# Grating-like Terahertz Metasurface for Large-Deflection-Angle Beam Manipulations
## 3 Results and Discussion  
Full-wave simulation of the metasurface grating is performed in the commercial software, CST Microwave Studio, to verify our theoretical calculations. As an example, we present the three-dimensional (3D) and one-dimensional (1D) far-field radiation patterns at 0.87 THz. As can be seen in Figure 2a,b, in addition to the zero-order diffraction beam, two first-order diffraction beams are generated at \(\pm\)59.2\({}^{\circ}\) for the perpendicularly incident terahertz plane wave. The normalized amplitude of the first-order diffraction waves to that of the zero-order diffraction beam is \(-\)9.49 dB. As for comparison, the far-field radiation patterns of the grating constructed by metallic strips with the same grating constant and slit width were also shown (see Figure 2c,d). Obviously, the CSRR-based grating has a higher intensity for the first-order diffraction beams, and hence CSRR structure is employed to construct the metasurface grating to obtain a high diffraction efficiency. The data for the diffraction angles at various operating frequencies can be extracted from the simulated far-field scattering patterns of the grating. The metasurface grating sample is fabricated using lithography technology, and the size of the grating is 12.8 mm \(\times\) 12.8 mm (32 lines). Figure 3a presents the optical micrograph of the fabricated metasurface grating. It can be found that the measured grating constant is around 404.2 um, close to the design value. The far-field radiation patterns of the reflective metasurface grating are measured on a terahertz time-domain spectroscopy mea \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Incident** & **Diffraction** & **Incident** & **Diffraction** \\
**Frequency/THz** & **Angle/Degree** & **Frequency/THz** & **Angle/Degree** \\ \hline
0.87 & \(\pm\)59.5 & 0.95 & \(\pm\)52.1 \\
0.88 & \(\pm\)58.5 & 0.96 & \(\pm\)51.4 \\
0.89 & \(\pm\)57.4 & 0.97 & \(\pm\)50.6 \\
0.90 & \(\pm\)56.4 & 0.98 & \(\pm\)49.9 \\
0.91 & \(\pm\)55.5 & 0.99 & \(\pm\)49.3 \\
0.92 & \(\pm\)54.6 & 1.00 & \(\pm\)48.6 \\
0.93 & \(\pm\)53.8 & 1.01 & \(\pm\)48.0 \\
0.94 & \(\pm\)52.9 & 1.02 & \(\pm\)47.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Diffraction angles calculated at different incident wave frequencies. Figure 2: The far-field radiation patterns for (**a**,**b**) CSRR-based metasurface grating and (**c**,**d**) metallic strip-based grating at 0.87 THz. (**a**,**c**) 3D far-field patterns; (**b**,**d**) 1D far-field patterns. In simulation, both the two 1D gratings have 16 lines. surement system. More details of the fabrication and experiments can be found in Ref. [30]. Figure 3b,c show the relationship between the reflection angle and terahertz amplitude under different frequencies (B-spline curves for the measured points). It can be obviously observed that the diffraction angle varies with the working frequency. Specifically, when the scanning frequency ranges from 0.87 to 1.02 THz, the corresponding scanning angle will be steered from 58.7\({}^{\circ}\) to 48.0\({}^{\circ}\) for the +1 st order diffraction wave and from \(-\)56.7\({}^{\circ}\) to \(-\)46.2\({}^{\circ}\) for the \(-\)1 st order diffraction wave, respectively. The two diffraction beams at the same frequencies are not strictly symmetric, which can probably be ascribed to the error of orientation angle between the incident terahertz beam and the metasurface sample, as well as the measurement error of the diffraction angle induced by beam broadening. Figure 4 shows the comparison among the theoretical, simulated, and measured scanning angles of the +1 st order diffraction wave covering the frequency range of 0.87-1.02 THz. It can be found that the simulation angles of the diffraction waves are consistent with the theoretical angles in the designed frequency band. The measured diffraction angles also agree well with the theoretical results except for the frequency point at 0.92 THz, where a slight deviation of around 1.2\({}^{\circ}\) can be observed.