Fig. 1. An overview of the development of Jones matrix-modulated metasurfaces

Fig. 2. Phase modulation of a single polarization component. (a) Plasmon waveguide model based on the slit width^[36]; (b) effective medium model based on periodic fill factor^[37]; (c) (d) truncated waveguide model based on high-refractive-index dielectric nanopillars^[38-39]; (e) (f) detour phase mechanism based on spatial positions^[43]; (g) (h) geometric phase mechanism based on rotation angles of optical axis^[45]

Fig. 3. Amplitude modulation of a single polarization component. (a)(b) Huygens' metasurfaces based on electric/magnetic dipole resonances^[56-59]; (c)(d) Malus metasurfaces based on the rotation angles of the optical axis^[61]; (e) (f) interference metasurfaces based on diatomic meta-atoms^[62]

Fig. 4. Independent modulation of two co-polarization components. (a) (b) Spatial multiplexing of the orthogonally-polarized-phase-modulated metasurfaces^[69]; (c) (d) independent phase modulation of t_{xxand tyy based on propagation phase^[70]; (e) (f) joint amplitude & phase decoupling modulation of txxand tyy based on the polyatomic interference regime^[63]}

Fig. 5. Independent modulation of two cross-polarization components. (a)(b) Combining propagation phases and PB phases for independent phase modulation of t_LR and t_RL^[71]; (c) (d) interference system of dual half-wave phates with propagation phases and PB phases for independent amplitude & phase decoupling regulation of t_LR and t_RL^[64]

Fig. 6. Independent modulation of a co-polarization component and a cross-polarization component. (a) (b) Diatomic interference system combined detour phases and PB phases^[66]; (c) full-color vectorial hologram images^[66] and (d) perfect vectorial vortex beam^[67] generated by the diatomic interference system

Fig. 7. Independent modulation of three polarization components. (a) (b) Detour phases and PB phases of four identical nanopillars^[75]; (c) (d) propagation phases and PB phases of two circular nanopillars and two half-wave plates^[76]; (e) (f) propagation phases and PB phases of two different nanopillars^[51]

Fig. 8. Independent modulation of four polarization components. (a)‒(c) Independent phase modulation realized by PB phases of the triple-layer structures^[83]; (d)‒(f) independent amplitude & phase modulation realized by bilayer interference meta-atoms^[77]

Fig. 9. Novel optical applications based on Jones matrix modulated metasurfaces. (a) (b) Three-dimensional vectorial vortex optical field generated by independent phase modulation of LCP and RCP components^[95-96]; (c) complex transmission of waveguide modes generated by independent phase modulation of x/y or LCP/RCP components^[101]

Fig. 10. Complex modulation combined Jones matrix and other degrees of freedom of the optical field. (a) Angle-dependent vectorial vortex beam generated by phase decoding of multiple diffraction orders and PB phases^[103]; (b) azimuth-dependent holographic imaging generated by detour phase modulation of different incident plane^[104]; (c) (d) wavelength-polarization complex modulation generated by the specific wavelength response of the nanopillars^[104-105]

Fig. 11. Dynamic modulation of Jones matrix by metasurface. (a) (b) Mechanically tuned wavefront modulation generated by the lateral displacement between the two layers of metasurfaces^[107]; (c) (d) electrically tuned polarization state switching generated by liquid crystal and PB phases^[108]; (e) (f) thermally tunable switchable focusing lens generated by VO₂ nanopillars^[109]