# 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
There is also a cost decrease along with the footprint reduction. Bear in mind that superior-standard graphene might be costly. The final cost of the modulator depends on the quantity of graphene used among others, with the 25% version being significantly cheaper than the 100% version. Lastly, the performance efficiency of the modulator as a function of the graphene's ring percentage is investigated. These results are shown in Figure 5d. Note the overall performance deteriorates by increasing the ring's graphene percentage. In this case, the reduction in the active resonator area via the increases of the graphene in ring broadening percentage renders a substantial reduction in the efficiency of the device. This happens since the large bandwidth obtained by the increasing graphene ring effect is compensated by the deleterious effect of the high-power consumption per bit. This indicates that, for the sake of minimizing power consumption, the quantity of graphene should be capped at a quarter of the total cavity, at the cost of reducing the bandwidth. Such a device can be built to fit an extremely small area of 22.1 \(\upmu\)m\({}^{2}\) and still offer a wide bandwidth of 42.6 GHz with very low levels of power consumption, such as 4.6 fJ/bit. Figure 4: The modulator’s transmission curves versus the wavelength considering both OFF (red) and ON (blue) states and different percentages of graphene. (**a**) At 25% graphene and (**b**) 100% graphene. Next, the RC constant is addressed. Initially, the contact resistance equals to 100 \(\Omega\cdot\upmu\)m for each graphene's plate capacitor (Ni/graphene contact). The plate capacitance equals to 12.48 fF/um\({}^{2}\)[71]. Then, according to the model for calculating \(f_{RC}\) (\(RC\) limited 3 dB bandwidth) [71], the quantum capacitance for a device with an active area of 1.68 um\({}^{2}\) (25% of graphene) is \(C_{Q}=0.87\) pF, while the plate capacitance is \(C_{P}=21.25\) fF. Accordingly, being the equivalent capacitance value of the circuit, we have \(C=(1/2)\left(C_{Q}C_{P}\right)/\left(0.5C_{Q}+C_{P}\right)=20.26\) fF. The equivalent resistance of the circuit is given by \(R=2\left(R_{g}+R_{c}\right)\), where \(R_{g}\) is the electrical resistance associated with the graphene layer, and \(R_{c}\) is the resistance of the graphene-metal interface. Considering that \(R_{g}\) is small for devices with dimensions in the order of a few microns [71], \(R_{c}\) becomes dominant. Additionally considering how the contact length between the graphene monolayer and electrode is represented by the graphene length around the resonator circumference, the experimental values of the contact resistance equivalent to the proposed device equal to \(R_{c}=35.77\)\(\Omega\). Finally, given the optical bandwidth of 42.6 GHz, the calculation of the modulation bandwidth is given by \(1/f_{-3\ dB}^{2}=1/f_{RC}^{2}+1/f_{opt}^{2}\approx 42.67\) GHz. Therefore, \(f_{-3\ dB}\) is close to the value associated with \(f_{opt}\) (optical limited 3 dB bandwidth) and \(f_{RC}\) (\(RC\) limited 3 dB bandwidth) presents reasonable values and does not limit \(f_{-3\ dB}\) (total 3 dB modulation bandwidth given by \(f_{opt}\) and \(f_{RC}\)) for the proposed modulator device. The same analysis holds true for different percentages of graphene used in the device design. Accordingly, the value of \(f_{RC}=110\) GHz, regardless of the device's active area. Nonetheless, the values of \(R\) and \(C\) change with the given active area. For example, for an active area of 1.68 um\({}^{2}\) (25% of graphene) \(R=71.54\)\(\Omega\) and \(C=20.26\) fF, for 3.36 um\({}^{2}\) (50% graphene) \(R=35.77\)\(\Omega\) and \(C=40.52\) fF, for 5.04 um\({}^{2}\) (75% graphene) \(R=23.84\)\(\Omega\) and \(C=60.78\) fF, and for 6.72 um\({}^{2}\) (100% graphene) \(R=17.88\)\(\Omega\) and \(C=81.04\) fF, respectively.