Fig. 1. (a) Three-dimensional (3D) and (b) cross-sectional view of the graphene-based Si₃N₄ waveguide electro–optic modulator.

Fig. 2. In-plane permittivity changes with Fermi level μ_c of graphene at 1550 nm.

Fig. 3. Im(N_eff) of SiN waveguide as a function of h_SiN and w_SiN when μ_c is 0 eV (λ = 1550 nm).

Fig. 4. Cross-section of (a) two-layer, (c) four-layer, and (e) six-layer GSNW configurations. Panels (b), (d), and (f) show field distributions of panels (a), (c), and (e), respectively.

Fig. 5. (a) Real and (b) imaginary parts of N_eff as a function of Fermi level for different graphene layers.

Fig. 6. Illustration of (a) quasi-linear variation of the optical phase, and (b) optical MPA versus Fermi levels for different numbers of graphene layer.

Fig. 7. Optical transmission of the MZI modulator changes with applied gate voltages for the 80-μm-long graphene with different layers.

Fig. 8. Illustration of (a) quasi-linear variation of the optical phase, and (b) insertion loss versus Fermi levels for different graphene modulation lengths.

Fig. 9. Normalized transmission of the MZI modulator changes with applied gate voltage for the two-layer graphene at different modulating lengths.

Fig. 10. Equivalent electrical circuits of (a) two-, (b) four-, and (c) six-layer graphene modulators.