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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 $p_d\approx\frac{1}{2}$ $p_d\approx\frac{1}{2} \frac{E Im(\epsilon_{eff})}{\abs{\epsilon_{eff}}}$