# Design of Tunable Broadband Graphene-Based Metasurface with Amplitude-Phase Modulation
## 4 Performance of Reconfigurable Graphene Metasurface
With the application of \(\triangle\varphi\) and amplitude in Equation (6), the beam reconstruction can be obtained for different encoding cases. In  
Figure 5: Graphene metasurface array. (**a**) Front view; (**b**) Side view; (**c**) Bottom view. Figure 6: Performance with different distances between standard waveguide WR-10 and graphene metasurface of column code 11,000. (**a**) S11; (**b**) Efficiency. the following 3D views, the square on the purple substrate is unit \"1\", corresponding to graphene with a Fermi energy level of 1 eV; the square on the orange substrate is the unit \"0\", which corresponds to graphene with a Fermi energy level of 0 eV. As shown in Figure 8a,b, the effect of single-beam steering in the E-plane and H-plane of the antenna at 87 GHz is illustrated. By encoding in \"columns\", the antenna was capable of achieving single-beam steering of \(\pm 60^{\circ}\) in the E-plane, as demonstrated in Table 2. Similarly, by encoding in \"rows\", single-beam steering of \(\pm 25^{\circ}\) in the H-plane could be achieved, as shown in Table 3. The 0 and 1 in Tables 2 and 3 correspond to the graphene units loaded at the Fermi energy level of 0 eV and 1 eV, respectively. Figure 8c-f illustrate the surface current distributions of the metasurface for states 3, 8, 11, and 16. It can be observed that the beam steering was directed towards the area where surface current was concentrated, which was caused by the conductivity difference between metasurface elements encoded with different amplitudes. When electromagnetic waves were incident on the metasurface, induced currents flowed from high-conductivity regions (i.e., unit 1) to low-conductivity regions (i.e., unit 0), and converged in areas of low conductivity. \begin{table}
\begin{tabular}{c c c c c c} \hline
**State** & **Column** & **\#1** & **\#2** & **\#3** & **\#4** & **\#5** \\ \hline
1 & \(-60^{\circ}\) & 0 & 0 & 1 & 1 & 1 \\
2 & \(-36^{\circ}\) & 0 & 0 & 0 & 1 & 1 \\
3 & \(-25^{\circ}\) & 0 & 0 & 0 & 1 & 0 \\
4 & \(-16^{\circ}\) & 1 & 0 & 0 & 1 & 0 \\
5 & \(-3^{\circ}\) & 0 & 1 & 1 & 1 & 1 \\
6 & \(+3^{\circ}\) & 1 & 1 & 1 & 1 & 0 \\
7 & \(+16^{\circ}\) & 0 & 1 & 0 & 0 & 1 \\
8 & \(+23^{\circ}\) & 0 & 1 & 0 & 0 & 0 \\
9 & \(+38^{\circ}\) & 1 & 1 & 0 & 0 & 0 \\
10 & \(+60^{\circ}\) & 1 & 1 & 1 & 0 & 0 \\ \hline \end{tabular}
\end{table} 
Table 2: The coded states mentioned in Figure 8a. Figure 7: Performance comparison of antennas loaded with different states of metasurface. (a) S11; (b) Efficiency. Figure 9 shows a single-beam azimuthal rotation of 360\({}^{\circ}\) in different encoding states, corresponding to beam steering coordinates of (26\({}^{\circ}\), 31\({}^{\circ}\)), (26\({}^{\circ}\), 148\({}^{\circ}\)), (26\({}^{\circ}\), 211\({}^{\circ}\)), and (26\({}^{\circ}\), 330\({}^{\circ}\)), respectively. In addition, dual-beam steering is possible at 87 GHz. Figure 10a-d show the dual-beam deflection realized in the E-plane, corresponding to dual-beam coordinates of (\(-11^{\circ}\), 0\({}^{\circ}\)) and (60\({}^{\circ}\), 0\({}^{\circ}\)), (\(-60^{\circ}\), 0\({}^{\circ}\)) and (12\({}^{\circ}\), 0\({}^{\circ}\)), (\(-26^{\circ}\), 0\({}^{\circ}\)) and (27\({}^{\circ}\), 0\({}^{\circ}\)), (\(-64^{\circ}\), 0\({}^{\circ}\)) and (67\({}^{\circ}\), 0\({}^{\circ}\)), respectively; Figure 10e,f show the dual-beam deflection realized in the D-plane, corresponding to the dual-beam coordinates of (43\({}^{\circ}\), \(-25^{\circ}\)) and (43\({}^{\circ}\), \(-158^{\circ}\)), (\(-43^{\circ}\), \(-25^{\circ}\)) and (\(-43^{\circ}\), \(-155^{\circ}\)), respectively. When the encoded state is no longer restricted to whole rows or columns, the metasurface is partitioned into multiple regions and the interaction between these regions produces multiple beams. Figure 11 illustrates the implementation of the metasurface for switching between one beam to four beams, along with the corresponding coding state surface current.