Here, we theoretically study a novel multi-mode modulator based on a double-layer graphene-on-silicon waveguide. Our method is based on the exploration of tunable interaction between patterned graphene nanoribbons (GNs) on the surface of a silicon waveguide and zeroth transverse electric (TE0) and first transverse electric (TE1) modes in the waveguide. By adjusting the Fermi level of graphene sheets in the double-layer graphene-on-silicon waveguide, we could simultaneously and separately obtain about pi phase shifts of the TE0 and TE1 modes in the same waveguide. Our study is expected to open an avenue to develop high-density MDM photonics integrated circuits for tera-scale optical interconnects.
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