Single-layer and double-layer GOMs. (a) Schematic of a single-layer GOM. The graphene film is separated from the silicon waveguide by a thin Al2O3 layer which is not shown. Pt- and Si-doped layers are deposited to connect graphene and gold electrode. The Si waveguide is also shallowly doped with boron to reduce the cascade resistance. (b) Cross section of a single-layer GOM. Left: cross section of the device with optical field distribution. Right: electric field distribution in the waveguide. (c) Transmission at different gating voltages in a single-layer GOM. When the Fermi level is close to the Dirac point, optical absorption occurs and transmission reduces. When large gating voltages are applied, optical absorption blocks and transmission increases. Reproduced from ref. . (d) Schematic of a double-layer GOM. The two graphene layers are separated by a thin film of Al2O3. And the bottom graphene layer directly contacts the Si waveguide. (e) Transmission of carrier light at different gating voltages, which is similar to that of the single-layer GOM. (f) Tuned Fermi level and optical absorption behavior in double-layer graphene. Even though the Fermi levels are different when large gating voltages are applied, both layers tend to be transparent. When the Fermi levels are close to the Dirac point, both layers absorb the incident light, which results in a higher modulation depth. Reproduced from ref. .