# Beyond 5G Fronthaul Based on FSO Using Spread Spectrum Codes and Graphene Modulators
## 3 Graphene Modulator for Next-Generation Fronthaul Networks
### Numerical Simulations and Results  
The new graphene modulator's performance was evaluated for four different graphene levels: 25%, 50%, 75%, and 100%. Only four discrete steps were considered due to the computational demand of the simulations. The goal was to determine the modulator's maximum efficiency in terms of power consumption per bit. Initially, we carried out an analysis of the graphene modulator properties considering the transmission parameter (\(S_{21}\)). The transmission parameter versus wavelength considering both OFF and ON states has been plotted in Figure 4 for 25% and 100% graphene only, for the sake of space. It can be noted that both curves (red and blue) have a minor displacement of the propagation wavelength. This happened due to the insignificant phase variation in comparison to the propagation wavelength. The latter occurred owing to the substantially smaller device's coupling propagation region than the beat length [82]. The extinction ratios are 34.27 dB, 39.13 dB, 51.52 dB, and 32.26 dB for 25%, 50%, 75%, and 100% graphene. Let \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Graphene (\%)** & **25** & **50** & **75** & **100** \\ \hline \(\mu_{OFF_{1}}\) **(eV)** & 0.51 & 0.51 & 0.51 & 0.51 \\ \(\mu_{OFF_{2}}\) **(eV)** & 0.444 & 0.444 & 0.444 & 0.444 \\ \(\mu_{ON_{1}}\) **(eV)** & 0.468 & 0.474 & 0.4815 & 0.485 \\ \(\mu_{ON_{2}}\) **(eV)** & 0.4095 & 0.4115 & 0.4115 & 0.4115 \\ \(BW_{3 dB_{1}}\) **(GHz)** & 18.1 & 22 & 25.1 & 28.6 \\ \(BW_{3 dB_{2}}\) **(GHz)** & 42.6 & 63.8 & 78.4 & 88.45 \\ \(Gap_{1}\) **(nm)** & 275 & 260 & 250 & 240 \\ \(Gap_{2}\) **(nm)** & 205 & 170 & 145 & 125 \\ \(Loss_{1}\) **(dB/\(\mu\)m)** & \(-\)0.0035 & \(-\)0.0043 & \(-\)0.0055 & \(-\)0.0056 \\ \(Loss_{2}\) **(dB/\(\mu\)m)** & \(-\)0.0089 & \(-\)0.015 & \(-\)0.0214 & \(-\)0.0285 \\ \(E/bit_{1}\) **(f/bit)** & 8.4 & 14.7 & 17.8 & 21 \\ \(E/bit_{2}\) **(f/bit)** & 4.6 & 8.75 & 13.1 & 17.5 \\ \(FOM_{1}\) **(\(\frac{\text{GHz}}{\text{/}}\text{/}\text{/}\text{bit}\times\text{mm}^{2}\))** & 0.0972 & 0.0677 & 0.0639 & 0.0616 \\ \(FOM_{2}\) **(\(\frac{\text{GHz}}{\text{/}}\text{/bit}\times\text{mm}^{2}\))** & 0.4184 & 0.3302 & 0.2704 & 0.2237 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Optimization of the modulator’s design and performance metrics. us analyze how the device's power consumption performs under different amounts of graphene used in the ring. The goal is to identify the more efficient approach that simultaneously ensures modulation within the GHz range whilst providing power efficiency. Thus, the power consumption per bit as a function of the graphene's ring percentage is shown in Figure 5a. Notice that the optical losses related to the graphene's absorption rapidly increase the power consumption per bit and are proportional with the graphene's ring percentage in the modulator. Although the power consumption remains within targeted levels, the modulation capacity of the device can be better understood by analysing the difference between the chemical potentials for the states ON and OFF. Then, the chemical potential ON-OFF variation as a function of the graphene's percentage was plotted in Figure 5b. Interestingly, these results provide clear evidence on how much graphene should be used. The modulator shows a decrease in the chemical potential ON-OFF variation as a function of the graphene ring percentage. The \(-3\) dB bandwidth as a function of the ring's graphene content levels in percentages is plotted in Figure 5c. Results show that the bandwidth increases significantly with the graphene ring percentage. This occurs due to increases of graphene-related losses as the graphene percentage is increased. Consequently, the modulator can offer ultra-high switching properties if higher percentages of graphene are used. Nevertheless, the 100% graphene modulator has 6.72 \(\upmu\)m\({}^{2}\), although the 25% graphene modulator has an active area of 1.68 \(\upmu\)m\({}^{2}\). This represents an effective 4-fold decrease in the modulator's active area.