## 3 Antenna Design  
### Single Element Patch Antenna  
Initially, a conventional microstrip patch antenna with a graphene plasmonic layer is engraved on the top side of Teflon with a relative permittivity of 2.1, and a thickness of 10 \(\upmu\)m. The proposed antenna is designed to resonate at 3.5 THz. The dimensions of the patch are recognized by the usage of the characteristic mode analysis (CMA) using the integral equation solver in the CST microwave studio. The optimum width and length of the patch are 32 \(\upmu\)m and 25 \(\upmu\)m, respectively. The single element of the patch antenna is matched to a transmission line of 50 \(\Omega\) characteristic impedance using a quarter-wavelength impedance transformation. The model significance and the characteristic angel curves are shown in Figure 2a,b. Mode 1 is the resonance mode (desired mode) at a frequency of 3.5 THz in which the characteristic angle is 180\({}^{\circ}\) and the model significance in this frequency is the highest value (closely to unity). The validation process of the CST result can be achieved by the usage of HFSS and the equivalent circuit model using ADS software. The values of the electrical RLC components are calculated, and the electric circuit model of the antenna is developed using the circuit theory approach [35].  
The desired current distribution specifies the optimum position for the excitation process so, the proposed structure of the single-element antenna is shown in Figure 3. The calculated value of the circuit parameters is listed in Table 1. Figure 4 shows the circuit model connection diagram of the proposed antenna. The results obtained from the HFSS and ADS circuit theory approach are in good agreement with those obtained using CST software. The \(\left|\mathrm{S}_{11}\right|\) curve of the graphene plasmonic antenna is illustrated in Figure 5. There is a small deviation in the \(\left|\mathrm{S}_{11}\right|\) curves, which may be due to the different numerical approaches used in different software. The 3D radiation pattern of the proposed graphene plasmonic antenna is depicted in Figure 6. Figure 7 shows the graphene's frequency-reconfigurable behavior of the graphene plasmonic antenna when the chemical potential applied varied between 0.5 and 2.5 eV. This figure reveals that the plasmonic resonance frequency of the proposed antenna increases via the chemical potential and can be dynamically controlled in a wide frequency range from 2.75 to 4 THz. So, this design has dynamic reconfigurability by applying an external electric field.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Par.** & **Value (\(\mu\)m)** & **Par.** & **Value (\(\mu\)m)** \\ \hline W\({}_{\text{S}}\) & 130 & L\({}_{\text{S}}\) & 85 \\ W\({}_{\text{P}}\) & 35 & L\({}_{\text{P}}\) & 25 \\ W\({}_{\text{f}}\) & 12 & L\({}_{\text{f}}\) & 25 \\ W\({}_{\text{f1}}\) & 5 & L\({}_{\text{f1}}\) & 10 \\ \multicolumn{4}{c}{Single Element Parameters of ADS Circuit} \\ L\({}_{1}\) & 5.25 pH & L\({}_{2}\) & 0.6499 pH \\ C\({}_{1}\) & 1.544 fF & C\({}_{2}\) & 3.5 fF \\ R\({}_{1}\) & 200.23 \(\Omega\) & \\ \multicolumn{4}{c}{Two Element Parameters of ADS Circuit} \\ L\({}_{3}\) = L\({}_{5}\) & 1.5 pH & L\({}_{6}\) = L\({}_{6}\) & 1.8 pH \\ C\({}_{3}\) = C\({}_{5}\) & 1.1 fF & C\({}_{4}\) = C\({}_{6}\) & 1.8 fF \\ R\({}_{2}\) = R\({}_{3}\) = R\({}_{4}\) & 100 \(\Omega\) & C\({}_{7}\) & 0.4 fF \\ L\({}_{7}\) & 0.6 pH & - & - \\ \multicolumn{4}{c}{Dumbbell-Structure MTM parameters} \\ r\({}_{0}\) & 12 & X & 7 \\ y & 25 & - & - \\ \hline \end{tabular}
\end{table}
Table 1: The proposed antenna parameters.  
Figure 3: Schematic of the graphene plasmonic patch antenna.  
Figure 2: (a) Significant and (b) characteristic angle of the first four modes of the proposed patch antenna.  
Figure 4: ADS equivalent circuit model of the proposed graphene antenna.  
Figure 5: \(|S_{11}|\) of the single element graphene plasmonic patch antenna with different simulation programs.  
Figure 6: 3D radiation pattern of the proposed antenna.