Fig. 1. Schematic of the stacked graphene. The free electrons traverse the stack, which consists of periodically arranged alternative graphene sheets and dielectric buffer with permittivity εd and thickness h, along the Z (parallel to the electrons) direction. The excited GPs propagate along the X and Y (perpendicular to the electrons) directions.

Fig. 2. Dispersion curves of the stack and the poles distribution. (a) The frequency dispersion curves with normalized excitation probabilities in the logarithmic scale; h is 100 nm, εd and εsub are 2.1, and the chemical potential of the graphene sheets is 0.15 eV. There appear 10 curves around two fundamental modes for the stack with 10 layers of graphene sheets, induced by the GP coupling. (b) The GP pole distributions at 12, 15, and 17 THz.

Fig. 3. Contour maps of the electric field along the R direction for individual modes. (a) The contour map and field amplitude profile of the 4th mode at 12 THz, in which a TM4-like mode is formed by the coupling, indicating a hyperbolic-like spatial dispersion. (b) The contour map and field amplitude profile of the 10th mode at 12 THz, in which the fields are mainly confined on the upper surface, indicating a plasmonic-like spatial dispersion.

Fig. 4. DCITR from the individual bulk GP modes. (a) The contour map of the electric field along the R direction of DCITR at 12 THz, in which the field propagates along an radiation angle normal to the Poynting vector. The inset is that at 22 THz, which is confined on the first several graphene sheets. (b) The contour map of the TR in normal medium at 12 THz. (c) The electric field contour map of the GPs on the monolayer graphene sheet at 12 THz; (d) and (e) the normalized field intensity via the number of graphene sheet, in which the field intensity of DCITR attenuates in the form of an inverse proportional function of the graphene sheet number.

Fig. 5. Radiation angle and normalized field intensities. (a) The dependences of the field intensities and radiation angle on the frequencies. (b) The dependences of the field intensities on the electrons velocities at 12 and 15 THz, respectively. (c) The dependence of the field intensity on the chemical potential of the graphene sheets. (d) The dependence of the radiation angle on chemical potentials of the graphene sheets.