Figure 1

(a) $\beta$ factor for an emitter at $\nu =$ 2.4 THz as a function of the distance to the graphene sheet, $z$, normalized to the free-space wavelength ${\lambda }_0$ for different values of the chemical potential ($\mu =0.2$, $0.1$, and $0.05$ eV). Inset panel: total decay rate ($\Gamma /{\Gamma }_0$) and decay rates through the plasmonic (${\Gamma }^{\mathrm{GSP}}/{\Gamma }_0$) and radiative (${\Gamma }^{\mathrm{rad}}/{\Gamma }_0$) channels. (b) Super- and subradiance between two emitters mediated by a graphene sheet when the two dipoles interact in transmission through it. $\gamma$ is plotted as a function of the vertical distance of the dipoles to the graphene sheet for the three values of the chemical potential $\mu$. The red line (long dashes) shows the vacuum interaction ${\gamma }_{\mathrm{vac}}$.Reuse & Permissions

Figure 2

Tuning super- and subradiance: $\gamma$ factor as a function of the in-plane distance $r$ between two dipoles in the reflection configuration for two different frequencies. (a) At $\nu =2.4$ THz, when the dipoles are placed at $z_1=2\mu$m ($\beta =0.98$, $\Gamma /{\Gamma }_0=105$), $z_2=15\mu$m ($\beta =0.55$, $\Gamma /{\Gamma }_0=2$), and $z_3=50\mu$m ($\beta =0.01$, $\Gamma /{\Gamma }_0=0.92$). The free-space wavelength is ${\lambda }_0=124\mu$m, the plasmon wavelength ${\lambda }_p={\lambda }_0/3.5$, and the propagation length $L_p=14.9{\lambda }_p$. The dashed black line corresponds to the free-space interaction and the dotted line to Eq. (7) for high $\beta$. (b) At $\nu =7.4$ THz, when the dipoles are at $z=0.2\mu$m, with $\beta =0.98$ and ${\Gamma }_{11}/{\Gamma }_0=2250$. The free-space wavelength is ${\lambda }_0=41\mu$m, the plasmon wavelength is ${\lambda }_p={\lambda }_0/10$, and the propagation length is $L_p=20{\lambda }_p$. The dashed black line shows the free-space $\gamma$ and the dotted line the decay of the interaction.Reuse & Permissions

Figure 3

Interaction mediated by graphene ribbons. (a)–(b) Electric field profile for a dipole decaying to the ribbon GSP. The dipole is placed at $x=0$, $y=0$, and $z={\lambda }_0/40$ in panel (a) and at $z={\lambda }_0/10$ in panel (b) [the same would be obtained for $z>{\lambda }_0/10$]. (c) Superradiance mediated by the ribbon-GSP mode shown in panel (a). The dotted green line shows the exponential decay of the interaction.Reuse & Permissions

Figure 4

Dependence of the dipole-dipole coupling in graphene ribbons on the lateral separation from the center of the ribbon, $y=0$. (a) $\gamma$ factor between two dipoles in the reflection configuration as a function of $x$ for several lateral separations from the center of the ribbon (solid blue lines). The scale in each subpanel is between 0 and 2. The dashed red line shows the corresponding interaction in vacuum. The inset panel shows a top view of the structure. (b) $\gamma$ factor as a function of the lateral separation $y$ in the transmission configuration for two cases. First (red line, with dots), $\gamma$ factor when the two dipoles are displaced simultaneously, as shown in diagram (1). The dots correspond to numerical simulations and the continuous line is a guide-to-the-eye. Second (blue line, no dots), $\gamma$ factor (from simulations) when the upper dipole is fixed at the center of the ribbon and the lower is displaced, as shown in diagram (2). The inset panel shows the corresponding interaction when the dipoles are placed in vacuum.Reuse & Permissions