Fig. 3. Active control of suspended graphene plasmons by changing the suspension height.

a Calculated imaginary part of the loss function Im{r_p(q, ω)} in the RPA for different suspension heights d, with fixed E_F = 0.65 eV and λ₀ = 10.87 μm (920 cm⁻¹). The black-dashed curves indicate the evolution of the energy splitting stemming from the coupling between GPs and phonon polaritons in SiO₂. b Experimentally measured (symbols) and theoretically calculated (solid curve) plasmon wave vector as a function of the suspension height d at λ₀ = 10.87 μm (920 cm⁻¹). Inset: illustration of a cross-sectional side view of the suspended graphene device. d₁ and d_2eff represent the depth of the dimple and the effective height of the graphene bubble, respectively. The former (d₁) is predetermined by the fabrication process, while d_2eff can be varied in situ by controlling the gas pressure from beneath the substrate film. c Extracted phase (orange curves) and group velocity (maroon curves) as a function of d. Solid curves are theoretical predictions, while symbols are values determined from the experiments. d Quality factor Q (left axis) and intrinsic propagation length L_SPP (right axis) of GPs as a function of d. Symbols are obtained from experimental data, while the curves are a guide to the eye. Error bars correspond to different line profiles in one scan image.