## 3 High-Performance Modulation Devices Based on Graphene
### Thermo-Optic Modulators Based on Graphene  
Thermo-optic phase modulators change the refractive index of the waveguide via a temperature differential. This is typically realized with a metallic microheater fabricated proximally to the silicon waveguide [31; 32; 33], or a conducting p-i-n structure close to, or part of the optical waveguide [34]. Typically, a \(\sim\)1 \(\upmu\)m layer of silicon dioxide is fabricated between the metallic microheater and waveguide to localize heating to the waveguide, while eliminating the strong absorption light by the metallic microheater (Figure 1a). However, this insulating layer impedes the speed and efficiency of heat transmission from the heater to the waveguide, resulting in high power consumption and low modulation speed. In p-i-n based structures, the induced carriers cause additional optical loss by photonic absorption by mid-band doner states.  
Graphene is considered to be an ideal replacement of the metallic microheater as close to transparent, while retaining strong Joule heating properties, removing the requirement an oxide layer (Figure 1a) [35]. Based on this principle, graphene microheaters have been applied in many fields including flexible heaters and heat conductors, while its application as a thermo-optic modulator in silicon photonics was first proposed by [PERSON] et al. in 2014 [21]. Figure 1b shows graphene acting as a heat conductor to deliver heat from a non-local traditional metal heater to the silicon waveguide integrated within a MZI structure. The tuning efficiency is around 0.07 nm/mW while the 90% rising and decaying times (the time it takes for the change in temperature to reach 90% of the maximum value from rest) are 20 \(\upmu\)s. It should be noted that in this work graphene only acts as a thermal conductor, rather than a microheater.  
In 2015, [PERSON] et al. reported a novel thermo-optic modulator where graphene operates as a transparent microheater fully covering a silicon MRR (Figure 1c). Thanks to the ultrahigh heat conductivity of graphene, the response time of the graphene-based thermo-optic MRR modulator is only 750 ns. Meanwhile, the tuning efficiency is enhanced to 0.1 nm/mW [22]. To further enhance the performance of the thermo-optic silicon modulator based on graphene, the shape of the graphene is patterned to only cover the optical mode, rather than covering the entire device. This method is widely applied in silicon MRRs and micro-disk resonators, with tuning efficiencies of 0.33 nm/mW and 1.67 nm/mW demonstrated respectively, leveraging efficient heat transport from the microheater to the resonator [23; 24].  
Photonic crystal waveguides are also proposed to enhance graphene microheater efficiency (Figure 1d). In 2017, [PERSON] et al. combined the graphene microheater with a photonic crystal waveguide, enabling a fast-tuning speed of 525 ns and slow-light enhanced tuning efficiency of 1.07 nm/mW [36]. Enhancement via photonic crystal nanocavities has also been demonstrated: Ref. [25] exhibits a tuning efficiency of 3.75 nm/mW, by virtue of the tight confinement of the optical mode within the cavity. These works demonstrate the significant advantages of graphene-based approaches when compared to the conventional microheaters approaches in silicon photonics, in terms of both tuning efficiency and modulation speed.