# Design of Tunable Broadband Graphene-Based Metasurface with Amplitude-Phase Modulation
## 4 Performance of Reconfigurable Graphene Metasurface  
As depicted in Figure 5, the graphene metasurface was fashioned into a 5 \(\times\) 5 array by utilizing a total of 25 metasurface units. To verify its functionality, the conventional horn antenna was replaced with a wide-beam open-ended waveguide antenna (WR-10) due to its simple architecture and compact size. R is the distance between the standard waveguide WR-10 and the graphene metasurface. The metasurface designed in this paper operates in the W-band. According to Equation (7), \(R\) should be in the range of 1.56-4.96 mm. The selection of a reasonable focal length plays a crucial role in the overall metasurface performance. The time domain simulator of the CST Studio Suite software was used to simulate and analyze the graphene metasurface. Figure 6 shows the S11 and efficiency of the metasurface and waveguide at different distances in the state of column code 11,000. Although the performance improves with greater distance, at larger distances, the encoded metasurface becomes ineffective. It should be noted that the electromagnetic waves can be reflected as much as possible under the condition of low antenna thickness. Therefore, \(R\) = 2 mm is chosen as the final option. The metasurface dimension \(D\) = 12.5 mm, and the corresponding focal diameter ratio \(R/D\) = 0.16. For convenience, we use \"m\" to denote the number of rows in the graphene metasurface unit \"0\" in the following simulation. The case where m = 0 corresponds to a situation that all rows are set to unit \"1\"; m = 1 means only row 1 is set to unit \"0\"; and m = 2 signifies that both rows 1 and 2 are in the \"0\" state and the rest in the \"1\" state, and so on. Figure 7 shows the S parameters and normalization efficiency of the graphene metasurface in different coding states. In the figure, the pink line depicts the S11 and normalization efficiency of the WR-10 without the loaded metasurface, while the remaining lines represent the WR-10 loaded metasurface in different coding states. In Figure 7a, it can be observed that the resonance point of the WR-10 shifted under different coding states after loading the graphene metasurface, though the bandwidth remained relatively constant. Furthermore, loading the graphene metasurface made the emission of electromagnetic waves in certain frequency bands more conductive. Loading the metasurface in different coding states changed the electrical characteristics of the feed antenna WR-10, which led to alterations in the interaction between the antenna and the metasurface. These alterationsaffected the magnitude of the S11 parameters and the frequency response. In Figure 7b, the normalization efficiency in most coding states is high. However, it was found that the efficiency decreased as the number of rows in which unit \"0\" is located increased. The main reason is the low conductivity of the unit \"0\" on the graphene metasurface and the low reflection amplitude of the electromagnetic waves. This phenomenon also leads to the low efficiency of the antenna when there are too many \"0\" units in the coded state. To verify the reconfigurable performance of this graphene-based reflective encoded metasurface beam, we encoded the metasurface according to Equation (8). The operating frequencies led to different far-field functions of the subarrays, which in turn led to differences in the directionality functions of the entire hypersurface at different frequencies. Due to the fact that each unit of the metasurface in this design had two states, there were a total of 225 encoding and array methods for the entire array. Combining Figure 7a,b, the S11 and efficiency of different coding states at 87 GHz were more similar, so some coding states at 87 GHz frequency point were selected to demonstrate the metasurface function in this paper. The phase difference between the two coding units at 87 GHz could be inferred as \(\triangle\varphi=30^{\circ}\) according to Figure 4c.