Fig. 1. Functional illustrations of LP multichannel transmission and superposition states of spherical and vortex waves. (a) Superposition state of spherical wave and vortex wave (l=+3) under 45° polarized wave incidence. (b) Four-channel transmission of two spherical waves and two vortex waves (l=+2 and +4) can be carried under 45° polarized wave incidence. (c) Superposition states of spherical wave and vortex wave (l=+2 and +4) under x and y polarized wave incidence, respectively. (d) Two-channel transmission of a spherical wave and a vortex wave (l=+2 or +4) can be carried under x (or y) polarized wave incidence.

Fig. 2. Database of metasurface units. (a) Schematic diagram of metasurface units and geometric parameters. (b)–(e) Transmission amplitude and transmission phase of metasurface units with different parameters.

Fig. 3. (a) Theoretical calculation and numerical simulation of the interferometric superposition process of the vortex and spherical waves, including electric field and phase. Yellow and white arrows represent the incident and transmitted polarization states, respectively. (b) Physical model of the metasurface array during numerical simulation.

Fig. 4. Physical models of two circular metasurface arrays (type A, 60 periods) corresponding to (a) focused superposition state and (b) dual-channel transmission functions. (c) Numerical simulation results of focused superposition states and dual-channel transmission. (d) IR-pumped electro-optic sampling terahertz imaging system. (e) SEM image and actual photograph of sample 1 (type A, 60 periods). (f) Measured 2D terahertz light field distributions and phases under different polarization states in the x−o−y plane (z=5.2  mm).

Fig. 5. Theoretical calculation and numerical simulation of the metasurface arrays under (a) x and (b) y polarized waves incidence, including the electric field and phase. (c) Physical model of the metasurface array (type B, 70 periods) during numerical simulation.

Fig. 6. Physical models of two circular metasurface arrays (type B, 70 periods) corresponding to (a) focused superposition state and (b) multichannel transmission functions. Numerical simulation results of focused superposition states and dual-channel transmission under (c) x polarized wave and (d) y polarized wave incidence. (e) Numerical simulation results of four-channel transmission under 45° polarized wave incidence. (f) SEM image and actual photograph of sample 2 (type B, 70 periods). (f) Measured 2D terahertz light field distributions and phases under x polarization state in the x−o−y plane (z=4.8  mm).

Fig. 7. (a) Phases (Φx1 and Φy1) of x and y polarized waves of 64 sets of Ln. (b) Phases (Φx2 and Φy2) of x and y polarized waves of 64 sets of Lm.

Fig. 8. Focused superposition between the x polarized vortex and y polarized spherical waves near the focus point from z=4.8  mm to z=5.6  mm when the 45° polarized wave is incident.

Fig. 9. Focused superposition of the x and y polarized waves near the focus point from z=4.5  mm to z=5.1  mm when the x and y polarized waves are respectively incident.

Fig. 10. Two focused superpositions of the x and y polarized waves near the focus point from z=4.2  mm to z=5.0  mm when the 45° polarized wave is incident.