Fig. 1. Principle diagram of changing spherical lens into plane lens

Fig. 2. Light path diagram of Fresnel lens

Fig. 3. Schematic diagram of structure of this review

Fig. 4. Optical path diagram of generalized Snell refraction

Fig. 5. Optical path diagram of generalized Snell reflection

Fig. 6. Plasmonic metalens based on propagation phase.（a） Schematic of SPP formation；（b） propagation mode of SPP in air slit^［4］；（c） schematic of nanoslit arrays with different widths formed on metal films^［5］；（d） metalens structure and simulation results based on nanoscale slit array^［6］

Fig. 7. Plasmonic metalens based on resonance phase. (a) Finite-difference time-domain (FDTD) simulations of scattered electric field for individual antennas composing array^[2]; (b) FDTD simulation results of phase shifts and scattering amplitudes in cross-polarization for eight elements used in metalens^[9]; (c) scanning electron microscope (SEM) image of metalens^[9]; (d) schematic designs and results of full-wave simulations of Babinet-inverted nano-antennas^[11]; (e) schematic of MIM unit structure^[12]

Fig. 8. Plasmonic metalens based on geometric phase. (a) Schematic of U-shaped aperture antenna^[14]; (b) schematic of rectangular antenna^[15]; (c) SEM images of catenary arrays for metalens^[16]; (d) scaled view of rectangular region in (c)^[16]

Fig. 9. Dielectric metalens based on propagation phase. (a) Schematic of dielectric waveguide phase modulation^[17]; (b) schematic three-dimensional view of an amorphous silicon post and its magnified top view^[18]; (c) functional relation of cylinder diameter and phase modulation^[19]; (d) schematic of a metalens operating in transmission mode^[19]

Fig. 10. Dielectric metalens based on resonance phase. (a) Field distributions for electric and magnetic dipoles^[23]; (b) SEM images of top view of a mid-infrared Huygens metalens structure^[24]; (c) mechanisms for realizing a 2π phase shift by functional relationship between wavelength and phase response period^[22]; (d) F-P resonance based lens with square-shaped holes^[26]

Fig. 11. Dielectric metalens based on geometric phase. (a) Schematic of metalens structure^[31]; (b) illustration of multidimensional manipulation based on photonic spin Hall effect^[32]

Fig. 12. Tunable metalens. (a) Schematic of concept of tunable metalens^[36]; (b) schematic of migration of silver ions and formation of silver filaments^[38]; (c) schematic of liquid crystals in off-state and on-state^[40]; (d) schematic of tunable metalens system^[41]

Fig. 13. Monochromatic aberration cancellation metalens. (a) Perfect flat lens transforms plane waves with any angle of incidence into spherical waves, which converge to a focal point on focal plane^[50]; (b) schematic of metalens structure^[51]; (c) schematic of design of flat metalenses and axicons^[9]; (d) schematic of metalens patterned on a spherical interface^[52]

Fig. 14. Broadband achromatic metalens. (a) SEM image of metalens^[55]; (b) schematic of a metalens element^[56]; (c) layout of a quadrant of metalens^[57]; (d) schematic of overall optical structure of metacorrector^[61]; (e) SEM image of achromatic metalens array (left) and zoomed-in SEM image of a single metalens in square (right)^[62]; (f) composition principle of retroreflector^[65]; (g) schematic of overall structure and unit structure of metalens^[66]