Fig. 1. Schematic of the metasurfaces for polarization-independent vortex and the multiplexing of polarization-rotatable multiple vortices in multiple spatial dimensions. (a) Polarization-independent vortex with identical topological charges generated by a geometric metasurface under illumination of THz waves with arbitrary polarization states. (b) Multiplexing of polarization-rotatable multiple vortices in both transverse and longitudinal directions under illumination of linearly polarized THz waves.

Fig. 2. Design and fabrication of the geometric metasurfaces. (a) Designed geometric metasurface consisting of meta-atoms with identical shapes but different in-plane orientations. (b) Transmission spectra (green and black curves) and phase difference (blue curve) of a meta-atom with the long-axis along the x axis for the incidence of transverse electric and transverse magnetic modes. Polarization conversion efficiency for the incidence of LCP waves is depicted as the pink curve. (c)–(f) Fabricated samples to realize the spin-independent vortex (c), multiplexing of polarization-rotatable vortices in the longitudinal direction (d) and multiple spatial dimensions (e), and the vortex with extended focal depth (f).

Fig. 3. Electric-field intensity and phase distributions of the spin-independent vortices. (a₁)–(a₅), (c₁)–(c₅) Simulated and measured electric-field intensity distributions after the designed geometric metasurface under illumination of LCP, LECP, LP, RECP, and RCP THz waves. (b₁)–(b₅), (d₁)–(d₅) Simulated and measured phase distributions of the corresponding vortices.

Fig. 4. Electric-field intensity and phase distributions of the multiplexing of two vortices with two orthogonal LP states in the longitudinal direction. (a₁)–(b₂) Simulated and measured electric-field intensity distributions at z=4.3  mm and z=7.9  mm, respectively. (a₃)–(b₄) Corresponding phase distributions for (a₁)–(b₂). (a₅)–(b₆) Simulated and measured electric-field intensity distributions in the x–z plane.

Fig. 5. Electric-field intensity and phase distributions of the multiplexing of four vortices with different LP states in longitudinal and transverse directions. (a₁)–(f₂) Simulated and measured electric-field intensity and phase distributions at z=4.3  mm, z=6.3  mm, and z=7.9  mm, respectively. (g₁)–(h₂) Simulated and measured electric-field intensity distributions in the x–z plane.

Fig. 6. Electric-field intensity distributions of a vortex with extended focal length. (a₁)–(c₂) Simulated and measured electric-field intensity distributions for |Ex|2, |Ey|2, and |Ex|2+|Ey|2 in the x–z plane. (d₁)–(e₆), (f₁)–(g₆), and (h₁)–(i₆) Simulated and measured electric-field intensity distributions for |Ex|2, |Ey|2, and |Ex|2+|Ey|2 in different x–y planes.

Fig. 7. Schematics of anisotropic meta-atoms without (a) and with (b) a rotation angle.

Fig. 8. Electric-field intensity distributions of spin-independent vortices in the x–z plane. (a₁)–(a₅) Simulated electric-field intensity distributions for the designed geometric metasurface under illumination of LCP, LECP, LP, RECP, and RCP THz waves in the x–z plane. (b₁)–(b₅) Measured electric-field intensity distributions of the corresponding vortices.

Fig. 9. Electric-field intensity and phase distributions for the polarization-rotatable vortex (l=1) under illumination of LP THz waves. (a₁), (a₂) Simulated x- and y-polarized electric-field intensity distributions at z=7.5  mm. (b₁), (b₂) Measured electric-field intensity distributions for (a₁) and (a₂). (a₃), (b₃) Simulated and measured phase distributions for the y-polarized converged vortex at z=7.5  mm. (a₄), (a₅) Simulated electric-field intensity distributions for |Ex|2 and |Ey|2 in the x–z plane. (b₄), (b₅) Measured results for (a₄) and (a₅).

Fig. 10. Electric-field intensity and phase distributions of the multiplexing of two vortices with two orthogonal LP states in the transverse direction. (a₁)–(a₄) Simulated and measured electric-field intensity and phase distributions for |Ex|2 at z=7.5  mm. (b₁)–(b₄) Simulated x- and y-polarized phase distributions at z=7.5  mm. (c₁), (c₂) Simulated electric-field distributions for |Ex|2 and |Ey|2 in the x–z plane. (c₃), (c₄) Measured electric-field intensity distribution in the x–z plane.

Fig. 11. Electric-field intensity and phase distributions of the multiplexing of two vortices with two orthogonal helical states in the longitudinal direction. (a₁)–(b₂) Simulated and measured electric-field intensity distributions at z=4.3  mm and z=7.9  mm, respectively. (a₃)–(b₄) Corresponding phase distributions for (a₁)–(b₂). (a₅)–(b₇) Simulated and measured electric-field intensity distributions in the x–z plane.

Fig. 12. Electric-field intensity and phase distributions of the multiplexing of two vortices with two orthogonal helical states in the transverse direction. (a₁)–(b₆) Simulated and measured electric-field intensity and phase distributions at z=7.5  mm, under the illumination of LCP (a₁)–(b₂), RCP (a₃)–(b₄), and LP (a₅)–(b₆) THz waves. (c₁)–(c₆) Simulated and measured electric-field intensity distributions in the x–z plane.

Fig. 13. Electric-field intensity and phase distributions of the multiplexing of three vortices with LP states and CP state. (a₁)–(b₈) Simulated and measured electric-field intensity and phase distributions at z=6.3  mm and z=7.9  mm, respectively. (a₉)–(b₁₁) Simulated and measured electric-field intensity distributions in the x–z plane.

Fig. 14. Electric-field intensity and phase distributions of the multiplexing of two vortices with two orthogonal CP (a₁)–(a₆) or LP (b₁)–(b₆) states in the longitudinal direction. (a₁), (a₂) Simulated and measured electric-field intensity distributions at z=4.3  mm and z=7.9  mm, respectively. (a₃), (a₄) Corresponding phase distributions for (a₁), (a₂). (a₅), (a₆) Simulated and measured electric-field intensity distributions in the x–z plane. (b₁), (b₂) Simulated and measured electric-field intensity distributions at z=4.3  mm and z=7.9  mm, respectively. (b₃), (b₄) Corresponding phase distributions for (b₁), (b₂). (b₅), (b₆) Simulated and measured electric-field intensity distributions in the x–z plane.

Fig. 15. Phase distributions of a vortex with extended focal length. (a₁)–(a₆), (b₁)–(b₆) Simulated and measured phase distributions for x component in different x–y planes. (c₁)–(c₆), (d₁)–(d₆) Simulated and measured phase distributions for y component in different x–y planes.