Fig. 2: Mode properties of the present silicon−graphene hybrid plasmonic waveguide when operating at λ = 2 μm.

a Calculated absorption coefficients (α_g, α_m) and the graphene absorption ratio η_g as the silicon ridge width w_si varies for cases with different silicon ridge heights h_si. Here, w_m = 200 nm, and h_m = 50 nm. b Calculated absorption coefficients (α_g, α_m) and the graphene absorption ratio η_g as the metal strip width w_m varies for cases with different metal heights h_m. Here, w_si = 3 μm, and h_si = 100 nm. c The electric field component \(\sqrt {\left| {\overrightarrow {E_x} } \right|^2 + \left| {\overrightarrow {E_z} } \right|^2}\) distribution of the quasi-TE₀ mode for the optimized silicon−graphene hybrid plasmonic waveguide. d Calculated graphene absorptance η as the propagation length L varies for cases with different metal widths of w_m = 100, 200, and 300 nm. Here, h_m = 50 nm, w_si = 3 μm, and h_si = 100 nm