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Particular interest in graphene is with its interaction with optical modulators in an integrated waveguide. Integrated modulatorsare  with high modulation speed, large bandwidth, and small footprint are wanted for on-chip optical interconnects [8]. Liu et al experimentally demonstrates an integrated electroabsorption modulator on monolayer graphene with the above characteristics. A problem with a direct graphene modulator is limited absorption in a monolayer. So to counter this one integrates graphene with an optical waveguide which increases interaction length through coupling between evanescent waves and graphene [8]. The advantages of such a setup include strong light-graphene interaction, broadband operation,high speed operation, and compatibility with CMOS processing. As before, the tunability of graphene properties will be used here for modulation by tuning the fermi level of the single layer graphene sheet. A 3d schematic is shown in figure 3a where a 50-nm thick silicon layer is connected to a 250-nm thick silicon bus waveguide one of the gold electrodes [8]. A graphene sheet is then transferred onto the silicon waveguide. A cross-sectional view of this device and field distribution is shown in figure 3b. To improve absoprtion modulation efficiency, silicon waveguide is designed to have maximized electric field at the top and bottom surfaces, so interband transitions are also maximized [8]. The end results showed that a graphene-based optical modulator has a broad optical bandwidth from 1.35-1.6 $\mu m$ with a footprint of 25 $\mu m^2$ and high operation speed of of 1.2 Ghz at 3 dB.\\ Kayoda et al also analyze a graphene optical modulator based on semiconductor-metal transition using the time-domain beam propagation method. This graphene-based optical modulator is made using a single-layer of graphene loaded on a Si photonic-wire waveguide made on a silicon on insulator wafer. Using the time-domain beam propagation method, the absorptions per $\mu m$ for TE and TM polarized light as a function of the chemical potential. It was found that when the chemical potential went from $0-0.46 eV$, absorption decreases due to interband transition being supressed. Notice the theoretical value calculated for $1.55 \mu m$ was $0.497 eV$ for when intraband dominates and their value for when interband transitions are supressed is consistent. Absorption for TM light is increased dramatically when the chemical potential is increased from $0.46 eV$ to $0.51 eV$. This is due to graphene becoming more metal like when intraband transitions are dominant. The absorption change is $0.61 \frac{db}{\mu m}$, this suggests a graphene modulator based on semiconductor-metal transition is promising [2].