Fig. 1. Overview of the functions and applications of metasurface devices in optical analog computation and optical imaging

Fig. 2. Amplitude and phase modulation of metasurfaces. (a) Metasurface composed of V-shape antennas to show the generalized Snell's law^[28]; (b) silicon nanodisk array and corresponding electric and magnetic dipole model profiles of all-dielectric Huygens metasurfaces^[39]; (c) schematic of the Poincaré sphere^[41]; (d) schematic and scanning electron microscopic image of geometric phase metasurface composed of plasmonic dipole antennas on a glass substrate with varied orientations^[42]; (e) schematic of a propagation phase metasurface composed of symmetrical unit structures^[48]; (f) high-resolution grayscale image based on a reflected Malus metasurface under the illumination of linearly polarized light^[55]

Fig. 3. Schematic of multifunctional metasurfaces. (a) Schematic of spatial multiplexing metasurfaces with their optical images and scanning electron microscopic images^[58]; (b) schematic of the angular momentum multiplexing metasurface to generate holographic images^[64]; (c) demultiplexer of the angular momentum channels based on all-dielectric metasurface^[66]; (d) schematic of the polarization-controlled multiplexing metasurface to generate holograms^[70]; (e) polarization-controlled trifunctional multiplexing single-layer metasurface composed of 2×2 superpixel^[74]

Fig. 4. Schematic of flat metalens. (a) All-dielectric metalens with a NA close to 0.8 at wavelengths of 405 nm, 532 nm, and 660 nm, and their imaging results^[97]; (b) schematic of achromatic metalens at wavelengths from 1200 nm to 1680 nm^[82]; (c) aplanatic metalens with a large chromatic dispersion^[86]; (d) schematic of immersion metalens constructed of nanoscale diamond pillars with a NA higher than 1.0^[104]; (e) schematic of high NAmetalens based on grating averaging technique with a measured focusing efficiency of 77%^[105]; (f) doublet metalens with a large FOV ^[106]; (g) schematic of wide-FOV aperture-based metalens^[107]

Fig. 5. Principles of lens-based optical analog computation. (a) Single convex lens as Fourier transformer; (b) 4f imaging system; (c) single-lens imaging system; (d) one-dimensional transfer function curve of first-order differentiation; (e) one-dimensional transfer function curve of second-order differentiation; (f) one-dimensional transfer function curve of integration

Fig. 6. Fourier domain filtering approach for optical analog computation. (a) 4f-type computational metamaterial unit that can perform mathematical operations of choice on the input function as the wave propagates through it^[117]; (b) schematic of 2D graphene-based computing system^[118]; (c) design of reflective plasmonic metasurface differentiator^[119]; (d) schematic demonstration of the dielectric meta-reflect-array structure and its constitutive unit cell^[120]; (e) schematic diagram of the meta-transmit-array for the solution of differential and integro-differential equations^[122]; (f) schematic diagram of analog computational system utilizing single-layer Huygens metasurface^[123]; (g) meta-imager composed of a metalens and complex-amplitude meta-modulator as the kernel of the convolution operation^[124]

Fig. 7. Green's function approach for optical analog computation based on the photonic crystal. (a) Object function f (x, y) may be decomposed as a superposition of plane waves of different angles; (b) resonant diffraction structure performed the spatial differentiation performed in transmission^[125]; (c) schematics of dielectric metasurfaces performing first-order spatial differentiation^[126]; (d) geometry of the photonic crystal slab differentiator^[127]; (e) schematics of nonlocal metasurfaces performing analog second-order spatial differentiation^[129]; (f) schematic of a photonic crystal slab acting as a Laplacian operator^[130]; (g) schematic representation of edge detection^[131]; (h) schematic of metasurface illuminated by a plane wave^[132]; (i) illustration of a dielectric metasurface transforming an input 2D spatial function to another function as a Laplace operator^[133]

Fig. 8. Green's function approach for optical analog computation based on the multi-layer and metasurface. (a) Geometry of the beam diffraction by a phase-shifted Bragg grating^[134]; (b) transverse field distributions of the incident and reflected beams in a phase-shifted Bragg grating^[135]; (c) schematic of the plasmonic spatial differentiator to excite the surface plasmon polariton^[136]; (d) Salisbury screen as a high-pass spatial frequency filter^[137]; (e) schematic of isotropic topological differentiator that operates at normal incidence and in transmission mode^[138]; (f) schematic of using a transmissive multilayer thin film with a nonlocal optical response to directly perform 2D image differentiation with arbitrary polarization of the incident light^[139]; (g) illustration of edge detection with multilayer films^[140]; (h) schematic of the incoherent optoelectronic differentiation system with the multilayer film^[141]; (i) schematic of a photonic chip acting as a spatial differentiator that transforms an image into its first-, second-, and even higher order derivative^[142]; (j) primary structure of the proposed approach to perform integration using mode excitation of a dielectric slab waveguide^[143]; (k) schematic showing an array of split-ring resonators parallel to implement a second- and first-derivative operation^[144]; (l) schematic diagram of multidimensional edge detection with light-field imaging system by the achromatic meta-lens array^[145]; (m) schematic illustration of the nonlinear computational imaging metalens^[146]

Fig. 9. Optical difference approach for optical analog computation. (a) Phase gradient metasurface performed edge detection^[147]; (b) schematics of a metasurface enabled quantum edge detection^[148]; (c) schematic figure of the 2D edge detection^[149]; (d) schematic of the monolithic metasurface^[150]; (e) concept of Fourier optical spin splitting microscopy and experiment setup^[151]; (f) schematic illustration of the chiral edge sensing^[152]

Fig. 10. Metasurface-based phase imaging. (a) Schematic of the photonic spin-multiplexing metasurface for switchable spiral phase contrast imaging^[159]; (b) schematic illustration of the spiral metalens^[160]; (c) schematic of a metasurface-based miniaturized quantitative phase gradient microscope and its operation principle^[161]; (d) schematic diagram of the isotropic DIC microscopy^[162]; (e) schematic diagram of the metasurface-based transport-of-intensity equation for quantitative phase imaging setup^[163]

Fig. 11. Metasurface-based 3D imaging. (a) Schematic diagram of light-field imaging with metalens array and rendered images^[167]; (b) images of an on-axis microhole moving along the optical axis by fixing the imaging distance at the focal plane of the double-helix-metasurface^[168]; (c) scheme showing the creation of a double-helix PSF by using a lens phase profile with the double-helix phase profile^[169]; (d) schematic diagram of the Moiré metalens^[170]; (e) bijective illumination collection imaging concept^[171]

Fig. 12. Metasurface-based polarization imaging. (a) Scheme of the generalized Hartmann-Shack beam profile^[172]; (b) concept of a metasurface polarization camera^[174]; (c) meta-grating full Stokes polarization camera^[173]

Fig. 13. Metasurface-based integrated camera. (a) Schematic drawing of a miniature planar camera realized using a metasurface doublet lens and a CMOS image sensor^[48]; (b) setup of the 3D-printed system integrating the metalens with a CCD camera^[175]; (c) schematic of the optical setup for metalens-integrated imaging device^[110]; (d) schematic image of the near-infrared microscopic imaging device^[176]; (e) schematic diagram of the principle and device architecture of single-layer metalens array integrated wide-angle camera^[112]; (f) schematic of the chip-scale polarizer-embedded metalens imaging device^[177]; (g) jumping spider and metalens depth sensor^[178]; (h) schematic of a CMOS camera integrated OAM sorter^[179]; (i) optical layout of polarization-dependent object classification for the metasurface-based diffractive neural network concept ^[180]