Fig. 1. Metamaterial spatial analog optical computing device designed by 4F system method^[6].

Fig. 2. Metamaterial spatial analog optical computing devices designed by 4F system method: (a), (b) MIM plasmon metasurface and corresponding reflective intensity distribution^[7]; (c), (d) dendritic plasmon metasurface and corresponding reflective intensity distribution^[11]; (e), (f) schematic of unit cell of SOI-based on-chip metasurface and corresponding first-order differentiator^[12]; (g), (h) ODE and IDE solvers based on silicon metasurfaces and corresponding electric field simulation results^[16].

Fig. 3. Spatial analog first-order differentiator based on plates and multilayer films: (a) PSBG differentiator and corresponding transfer function^[21]; (b) dielectric plate differentiator working at Brewster’s angle and corresponding transfer function^[23]; (c) SPP-based differentiator and experimental results of edge detection^[8].

Fig. 4. Grating/metamaterial-based spatial analog first-order differentiator: (a) Differentiator based on all-dielectric grating and experimental results of edge detection^[26]; (b) differentiator based on structure-symmetry-broken SRRs and corresponding transfer function^[18]; (c) dielectric-metal metasurface differentiator and experimental results of edge detection^[30].

Fig. 5. Metamaterial spatial analog second-order differentiator: (a) On-grating graphene differentiator and magnitude of corresponding transfer function^[37]; (b) differentiator based on plasmonic circuit and corresponding cross-polarized scattering intensity as function of incident angle^[33]; (c) differentiator based on photonic crystal slab and magnitude of corresponding transfer function^[32].

Fig. 6. Multilayer spatial analog first-order integrator^[40]: (a) Schematic of integrator; (b) corresponding transfer function.

Fig. 7. Metamaterial spatial analog equation solver using Green’s function^[9]: (a) Schematic diagram; (b) simulation result of electric field distribution when excited at Port 3.

Fig. 8. SHEL-based first-order differentiator: (a) Dielectric plate differentiator and experimental results of edge detection^[45]; (b) differentiator based on PB-phase metasurface and experimental results of edge detection^[49].