# Design of Tunable Broadband Graphene-Based Metasurface with Amplitude-Phase Modulation
## 3 Unit Design of Proposed Graphene-Based Metasurface
Equations (1) and (2) show that the Fermi level of graphene is proportional to the applied electric field voltage. Figure 2 also demonstrates that the trend of increasing the reflection amplitude of the metasurface unit gradually slowed down as the Fermi level of graphene increases. Therefore, considering the coding standard and to avoid excessive applied voltages, we selected the graphene metasurface units with Fermi levels of 0 eV and 1 eV as encoding units \"0\" and \"1\", respectively. Figure 3 depicts the impact of substrate size (a), graphene size (b), and bottom feed-line dimensions (c) and (d) on the encoding performance of metasurface unit reflection amplitude. The results in Figure 3a,b demonstrate that the parameters a and b have a significant impact on the band range of graphene metasurface reflection amplitude encoding. As a and b increase progressively, the frequency band satisfying the coding amplitude difference shifts towards lower frequencies, leading to a gradual reduction in the frequency band range. Additionally, Figure 3c,d indicate that while the size of the bottom feeder has a negligible effect on the amplitude difference between coding units, it is evident that c = 1.4 mm and d = 0.3 mm produce the highest amplitude difference between them. In conclusion, we determined that selecting key parameters such as a = 2.5 mm, b = 2 mm, c = 1.4 mm, and d = 0.3 mm yields the optimal encoding performance for metasurface unit reflection amplitude. Based on the data presented in Figure 4a,b, it can be observed that both the reflection amplitude and phase of the metasurface units remained constant regardless of whether they were excited by transverse electric (TE) or transverse magnetic (TM) polarized waves. This phenomenon can be attributed to the centrosymmetric structure of the metasurface unit, which rendered it insensitive to TE and TM polarization when illuminated normally by an incident electromagnetic wave. The graphical representation in Figure 4a clearly demonstrates that the amplitude of the coding unit \"0\" remained below 0.33 throughout the entire frequency range, while the amplitude of the coding unit \"1\" exceeded 0.8 for a significant portion of the frequency range. Additionally, it can be observed that the amplitude difference between the two states was generally equal to or greater than 0.5 across most bands within the frequency range of 75-115 GHz. Figure 2: Reflection amplitudes of graphene metasurface unit at different Fermi levels. However, an exception can be seen within the shaded area of Figure 4a, which corresponds to frequencies between 92.5 and 99.3 GHz where the amplitude difference fell below 0.5, thus failing to meet the coding conditions. It should also be noted that during  
Figure 4: Comparison of amplitude and phase of different coding units under TE polarization wave and TM polarization wave irradiation. (**a**) Reflection amplitude; (**b**) transmission amplitude; (**c**) reflection phase. Figure 3: Influence of key parameters on the performance of metasurface coding unit. (**a**) Effect of substrate size a on unit performance when b = 2 mm, c = 1.4 mm, and d = 0.3 mm; (**b**) Effect of graphene size b on unit performance when a = 2.5 mm, c = 1.4 mm, and d = 0.3 mm; (**c**) Effect of bottom feed-line length c on unit performance when a = 2.5 mm, b = 2 mm, and d = 0.3 mm; (**d**) Effect of bottom feed-line width d on unit performance when a = 2.5 mm, b = 2 mm, and c = 1.4 mm. this particular frequency band, there was a gradual decline in the reflection amplitude of units, which ultimately approached 0. The results depicted in Figure 4b indicate that the transmission amplitude of both coding units was higher when subjected to incident TM polarization waves, particularly around 95 GHz. This phenomenon can be attributed to the placement of the bottom feeder along the x direction, which provided greater ease for the transmission of TM polarization waves while simultaneously suppressing TE polarization wave transmission.