Fig. 1. Upper panel: real part of the graphene conductivity for ℏω=0.8  eV (corresponding to a free-space wavelength equal to 1550 nm) versus the applied chemical potential μC. Inset: same quantity on a broader range of applied chemical potentials. Lower panel: relative dielectric constant of graphene versus the applied chemical potential.

Fig. 2. Schematic diagram (not to scale) of a waveguide comprising two graphene layers (red lines) biased so as to obtain electrochemical doping inside the waveguide core. The blue region is alumina.

Fig. 3. Upper panel: variation of the phase constant versus the chemical potential. Zero is arbitrarily chosen in correspondence to the phase displacement experienced by the wave when μC=0.50  eV. Lower panel: attenuation across a 1 cm long straight waveguide versus the applied chemical potential. Note the log scale in the vertical axis. Computations have been made for λ=1550  nm.

Fig. 4. Upper panel: schematic diagram of the ring configuration phase modulator. Lower panel: fields in the ring structure, with definition of the straight waveguide and ring single-pass transmission, t and α, respectively. The cross section of the waveguide in the ring is the same as in Fig. 2.

Fig. 5. Upper panel: overall bus-to-bus transmission for coupler transmission t=0.9 and ring transmission α=0.99 (dashed line) or α=0.999 (solid line). The abscissa is the round-trip phase shift φ. Lower panel: overall bus-to-bus phase shift. Dashed and solid lines still refer to α=0.99 and α=0.999 and coincide.

Fig. 6. Upper panel: phase displacement ψ versus frequency for chemical potential |μC|=0.56  eV (filled diamonds), |μC|=0.58  eV (filled squares), |μC|=0.60  eV (filled circles), |μC|=0.62  eV (empty diamonds), |μC|=0.64  eV (empty squares), and |μC|=0.66  eV (empty circles). Lower panel: insertion loss versus the applied chemical potential.