Fig. 1. Schematic representation of the twisted bilayer metasurfaces. (a) The proposed design is divided into two layers: Layer I and Layer II. Layer I comprises silicon pillars that exhibit polarization-maintaining properties, while Layer II consists of silicon pillars with polarization-converting capabilities. (b) Encoding phase profiles utilized in the construction of Layer I and Layer II. (c) Normalized intensity of LCP and RCP components acquired under x-LP illumination by varying the relative rotation angles p and q between Layer I and Layer II. (d) Calculated focal lengths of the generated focused beams within the LCP and RCP channels as a function of relative rotation angles p and q.

Fig. 2. Characterization of the fundamental units utilized in the assembly of Layer I and Layer II. (a) Cylindrical silicon pillars exhibiting polarization-maintaining properties are designated as PMMs. By varying the parameter R, eight elements that meet the specified phase requirements are selected at intervals of π/4, corresponding to (b) amplitudes and (c) phase delays. (d) The normalized magnetic field distributions (H-fields) obtained from the time domain solver for a PMM with periodic boundary conditions. (e) Rectangular silicon pillars exhibiting polarization-converting properties are designated as PCMs. By varying the parameters L and W, eight elements that meet the desired phase requirements are selected at intervals of π/4, corresponding to (f) amplitudes and (g) phase delays. (h) The normalized magnetic field distributions (H-fields) obtained from the time domain solver for a PCM with periodic boundary conditions.

Fig. 3. Simulation results obtained in the time domain solver by varying the twist angle p of Layer I with respect to Layer II. (a) Encoding phase profiles for Layer I. (b) Encoding phase profiles for Layer II, corresponding to p=90°, 120°, 150°, 180°, 210°, and 240°. (c) Joint phase modulation profiles through paired metasurfaces. Based on the simulations, the evaluated focal length related to different mutual rotation angles p=90°, 120°, 150°, 180°, 210°, 240°, are 9.4 mm, 7.1 mm, 5.6 mm, 4.8 mm, 4.1 mm, and 3.9 mm, respectively. (d) The electric field distribution corresponding to the RCP component is captured in the xoz plane by using a field monitor. The electric field distribution, including the (e) RCP and (f) LCP components, was captured in the xoy plane utilizing a field monitor. (g) The focal lengths and focusing efficiencies of the Moiré metasurfaces were calculated across a broadband range of 0.65–0.95 THz, taking p=120° as an example. (h) A color map with reversible polarization conversion properties, where different colors correspond to different polarization conversion intensities.

Fig. 4. Experimental characterization of the proposed Moiré metasurface. (a) SEM images of the fabricated Layer I under top and tilted view. (b) SEM images of the fabricated Layer II under top and tilted view. Scale bar: 1 and 0.5 mm. (c) The electric field distribution at different focal planes was recorded pixel by pixel using a microprobe-based near-field THz imaging system. (d) Optical components for assembling cascade metasurfaces, model GCT-090101.

Fig. 5. Experimental results obtained by varying the mutual rotation angle p from 90° to 240°. (a) Normalized electric field intensity extracted along the z-direction in the xoz plane. (b) The experimental field-intensity distributions obtained from measurements on the z=9.2  mm, 7.2 mm, 5.1 mm, 4.7 mm, 3.8 mm, and 3.5 mm planes correspond to the RCP component in the transmission mode. (c) Normalized electric field intensity extracted along the x-direction in the xoy plane, including simulation and experimental results. Theoretical, simulated, and experimental results of Moiré metasurfaces at different rotation angles, including (d) focal length and (e) NA. (f) Focusing efficiency and APE parameters of Moiré metasurfaces under x-LP illumination.

Fig. 6. Experimental results obtained by varying the mutual rotation angle q from 90° to 240°. The experimental field-intensity distributions obtained from measurements on the z=8.9  mm, 6.8 mm, 5.5 mm, 4.3 mm, 3.8 mm, and 3.6 mm planes correspond to the (a) RCP and (b) LCP components in the transmission mode. (c) Comparison of the intensities of the normalized electric field generated by such Moiré metasurfaces at different rotation angles, including theoretical, simulated, and experimental results for the RCP and LCP components. Theoretical, simulated, and experimental results of Moiré metasurfaces at different rotation angles, including (d) focal length and (e) NA. (f) The APE parameters of Moiré metasurfaces under x-LP illumination.

Fig. 7. Numerical simulation results obtained by varying the mutual rotation angle p from 90° to 180°. The electric field and phase distributions collected in the xoy plane using the field monitor in the time-domain solver, corresponding to the (a), (b) RCP component and (c), (d) LCP component, respectively. (e) Simulated and theoretical focal length and NA of Moiré metalens (at λ=333  μm) at different relative rotation angles. (f) Focusing efficiency of the RCP component corresponding to different rotation angles.

Fig. 8. Simulation results of the focused field produced by the designed Moiré surface under x-LP illumination as the mutual rotation angle q is gradually increased from 90° to 240°, including (a) RCP and (b) LCP components. (c) The normalized intensity profiles extracted along the x-direction, corresponding to 90°, 120°, 150°, 180°, 210°, and 240°.

Fig. 9. THz vortex beam generator with simultaneous polarization filtering and varifocal characteristics. The phase distributions obtained by setting the rotation angle of Layer I with respect to Layer II, q, as (a) 90°, (b) 120°, (c) 150°, and (d) 180°. (e) Electric field distribution of the RCP component collected in the xoz plane.