Fig. 1. Generalized laws of reflection and refraction. (a) Schematic of generalized laws of reflection and refraction^[44-45]; (b) anomalous refraction of wave in the plasmonic metasurface^[46]; (c) anomalous refraction of wave in the all-dielectric metasurface^[47]

Fig. 2. Wavefront control of plasmonic metasurfaces. (a)(b) Anomalous reflection realized by the MIM metasurface^[56]; (c)(d) vector vortex beam generated by the MIM metasurface^[58]; (e)(f) simultaneous generation of anomalous refraction and reflection of the few-layer metasurface^[59]

Fig. 3. Wavefront control at all-dielectric metasurfaces. (a) Electric and magnetic dipole responses in dielectric nanoparticles^[62]; (b) schematic of the unidirectional scattering^[63]; (c)(d) metalens^[67-68]; (e)(f) hologram^[64,69]; (g) wide-angle Fourier lens^[73]; (h) optical wavelength multiplexing with spin selective arbitrary energy distribution^[74]; (i) focusing beyond the diffraction limit^[75]; (j) nonlinear wavefront control^[77]

Fig. 4. Quantum emitters integrated with metasurfaces. (a) Schematic of metasurface-enhanced single-photon emission in hBN flake^[36]; (b) photoluminescence (PL) spectra before and after the coupling between quantum emitter and supersurface; (c) second-order autocorrelation functions measured from the pristine and coupled systems; (d)(e) schematic of spinning single photons generated by a hybrid system of metasurface and NV center in diamond^[37]; (f)(g) far-field intensity and polarization distributions of right-hand and left-hand circularly polarized photons; (h)(i) measured far-field emission intensity distributions before and after the metasurface fabrication; (j)(k) second-order autocorrelation functions measured before and after the metasurface fabrication

Fig. 5. Quantum emitters integrated with SSBM^[38]. (a) Schematic of metasurface-enabled on-demand spin-state control of single-photon emission; (b)(c) simulated results of far-field scattering patterns of device 1 and device 2

Fig. 6. Quantum interference among the decay channels in a quantum emitter^[89]. (a)(b) Principle of metasurface-enabled remote anisotropic quantum vacuum; (c) simulated field intensity distribution of a dipole source; (d)(e) simulated reflection field intensity distribution of the x dipole and y dipole respectively; (f) anisotropic decay rate of a two-level atom; (g) excited state populations of a three-level atom

Fig. 7. Metalens-array-based high-dimensional and multiphoton quantum source^[39]. (a) Schematic of the quantum source; (b)image of SPDC photon-pair array recorded by EMCCD; (c)(d) four-photon and six-photon coincidence dependence to pump power; (e)(f) schematic and the measured result of the four-photon HOM interference

Fig. 8. Spontaneous photon-pair generation from a dielectric nanoantenna^[40]. (a) Schematic of photon-pair generation from AlGaAs nanoantenna through the SPDC process; (b) SFG process of polarization correlations in the nanoantenna; (c) measured coincidences counts of photon-pair

Fig. 9. Polarization entanglement manipulation and measurement of metasurfaces. (a)(b) Entanglement of the spin and orbital angular momentum of photons using all-dielectric metasurface^[41]; (c)-(e) reconstruction of multiphoton quantum states using all-dielectric metasurface^[42]

Fig. 10. Path entanglement manipulation and measurement of metasurfaces^[43]. (a) Schematic of entanglement and disentanglement achieved by metasurface; (b) experiment setup for the generation and measurement of path-entangled two-photon NOON state; (c) normalized coincidence counts between detector D₁ and detector D₂+D₃; (d) schematic of quantum measurements on a metasurface-based interferometer; (e) experimental results of two-photon state with different time delays

Table 1. Comparison of single-photon sources based on isolated quantum systems^[79]