Fig. 1. Metasurfaces based on plasmonic and all dielectric structures. (a) Metagrating based on a GSP structure for the determination of full Stokes parameters^[84]; (b) the metagrating consists three kinds of micro-nano structure arrays with different phase gradients, which can manipulate orthogonal polarization states (x, y), (a, b), (l, r)^[84]; (c) circular polarization splitting GSP-based metagrating^[85]; (d) polarization splitting and focusing metasurface GSP-based metalens^[86]; (e) meta-atom includes two kinds of TiO₂ nano-micro structures manipulating left-handed and right-handed circular polarization light, respectively; (f) polarization image of the exoskeleton of a chiral beetle^[92]; (g) meta-pixel is composed of metalenses focusing x，y，a，b，l，r polarization states, respectively^[93]; (h) the metasurface can be served as Hartmann-Shack wavefront sensor, intensity distribution of radially polarized beam (left), and calculated polarization profile (right)^[93]

Fig. 2. All dielectric metasurface based on geometric phase and propagation phase theory. (a) The metasurface is composed of elliptical amorphous silicon posts^[101]; (b) polarization splitting metagrating, polarization splitting metalens, polarization-dependent holographic metasurface and polarization-dependent special optical field metasurface^[101]; (c) polarization splitting metalens array^[102]; (d) targeted polarization mask (left), the fabricated mask imaged using conventional polarimetry (middle), the same mask imaged using the metasurface (right)^[102]; (e) polarization splitting metalens^[103]; (f) planar metasurface consisting of three polarization splitting metalenses^[104]; (g) the comparison of measured and simulated results of the metasurface focusing effect with the incidence of six basic polarization states^[104]

Fig. 3. Theory, imaging and system of a polarimetric metagrating based on matrix Fourier optics. (a) Theoretical model of a polarimetric metagrating^[105]; (b) combination with a rear lens and a detector can achieve polarization imaging^[105]; (c) four kinds of unconventional polarization states^[105]; (d) full Stokes polarization imaging system integrated with the metagrating^[105]; (e) polarimetric measurement image^[105]; (f) angle of polarization image^[105]; (g) full Stokes polarimetric module^[106]

Fig. 4. Broadband achromatic polarization splitting metasurfaces. (a) Coupled rectangular dielectric resonators^[110]; (b) the focusing phase can be divided into the basic phase and the chromatic phase^[111]; (c) there are several resonant peaks in the specially designed micro-nano metallic structure element^[111]; (d) measured and simulated focal lengths as a function of wavelength for both polarizations^[113]; (e) measured intensity profiles along with longitudinal directions at various incident wavelengths. The left panel is for x-polarized incidence and the right panel is for y-polarization incidence^[113]; (f) near-infrared achromatic metalens array for multiparameter detection^[115]; (g) measured intensity profiles under incidence of XLP and LCP light^[115]

Fig. 5. Metasurface design based on machine learning. (a) Visible chromatic multilevel diffractive lens^[119]; (b) flow chart of the direct binary search algorithm^[119]; (c) inverse design network^[124]; (d) polarization splitting metalens^[124]; (e) end-to-end statistical machine learning framework^[126]; (f) simulated and measured results of four-frequency polarization splitting metalenses^[126]

Fig. 6. Metalens with dynamically tunable focal length. (a) Dynamically tunable metasurface based on a flexible substrate^[136]; (b) a group of metasurfaces with adjustable longitudinal spacing, schematic diagram (left), optical microscopy image of device (top right), illustration of the bonding of two metasurfaces (bottom right)^[138]; (c) dynamically tuning the focal length through liquid crystal infiltration^[141]; (d) near-infrared thermally modulated varifocal metalens based on a low-losses phase change material Sb₂S₃^[143]; (e) polarization splitting metalens with a dynamically tunable focal length by circumferential stretching; (f) the variation curves of focal length and transmission with unit period; (g) the variation curves of the electric field intensity with the longitudinal direction at different unit periods