Fig. 1. CR excited by low-energy electrons in the GHM. Features of the hyperbolic CR in the hyperbolic state (left half) and conventional CR in the elliptical state (right half).

Fig. 2. Basic principles of SMT. T and R represent the transmission and reflection coefficients, respectively. The purple and red boxes indicate the connection of scattering matrices in the interface and inside the region, respectively.

Fig. 3. Effective in-plane permittivity of the GHM described by the EMT. Re(εeff-in) for (a) EF=0.15  eV and (b) d=30  nm. (c) Effective refractive index neff and (d) normalized electron velocity vn at different electron velocities, EF=0.15  eV, and d=30  nm (ft, OTT frequency).

Fig. 4. Effective CR properties. (a) Directions of wave vector k and energy flux S. (b) Normalized CR intensity (for EF=0.15  eV and d=30  nm).

Fig. 5. (a) Dispersion of plasmon modes in the GHM characterized by the imaginary part of reflection coefficient, Im(rp), displayed in log100 scale. (b) Imaginary part of reflection coefficient: Im(rp) at 15, 25, 35, and 45 THz.

Fig. 6. Electric field spatial distributions of excited plasmon modes parallel to the x axis corresponding to the white labels shown in Fig. 5(a). (a) Point A with the optical mode at 45 THz. (b) Point B with the optical mode at 35 THz. (c) Point C with the second mode at 25 THz. (d) Point D with the fourth mode at 25 THz. (e) Point E with the fourth mode at 15 THz. (f) Point F with the tenth mode at 15 THz. The white dashed lines indicate graphene layers.

Fig. 7. Temperature-dependent photothermal properties. (a) Imaginary part of temperature-dependent conductivity, Im(σ). (b) Real part of temperature-dependent effective in-plane permittivity, Re(εeff-in). The white line indicates Re(εeff-in)=0. (c) Effective refractive index neff at u=0.1c. The white line indicates neff=10, or vn=1. (d) Normalized CR intensity at u=0.1c. The white line indicates the boundary for CR generation.

Fig. 8. Nonlocal properties. (a) Imaginary part of nonlocal graphene conductivity, Im(σ). (b) Real part of effective in-plane permittivity, Re(εeff-in). The black dashed line indicates the new lower electron velocity threshold for CR, which is equal to the Fermi velocity of graphene, vF. (c) Dispersion relation: the imaginary part of the reflection coefficient, Im(rp), is displayed on log100 scale. The white dashed lines indicate the positions of the Fermi velocity of graphene, vF, and the phase velocity of light in the buffer layer, vb.