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Lu et al continues investigation into graphene integrated into waveguides and tuning the absorption with chemical potential.First they solved for TM modes of graphene on a 250 by 600 nm silicon waveguide with a 7 nm $AL_2O_3$ buffer operating at a wavelength of $1.53 \mu m$. Attenuation is $0.134 \frac{dB}{\mu m}$ for $\mu_c=0$ and $0.044 \frac{dB}{\mu m}$ at $\mu_c=\mu_t$ where $\mu_t$ is the transition chemical potential from before. Absorption can be continued to be reduced when $\mu_t$ is increased [1]. An interesting case is when graphene is sandwiched inside a silicon waveguide, created a "graphene-slot waveguide". It was shown that for a TM mode, the power per unit area absorbed $p_d\approx\frac{1}{2} \frac{E *Im(\epsilon_{eff})}{|{\epsilon_{eff}|}}$. Referencing figure 1, it can be seen that at the transition chemical potential, the $|\epsilon_{eff}|$ is near zero. So the power absorbed is greatly increased. These properties suggest that nanoscale graphene electro-optic modulators can be developed for silicon platforms [1].\\  Graphene has shown promising applications to real technological issues. It could be used to make chips smaller,faster, and with a wider choice of wavelength. For it light coupling properties, it can be used to be integrated onto waveguides and its special property being a zero-gap semiconductor allows tuning of chemical potential, conductivity, and dielectric constant to name a few. This can help with absorption of modes with an integrated graphene waveguide as in  [1]. Graphene can also support TE and TM surface waves given certain conditions shown in [6], whereas at a dielectric metal interface surface TM modes are only supported. The tunability of chemical potential by electrical gating can allow you to choose which modes you would like to propagate by $0<\frac{\hbar\omega}{\mu}<1.667 and $1.667 <\frac{\hbar\omega}{\mu}<2$ for TE and TM modes respectively showing flexibility.