Figure 3. Transmission modulation of C-SRR-GR hybrid metamaterials operating at ∼10 THz.

(a) Transmission spectra (normalized to the substrate transmission) of the C-SRR-GR hybrid metamaterial HM1 at different graphene carrier densities in comparison with the transmission spectrum of a reference bare C-SRR array. The transmission spectrum of a GR array exhibiting the localized SP resonances is also shown. (b) Stacked transmission spectra of HM1 (5% offset) at varied carrier densities (from the CNP to ∼1.2 × 10¹³ cm⁻²). The coloured curves in b correspond to those in a of the same colour. (c) Symbols are the extracted peak frequencies of the two hybridized modes in the corresponding transmission spectra in b, plotted as a function of the carrier density (n^1/4). The choice of n^1/4 as the x-axis variable in c is because of the fact that the resonance frequency of uncoupled graphene surface plasmon is proportional to n^1/4, which is different from the n^1/2 dependence associated with two dimensional electron gas in semiconductor heterostructures26. The solid curves are fits of the data points with equation (1) describing the anti-crossing of two strongly coupled resonances, that is, the localized SP resonances in the GRs (blue dashed line) and the C-SRR LC-resonance (green dashed line). See Supplementary Note 3 for more details of the fitting procedure.