channels^[65]; (b) left panel is a quarter-waveplate metasurface composed of two Au V-shaped antenna subunits, and the right panel is simulated phase difference and amplitude ratio between two scattered waves as a function of wavelength^[66]; (c) angle-multiplexed waveplate metasurface^[67] (the arrows in left panel indicate the angle-dependent intrinsic polarization state λeig+(θ) of the device; the device can be continuously tuned between linear and elliptic birefringence as the incident angle varies; the right panel is the generation of polarization dependent on incident angle); (d) electrically tunable waveplate metasurface^[68] (the right panel is the schematic of electrically tunable polarization conversion and the left panel is measured reflection polarization ellipse for selected voltages and nine different wavelengths)

Fig. 2. Polarizer metasurface. (a) Linear polarizer metasurface^[69]; (b) circular polarizer metasurface^[70]; (c) full Poincaré sphere surface polarizer metasurface^[71]; (d) solid full Poincaré sphere polarizer metasurfaces^[72]

Fig. 3. Metasurface polarizing beam splitter. (a) Metasurface elliptical polarization beam splitter^[73]; (b) four-channel metasurface polarization beam splitter applied to full Stokes polarization imaging^[44]; (c) six-channel metasurface polarization beam splitter for quantum entanglement state reconstruction^[74]

Fig. 4. Gray image information is encoded in the polarization profile distribution, and the image information is encrypted with Malus law. (a) Realization of high-resolution gray image hiding based on the metal structure^[87]; (b) based on the dielectric nanostructure, high-resolution and continuous gray-scale image display can be realized^[86]

Fig. 5. Combining Malus metasurface with other properties manipulation of light. (a) Combining with wavelength manipulation^[82]; (b) combining with phase information manipulation^[88]; (c) combining with amplitude manipulation^[83]

Fig. 6. Application of polarization adjustment based on Malus law. (a) Three-channel metasurface based on single-rod structure^[85]; (b) single wavelength holographic mimicry camouflaged metasurface^[81]; (c) optical security multi-channel metasurface^[94]; (d) cryptographic metasurface fused with computational holography^[84]

Fig. 7. Metasurface polarization multiplexing holography. (a) Linear polarization multiplexing holography^[122]; (b) linear polarization multiplexing capacity limit^[123]; (c) circular polarization multiplexing holography^[124]; (d) arbitrary polarization multiplexing holography^[125]

Fig. 8. Metasurface vectorial holography. (a) Vectorial holography of spatially varying polarization based on geometric phase and detour phase modulation^[126]; (b) multi-channel vectorial holography based on geometric phase and propagation phase^[127]; (c) vectorial Fourier metasurface of arbitrary far-field light intensity distribution and continuous polarization distribution^[128]

Fig. 9. Metasurface full-color vectorial holography. (a) Non-interleaved single-size silicon nanopillar arrays and a multitasking metasurface with minimal spatial freedom can display a large amount of information on simultaneously displaying color- and polarization-encoded vectorial holographic images^[136]; (b) a full-color vectorial holographic image that simultaneously controls the amplitude, phase, and polarization, and multiplexes the wavelength^[137]; (c) full-color vectorial holographic image generated by red, green, and blue three-color linearly polarized laser incidence (left panel) and the schematic of a tetratomic metasurface (right panel)^[138]

Fig. 10. Metasurface Jones matrix vectorial holography. (a) Jones matrix holograms with designed-specific waveplate or polarizer response in the far-fields^[139]; (b) combination of six degree of freedoms (DOFs) Jones matrix-based metasurface nanoprinting with vectorial holographic images^[140]; (c) spatially varied Jones matrix metasurface with eight DOFs (left panel) and measurements of the nanoprinting image versus the vectorial hologram (right panel), the incident and analyzed polarizations are at the bottom left and right of each subplot^[141]