## 3 High-Performance Modulation Devices Based on Graphene
### E-O Modulation  
Although the modulation speed of thermo-optic modulator based on graphene microheater can be in the MHz range, this is insufficient for high-speed optical communication systems where the operation bandwidth is in the tens of gigahertz (GHz). Here, electro-optical silicon/graphene modulators, which utilize the electro-optic effect to modulate light, are more applicable. Indeed, graphene's ultra-high carrier mobility may enable modulation speeds of hundred gigahertz, which is particularly attractive for data- and tele-communication systems. The first experimental demonstration of a silicon/graphene electro-optical modulator operating at communication wavelengths is reported by [PERSON] et al. in 2011 [37]. Here, a capacitor formed by graphene, Al\({}_{2}\)O\({}_{3}\), and silicon waveguide forms the core of the electro-optical modulator. The Fermi level of the graphene sheet is manipulated by applying external voltage on the electrical pad. When the Fermi level is close to the Dirac point, the guided light within the silicon waveguide experiences absorption from graphene, while shifting the Fermi level away from the Dirac point results in transparency. Although this first result is not as impressive as the state-of-the-art silicon modulators, it lays the theoretical foundation for the practical use of graphene within electro-optical modulators. To enhance the modulation depth of the graphene modulator, various schemes have been reported, focusing on increasing the graphene absorption. The most straightforward method is to use more than one layer of graphene [38; 39; 40; 41], which was first proposed by [PERSON] et al. in 2012 [38]. Here, the double layer graphene and a thick oxide layer form a p-i-n junction as the active region for modulation (Figure 2a), leading to a larger modulation depth of 6.5 dB, though the bandwidth is limited to around 1 GHz. By optimizing the RC constant, [PERSON] et al. showed a double-layer graphene modulator exhibiting a bandwidth of 29 GHz, which is capable of transmitting 50 Gbit/s non-return-to-zero data [40]. Another method to reach higher modulation depths is to employ resonance structures such as photonic crystal cavities and MRRs. Photonic crystal cavities have the advantages of ultra-compact light confinement and could be a promising way to reach higher modulation depth [42; 43; 44]. According to [PERSON] et al. 's report, a high modulation more than 10 dB is demonstrated by modulating both the quality factor and the resonance wavelength of the cavity (Figure 2b). Meanwhile, the hybrid integration of a MRR with a graphene monolayer was first introduced in 2014 (Figure 2c) [43]. By altering the resonance wavelength and the quality factor of the MRR, the resonance is modulated with a depth of 40% via gate tuning of the Fermi level in the graphene. Here, the coupling condition of the MRR could also leveraged to reach higher modulation depths. [PERSON] et al. demonstrated that the modulation depth could be as high as 12.8 dB when the MRR is covered with the optimum length of graphene and working in the slightly under-coupled regime, close to the critical-coupling condition (Figure 2d) [45]. Recently, the silicon slot waveguide is also reported to enhance  
Figure 1: Thermo-optic modulators based on graphene for silicon photonics: **(a)** Schematic of the cross-section of a thermo-optic modulator based on metallic microheater (left) and graphene microheater (right). **(b)** Silicon thermo-optic modulator employing graphene as the heat conductor [21]. Reprinted from [_Appl. Phys. Lett._ 105, 251104 (2014)], with the permission of AIP Publishing. **(c)** MRR silicon thermo-optic modulator covered by graphene microheater. Reproduced from Ref. [22] with permission from the Royal Society of Chemistry [22]. **(d)** Hybrid integration of silicon photonic crystal structures and the graphene microheater [36]. the modulation depth of the graphene photodetector, with a modulation depth up to 25 dB experimentally demonstrated [46; 47; 48; 49].