# Beyond 5G Fronthaul Based on FSO Using Spread Spectrum Codes and Graphene Modulators
## 3 Graphene Modulator for Next-Generation Fronthaul Networks  
### Design, Optimization, and Numerical Simulations  
The design of the proposed modulator is also illustrated in Figure 3. The modulator is based on a silicon core bus waveguide having a width of \(W_{1}=340\) nm coupled to a ring-shaped silicon resonator of a fixed waveguide width of \(W_{2}=600\) nm. Both waveguides have the same thickness of \(h_{Si}=220\) nm. Moreover, the resonator is partially covered with three thin layers. The first layer is composed of graphene and has a thickness of \(h_{g}=0.34\) nm, followed by an alumina layer with a thickness of \(h_{a}=7\) nm, and finally another graphene with \(h_{g}=0.34\) nm. The whole structure is on the silica substrate and is more propitious for footprint reduction due to its double-layered structure [72]. The device also has two metal contacts on the top of the silica substrate, each connected to a graphene layer, forming a capacitor. Such a device can be eventually fabricated using chemical vapor deposition, photolithography, and etching. To simplify the simulation procedure but without losing any accuracy, both layers of graphene and the alumina one are replaced by a homogeneous waveguide, with the refraction index \(n_{homog}\) given as \(n_{homog}=n_{Si}+\alpha(\mu,\lambda)+j\beta(\mu,\lambda)\) and \(neff_{graphene}=neff_{homog}\), where \(\alpha(\mu,\lambda)\) and \(\beta(\mu,\lambda)\) are the real and imaginary parts of the silicon refractive index being a function of the wavelength and chemical potential, respectively. Here, \(n_{Si}\) is the silicon refractive index, and \(neff_{homog}\) and \(neff_{graphene}\) are the effective refraction index of the homogeneous and graphene-assisted waveguides, respectively [78]. In particular, this method renders a  
Figure 2: Block diagram of the decoder at the receiver side showing the OCDMA decoder, the avalanche photodetector (APD), the integrator with \(T_{c}\) as chip duration, the threshold decision device, and recovered data. homogeneous waveguide instead of a classical heterogeneous waveguide with many layers, and consequently, several different indexes of refraction, with an estimated error of \(\sim\)0.05% only. Subsequently, the chemical potential properties of the modulator for different amounts of graphene are analyzed. A schematic illustration of the waveguide homogenization technique is depicted in detail in Figure 3a. The variation of the real and imaginary parts of the index versus the chemical potential for a wavelength of 1.5344 \(\upmu\)m is plotted in Figure 3b. The modulator operates in the OFF state with a chemical potential of 0.444 eV, which represents the highest value from the optimal range of the graphene's real and imaginary conductivity (see Figure 3). This range maximizes the modulator's optical absorption and phase variation ratio, reducing power consumption. The ON state of the modulator is obtained when the insertion loss is \(-3\) dB. The analysis was repeated for different amounts of graphene, ranging from 25% to 100% in four increments, with a ring's external radius of 2.08 \(\upmu\)m. Accordingly, the modulator demonstrates a maximum modulation depth of 27 dB at 1534.4 nm, with a ring's external radius of 2.08 \(\upmu\)m, and graphene and alumina layers of 0.34 nm and 7 nm. Next, the device's bandwidth is given by Ref. [82]  
\[BW_{-3\text{ dB}}(\text{nm})=\frac{\left(1-\alpha^{2}\right)\lambda_{0}^{2}}{2 \pi^{2}Rn_{g}\alpha}, \tag{1}\]  
where \(n_{g}\), \(R\), and \(\lambda_{0}\), are the group index, mean radius, and resonance wavelength of the resonator for the propagated mode, respectively. It is considered the same criterion of insertion loss for the ON state (\(-3\) dB) and identical external radius for different amounts of the graphene's ring percentage.