Fig. 1. Schematic of asymmetric focusing. Under the illumination of x-polarized THz waves in the forward direction, a y-polarized focal spot is observed, while the focal spot is not generated for backward x-polarized incidence.

Fig. 2. Design of dual-layered metasurfaces: (a₁) and (a₂) schematic and the corresponding geometric phase of the microrod; (b₁) and (b₂) schematic and the corresponding transmission spectra of the metallic gratings; (c₁) and (c₂) schematic and the corresponding transmission spectra of the metasurface combined with metallic gratings; (d₁) and (d₂) optical images of the metasurface and metallic gratings.

Fig. 3. (a₁)–(f₁) Numerical simulation of electric field distributions in the x−z plane under the illumination of x-polarized THz waves in the forward/backward direction at 0.6, 0.85, and 1.1 THz; (a₂)–(f₂) the corresponding electric field distributions in the x−y plane.

Fig. 4. (a₁)–(f₁) The measured electric field distributions in the x−z plane under the illumination of x-polarized THz waves in the forward/backward direction at 0.6, 0.85, 1.1 THz; (a₂)–(f₂) the corresponding electric field distributions in the x−y plane.

Fig. 5. Numerical simulation of asymmetric transmission with (a) and (b) longitudinal and (c) and (d) transversal multiple focal spots.

Fig. 6. (a₁)–(c₁) Schematics of a microrod, metallic gratings, and a unit cell of the directional device. The intersection angle between the long axis of the microrod and the x axis is 45°, while the long axis of gratings is along the x axis. (a₂)–(a₄) The co-polarized/cross-polarized/total transmission and reflection of the microrod under the illumination of linearly polarized THz waves. (b₂)–(b₄) The co-polarized/cross-polarized/total transmission and reflection of the metallic gratings under the illumination of linearly polarized THz waves. (c₂)–(c₄) The co-polarized/cross-polarized/total transmission and reflection of the unit cell of the directional device under the illumination of linearly polarized THz waves. Tij (Rij) is the transmission (reflection) of the i-polarized THz waves under the illumination of j-polarized THz waves (i,j=x,y). Ti (Ri,i=x,y) is the total transmission (total reflection) under the illumination of i-polarized THz waves.

Fig. 7. (a₁)–(f₁) Numerical simulation of electric field distributions in the x−z plane under the illumination of y-polarized THz waves in the forward direction at 0.6, 0.85, and 1.1 THz; (a₂)–(f₂) the calculated electric field distributions for backward incidence.

Fig. 8. The calculated and measured electric field distributions in the x−z plane under the illumination of the x-polarized THz waves from the (a₁)–(f₁) forward and (a₂)–(f₂) backward directions at 0.6, 0.85, and 1.1 THz.

Fig. 9. The calculated electric field distributions in the x−z plane under the illumination of the x-polarized THz waves in the (a₁), (b₁) forward and (a₂), (b₂) backward directions at 0.85 THz.

Fig. 10. Calculated efficiency of the directional device under the illumination of x-polarized THz waves in the forward direction.

Fig. 11. Schematic of multiple transmissions from the dual-layered metasurfaces.

Fig. 12. Comparison of the numerical (blue curves) and experimental (red curves) focusing properties: (a)–(c) the corresponding electric field distributions at x=0 in the focal plane.

Fig. 13. Schematics for the extinction ratio defined as (a) TEy/TEx and (b) TEy1/TEy2.

Fig. 14. (a₁)–(c₁) Calculated electric field (|Ey|2) distributions in the x−z plane under the illumination of x-polarized THz waves (with different incident angles) in the forward directions at 0.85 THz; (a₂)–(c₂) the calculated electric field distributions for backward incidence. Insets show the schematics for the incident THz waves with a tilted wavefront.

Table 1. Size of the Focal Point

Table 2. Comparison Between the Diffraction Limit in Theory and the FWHM of the Focal Spots

Table 3. Extinction Ratio Between ${|E_y|}^2$ and ${|E_x|}^2$

Table 4. Extinction Ratio Between the Forward and Backward Directions

Table 5. Extinction Ratio for the Directional Device with Two Focal Spots