Fig. 1. Principle of geometric-phase and resonance-based metasurfaces and their applications[21,34,50,52-53]

Fig. 2. Origin of geometric phase. (a) Electromagnetic waves scattered by microstructure; (b) schematic of Poincare sphere

Fig. 3. Linear gradient geometric-phase metasurfaces. (a) Left: linear gradient resonance-based metasurface, right: linear gradient geometric-phase metasurface; (b) geometric-phase optical elements with computer-generated subwavelength gratings[36]; (c) photonic spin Hall effect in plasmonic chains[37]; (d) efficient geometric-phase metasurface for spin-dependent wavefront control[56]; (e) geometric-phase metasurface composed of gold nanorods for beam-refraction[57]; (f) geometric-phase metasurface and

Fig. 4. Flat metalens based on metasurfaces. (a) Left: focusing schematic of resonance-based metalens, right: focusing and defocusing schematic of geometric-phase metalens; (b) plasmonic metalens component of single layer nanorod array in visible band[61]; (c) metalens based on Si nanobeam array[62]; (d) metalens and its building block, TiO2 nanofin[63]; (e) one-dimensional flat lens based on catenary array[64]

Fig. 5. Vortex beam generators based on geometric-phase metasurfaces. (a) l=±1 vortex beam measured from diffraction q-plate using spiral wave plate[68]; (b) vortex beam generation based on geometric-phase metasurface[57]; (c) V-shaped vortex beam generator[69]; (d) OAM generators based on catenary arrays[74]; (e) planar chiral metasurface for optical vortex generation[75]; (f) single plasmonic metasurface for vortex beam generation[76]

Fig. 6. Highly efficient geometric-phase metasurfaces. (a) About 25% efficiency geometric-phase metasurface in transmissive geometry[78]; (b) highly efficient vector Bessel beams generator[79-80]; (c)(d) photonic spin Hall effect with nearly 100% efficiency in reflective geometry working in microwave and terahertz regions[81-82]; (e) photonic spin Hall effect with nearly 100% efficiency in transmissive geometry[84]

Fig. 7. SPPs generation and control. (a) Outgoing spin-dependent surface waves generated by circular nanoslot, and interference fringes between surface and plane waves for two circular polarization incidences are shown in the right panel[99]; (b) surface waves focused by semicircular nanoslot, and spin-splitting of focal spot is shown in the right panel[100]; (c) schematic of Archimedes spiral; (d) electric-field profile of generated surface plasmon on metal surface[102]; (e) near-field measurement of O

Fig. 8. SPPs trajectories enabled by geometric-phase metasurfaces. (a) Schematic of SPPs generated by dipole source on metal surface; (b) unidirectional propagation of SPPs through nanoslots[111]; (c) unidirectional propagation of SPPs, where nanoslots are used in the unit cell[114]; (d) schematic of flexible coherent control of plasmonic spin Hall effect (left: local orbitals produced by two incident spins; right: dynamic images produced by rotating linear polarization of incidence when letter ‘b’ is w

Fig. 9. Applications of geometric-phase metasurface in holograms. (a) Three-dimensional hologram enabled by metasurface[39]; (b) highly efficient holographic images based on geometric-phase metasurface[40]; (c) hologram generated by chiral metasurface[41]; (d) holographic images at three separate planes based on silicon metasurfaces in broad visible band[42]; (e) multiplexed metasurface for generating holographic images[43]; (f) multicolor hologram[44]

Fig. 10. OAM generators and detectors. (a) Holographic detection of OAM[137]; (b)(c) refraction of different polarized beams by geometric-phase metasurfaces[135-136]; (d) optical OAM generated by metasurface[139]

Fig. 11. Active control of metasurfaces. (a) Tailor functionalities of metasurfaces based on complete phase diagram[143]; (b) tunable geometric-phase metasurface with PIN diodes[144]; (c) amplitude modulation with gated-graphene metasurfaces[145]; (d) metalens with tunable phase gradient by using random access reconfigurable metamaterial[146]

Fig. 12. Applications of composite metasurfaces. (a) Different holographic images generated by LCP and RCP incident waves[147]; (b) different OAMs for two opposite spins[148]; (c) left: asymmetric transmission in composite unit cells, right: diffraction patterns in transmission and reflection field illuminated by LCP and RCP waves[149]

Fig. 13. Applications of geometric-phase metasurface in planar optics. (a) Multiwavelength achromatic dielectric meta-devices[49]; (b) schematic of broadband reflective achromatic metalens[50]; (c) broadband transmissive achromatic metalens[51]