Fig. 1. Distribution of isotropic materials in permittivity and permeability space under optical frequency. ϵ0 and μ0 are permittivity and permeability of vacuum, respectively

Fig. 2. Design principles of metasurfaces. (a) Illustration of MIM structure; (b) field distributions of dielectric sphere under magnetic dipole resonance, electric dipole resonance, magnetic quadrupole resonance and electric quadrupole resonance^[96]; (c) coordinate system established in mathematical analysis of meta-atom using Jones matrix; (d) schematic used for derivation of generalized law of refraction^[93]; (e) schematic of generalized laws of refraction and reflection in two-dimensional case^[92]; (f) FDTD simulation results of scattered electric field for each meta-atom in V-shaped meta-atom array for beam deflection^[93]

Fig. 3. Polarization multiplexed metasurfaces. (a) Holographic images of polarization multiplexed metasurface hologram. When illustrated by RCP (LCP) light, holographic image of dog (cat) is generated^[103]. (b) Holographic images of multi-channel polarization multiplexed metasurface hologram. When there are two white arrows in the lower right corner, the arrows represent polarization states of input and output light respectively. When there is only one white arrow in the lower right corner, the arrow represents polarization state of input light, and polarization state of output light is not specified^[104]. (c) Holographic images illuminated by incident light of different polarizations of 11-channel polarization multiplexed metasurface (experimental results)^[105]. (d) Matrix grating diffracts light with different polarization states to different orders, and then is integrated with imaging lens to image object onto image sensor array^[106]. (e) Full-Stokes polarization imagery. The first column shows unprocessed raw exposure image, the second column shows S₀ (traditional grayscale image), the third column shows azimuth of polarized ellipse, defined as arctanS2/S1, and the fourth column shows degree of polarization, defined as S12+S22+S32/S0^[106]. (f) Schematic of segmented metalens imaging polarimeter^[107]. (g) Schematic of interleaved metalens imaging polarimeter^[108]. (h) Full-Stokes polarization imagery of interleaved metalens^[108]

Fig. 4. Wavelength multiplexed metasurfaces. (a) Schematic of unit of metasurface based on space division multiplexing^[110]; (b) schematic of principle of metasurface integrated with color filters^[112]; (c) color holographic display results based on principle shown in (a) (experimental results, the same below)^[110]; (d) schematic of variant of space division multiplexing strategy^[111]; (e) color holographic display results based on principle shown in (d)^[111]; (f) broadband characteristic of multi-channel polarization multiplexed metasurface^[109]; (g) color holographic display results based on principle shown in (f) ^[109]; (h) schematic of principle of color holographic display based on different incident angles^[113]; (i), (j) color holographic display results based on principle shown in (h)^[113-114]

Fig. 5. Achromatic metalenses. (a) Schematic of focusing principle of metalens; (b) schematic of two types of meta-atoms used in design of achromatic metalenses^[89]; (c) imaging results of achromatic metalens, where origin images are shown on the top, imaging results are given in the middle, and imaging results after color correction are shown in the bottom^[89]; (d) schematic of another type of meta-atom used in design of achromatic metalenses^[78]; (e) intensity distribution measured in xOz plane (color bar is set to correspond to each wavelength), where white dashed line indicates position of focal length^[78]; (f) meta-atom library in design of polarization-independent achromatic metalens^[118]; (g) focusing effects of quasi-achromatic metalens at extended wavelengths^[119]; (h) focal lengths of quasi-achromatic metalens at different wavelengths^[119]; (i) absolute focusing efficiencies of quasi-achromatic metalens at different wavelengths^[119]

Fig. 6. Incident angle multiplexed and wide field-of-view (FOV) metasurfaces. (a) Schematic of wide FOV imaging system composed of single metalens and front aperture^[127]; (b) schematic of wide FOV imaging system composed of two metalenses^[126]; (c) MTF curves along x direction at different incident angles of imaging system composed of two metalenses^[126]; (d) imaging results at different incident angles of imaging system composed of metalens and aperture^[127]; (e),(f) imaging results of single quadratic metalenses^[130-131]

Fig. 7. Cascaded metasurfaces. (a) Image taken with bilayer metasurface, with scale bar representing 100 μm. Insets show enlarged view of image at locations indicated by rectangles that have the same outline color and correspond to viewing angles of 0°, 15° and 30°, with scale bar representing 10 μm^[125]. (b) Imaging results of metalens doublet at two wavelengths^[139]. (c) Achromatic effect of three-layer metalens: light with wavelength of 450 nm, 550 nm, and 650 nm is focused at preset focal lengths^[140]. (d) Holographic image of multi-wavelength metasurface hologram at 1180 nm and 1680 nm. Top: simulation results; bottom: experimental results^[141]. (e) SEM pictures of bilayer metasurface from cross-sectional view^[142]. (f) Normalized light intensity distribution along y direction of cross-section at focal length: light of different wavelengths is focused at different focuses^[142]

Fig. 8. Nonlocal metasurfaces. (a) Schematic of meta-atom structure of differentiator metasurface^[146]; (b) images of systems without (top) and with (bottom) differentiator metasurface^[146]; (c) system schematic of utilizing metasurface to realize eye tracking on ordinary glasses^[156]; (d) images of eye at different rotation angles taken by near-infrared camera^[156]