Fig. 1. Schematic for comparison between phase-gradient metasurfaces and single unit-cell metagrating structures. (a) Reflection and (b) transmission phase-gradient metasurfaces; (c) reflection and (d) transmission single unit-cell metagrating surfaces

Fig. 2. Symmetric reflection metagrating^[29]. (a) Schematic of metallic groove metagrating; (b) k-space diffraction order chart composed of multiple Wood anomaly lines;(c) R-12 versus incident angle and wave number; (d) -1th and 0^th order diffraction efficiency spectra and local mode amplitude spectra; (e) magnetic field (H_y) distribution diagram for perfect retro-reflection with incident angle of 30°

Fig. 3. Asymmetric reflection metagrating^[28]. (a) Metagrating composed of bianisotropic unit cells array with perpendicular electric resonance and magnetic resonance as well as schematic of asymmetric perfect diffraction; (b) parameter scanning image of cancellation factor under normal incidence; (c) diffraction efficiency of each diffraction order corresponding to normalized frequency denoted by red star in Fig.3 (b); (d) distributions of incident and reflected fields at designed frequency

Fig. 4. Symmetric transmission metagrating. (a) Principle diagram of plane wave diffraction from all-dielectric metagrating^[69];(b) normalized scattering spectra of electromagnetic multipoles excited by p-polarized wave and s-polarized wave, respectively^[69];(c) experimental demonstration of realization of beam bending with all-dielectric metagrating^[71]; (d) schematic of transmission SiN_x metagrating^[72];(e) theoretical efficiency diagram of perfect transmission end diffraction^[72]; (f) -1th order diffraction efficiency diagram for large angle and wide bandwidth^[72]; (g) magnetic field pattern of perfect transmission end diffraction^[72]

Fig. 5. Asymmetric transmission metagrating. (a) (Left) dielectric double-ridge waveguide with different widths and free-space radiation under certain phase difference and (right) far-field response image of double-ridge metagrating^[64]; (b) extraordinary diffraction of bianisotropic transimission metagrating^[61]; (c) transmission metagrating with fish-shaped structure^[65]; (d) broadband large-angle asymmetric diffraction kissing double-nanopillar metagrating^[74]; (e) freeform metagrating constructed using topological optimization^[66]; (f) metagrating constructed by deep learning^[77]

Fig. 6. Reconfigurable metagrating. (a) Schematic of reconfigurable metagrating composed of metal-graphene-metal sandwiched structure^[79]; (b) schematic of spin-locked reflection of right-handed circularly polarized beam under varying incident angles with reconfigurable spin-locked reflection metagrating^[82]

Fig. 7. Applications of metagrating lenses with large numerical aperture. (a) (Upper)SEM images of metagrating lens are displayed (scale bars indicating 10 μm, 5 μm, and 500 nm from left to right), (middle) focal field distributions of metalens in xz plane and xy plane, and (down) normalized intensity map along z direction at x=0 and normalized intensity map along x direction at z=45.05 μm^[83]; (b) (upper) design diagram of hybrid metalens and actual metalens (bottom left) phase distribution and structure diagram of phase-gradient metasurface, (bottom right) structure diagram of wide angle deflection metagrating, diffraction efficiencies of metagrating (dot) and diffraction efficiencies of phase-gradient metasurface (solid line) under different diffraction angles^[84]

Fig. 8. Achromatic focusing of metagrating^[85]. (a) Schematics of beam deflection of coaxial small-angle achromatic metasurface and off-axis wide-angle achromatic metasurface; (b) structural diagrams of off-axis wide-angle achromatic metal groove metagrating; (c) effect diagrams of achromatic focusing

Fig. 9. Multifunctional device with angle selectivity of metagrating^[86]. (a) Flow chart of extraordinary optical transmission (EOT), total internal reflection (TIR) and extraordinary optical diffraction (EOD) of multifunctional metasurface; (b) phase profiles of EOT, TIR and EOD at different incident angles and incident wavelengths; (c) numerical simulation results of EOT, TIR and EOD focusing at different incident angles

Fig. 10. Applications of metagrating holograms with ultra-large angle tolerance. (a) Metasurface hologram device designed by sub-wavelength dielectric metagratings and detour phase^[32]; (b) metasurface hologram device with large angle tolerance designed by subwavelength metal metagratings^[46]; (c) metasurface hologram device based on perfect diffraction dielectric metagratings^[72]

Fig. 11. Metagratings used for converting surface plasma polariton (SPP) into arbitrary free-space wavefront. (a) Schematic of conversion from SPP wave to free-space wave through diffraction orders of metagrating^[88]; (b) modulated metagrating for free-space Airy beam generation by SPP excitation^[88]; (c) modulated metal metagrating used for 3D plasmonic micro-projector^[89];(d) modulated metallic slit metagrating used for conversion from SPP waves with different polarization and propagation directions to different free-space holographic images^[90]

Fig. 12. Circular metagratings used for mutual conversion between cylindrical SPP wave and arbitrary free-space wavefront. (a) Circular metallic groove metagrating with central hole^[91]; (b) circular metallic slit metagrating formed by interference between SPP wave and free-space vortex beam^[92]