Fig. 1. Two geometric phase modulations and their surface currents. The blue arrow represents the surface current JR induced by the RCP, while the red arrow represents the surface current JL induced by the LCP. (a) The spin-coupled P-B phase. When the meta-atom rotates around the center, the surface currents (JR and JL) must rotate along with it. Due to the opposite spin for the RCP and LCP wave, the generated geometric phase is φR=−φL. (b) The spin-decoupled geometric phase. When one end of the circular arc is changed, only the JR rotates, resulting in a geometric phase generated for the RCP wave.

Fig. 2. Geometric phase by rotation. (a) Schematic diagram of the Poincaré sphere. (b) Schematic diagram of the evolutionary path for the circular polarization on the Poincaré sphere. IN represents the incident polarization state, and OUT represents the reflected polarization state. The evolutionary path for the circular polarization on the Poincaré sphere must pass a point at the equator (middle row). Each column represents an evolutionary path. The top row is the RCP state, the middle row is the linear polarization state with a different polarization angle, and the bottom row is the RCP state. Green and purple arrows indicate the electric and magnetic fields, and black arrows show the polarization vectors, respectively [32].

Fig. 3. Geometric phases generated by rotating meta-atom, where α is defined as the rotation angle of the meta-atom, and χ is defined as the rotation angle of the current path. The two meta-atoms have a similar structural form, which is depicted in Fig. 4(a). F4B microwave laminate (εr=2.65, tan δ=0.001) [30] is selected as the dielectric spacer separating the metallic structure and ground sheet and the metallic material is copper (conductivity: 5.8×107  S/m). The length of the dipole structure is equal to the diameter of the SRR structure. The structure parameters of the SRR are presented in Fig. 4. The width of the structure is 0.4 mm. (a) Rotation of the surface current on the short straight strip and the corresponding reflection phases (α=0°, 60°, and 120°). (b) Rotation of the surface current on SRR and the corresponding reflection phases (α=0°, 60°, and 120°). The blue arrow represents the normal direction of the current path. The rotation direction and angle of the current path are indicated by the position change of the arrow around the center.

Fig. 4. Spin-decoupled geometric phase obtained by engineering the surface current path on meta-atoms. (a) Schematic diagram of the SRR meta-atom, where P=10.0  mm, d=4.0  mm, r=4.0  mm, and β1=80°, β2=0°. (b) Reflection performances under incident LCP and RCP waves. (c) Surface current paths under different β1: (i) β1=40° (original state), (ii) β1=85°, (iii) β1=130°, and (iv) β1=175°. The top row is the current path under RCP wave illumination, while the bottom row is the current path under LCP wave illumination. The right panel of (c) is the corresponding geometric phase varying with β1.

Fig. 5. Design and simulated results of the three prototypes of a phase-gradient metasurface based on geometric phases. Note that the diffraction efficiency at the center frequency 11.0 GHz is calculated. (a) Completely spin-decoupled metasurface based on the β1-geometric phase. The diffraction efficiency is 94.7% for the LCP wave and 89.1% for the RCP wave. (b) Spin-coupled metasurface based on the α-geometric phase. The diffraction efficiency is 83.3% for both the LCP and RCP waves. (c) Spin-decoupled metasurface based on the (α+β1)-geometric phase. The diffraction efficiency is 85.1% for the LCP wave and 87.1% for the RCP wave.

Fig. 6. Deflection performance of the metasurfaces under x-polarization illumination. (a) α-geometric phase metasurface for (i) normalized far-field spectra and (ii) far-field scattering pattern at 11.0 GHz. The diffraction efficiencies for the two beams are 37.2% and 42.6%, respectively. (b) (α+β1)-geometric phase metasurface for (i) normalized far-field spectra and (ii) far-field scattering pattern at 11.0 GHz. The diffraction efficiencies for the two beams are 42.7% and 40.7%, respectively. (c) (i) The metasurface prototype based on the (α+β1)-geometric phase in the measurement system and the measured far-field pattern results at (ii) 8.0 GHz, (iii) 11.0 GHz, and (iv) 13.0 GHz.

Fig. 7. Reflection amplitude of the rRL and rLR.

Fig. 8. Geometric phase generation for the LCP wave. (a) Surface current paths under different β2: (i) β2=0° (original state), (ii) β2=45°, (iii) β2=90°, and (iv) β2=135°. (b) Reflection phase and amplitude under CP wave illumination: (i) rRL and (ii) rLR.

Fig. 9. Reflection phase and amplitude of the 24 meta-atoms: (a) rLR (the reflection under RCP wave illumination) and (b) rRL (the reflection under LCP wave illumination).