Fig. 4: Influence of |μ_r| and |ε_r| on TE graphene plasmons in negative refractive-index environments.

Here the in-plane wavevector Re(q) of TE graphene plasmons is normalized by the wavevector \(k = k_0\sqrt {\varepsilon _r\mu _r}\) of light in the surrounding environment. The setup of monolayer graphene is the same as that in Fig. 2a with the relaxation time τ = 0.2 ps. For comparison, the influence of |μ_r| and |ε_r| on TE graphene plasmons in positive refractive-index environments is also shown. For the negative refractive-index environments, ε_r < 0 and ε_r < 0 and T = 300 K; for the positive refractive-index systems, μ_r > 0, ε_r > 0 and T = 100 K. The environments with ε_r near zero or μ_r near zero can be effectively constructed for example via metamaterials^36,41,51, photonic crystals^52,53,54,55, and waveguides^57,58,59.