Fig. 1. Basic principles of optical analog computing

Fig. 2. Metasurface-based spectral filtering for optical analog computing. (a) Spectral filtering model based on optical analog computing^[90]; (b)(c) metasurface unit structure and its amplitude transmittance for second-order differential operations in a wideband based on^{amplitude modulation[92]; (d) switchable differential operation based on spin-related phase modulations[93]; (e) switchable differential operation based on reconfigurable phase of phase-change materials[94]; (f) simultaneous acquisition of image depth and edge information based on vortex phase modulation[95]}

Fig. 3. Optical analog computing based on geometric phase metasurfaces. (a) 1D differentiation operation based on one-dimensional polarization grating^[98]; (b) 2D differentiation operation based on radially polarized grating^[101]; (c) polarization dependent first- and second-order optical differentiation operations based on Marius metasurface^[104]; (d) 2D differentiation operation based on dual-geometric phase metasurface^[105]

Fig. 4. Parallel optical analog computing. (a) Three kinds of functional imaging based on space and polarization multiplexing metasurfaces^[106]; (b) parallel differential and integral operations based on polarization multiplexing metasurface^[107]

Fig. 5. Optical differential operations of multilayer-film metasurfaces. (a) Conceptual diagram of optical analog computing performed on multilayer-film metasurface^[90]; (b) second-order differential operations performed on reflective metasurfaces^[111]; (c) polarization-insensitive differential operation^[112]; (d) second-order differential operation for spatiotemporal signals based on dual-MDM metasurfaces^[113]; (e) different differential operations performed on single metasurface^[114]

Fig. 6. Non-local metasurfaces enabled optical analog computing. (a)(b) Metal split-ring resonators and their transmission spectra at different incidence angles^[116]; (c) Fano-resonance spectra of high refractive index dielectric metasurface at different incidence angles^[117]; (d) Laplace operation performed on flat photonic crystal metasurface^[118]; (e) 2D Laplace operation performed on BIC metasurface^[121]; (f) approximately polarization-independent differentiation of plate photonic crystal metasurface with triangular lattice^[122]; (g) simultaneous differentiation of time and space domains enabled by bilayer metasurface^[123]

Fig. 7. Optical analog computational imaging based on pupil function modulations of metalenses. (a) 1D differential imaging of metalens with spin-dependent linear phase^[124]; (b) first-order 2D differential imaging of metalens with vortex phase^[125]; (c) inverse design of arbitrary optical analog computing metalens using convolutional kernel^[126]; (d) designs and imaging of superlenses for direct imaging and first-order two-dimensional differential imaging^[127]; (e) angular multiplexing of different order differential imaging by single metalens^[128]

Fig. 8. Optical analog computational imaging under incoherent conditions. (a) First-order differential imaging based on dual-wavelength multiplexed photonic crystal metasurface^[129]; (b) first-order differential imaging based on dual-wavelength multiplexed multilayer-film metasurface^[130]; (c) first-order differential imaging based on orthogonally linear polarization-coded metalens^[131]; (d) Laplace operation based on orthogonally circular polarization-coded metalens^[132]; (e) diagram of meta-imager composed of two cascaded metalenses and a polarization camera^[133]; (f) optical convolution operation of cascaded metalenses^[133]

Fig. 9. Optical analog computational microscopic imaging. (a) Schematic diagram and experimental results of differential microscopic imaging system based on flat photonic crystal metasurface^[118]; (b) isotropic differential interferometric contrast microscope and cell edge detection results based on single metalens^[136]; (c) schematic diagram of Fourier optical spin spectroscopy based on one-dimensional polarization grating, and quantitative phase imaging results of NIH3T3 cells^[137]