Fig. 1. A platform for programmable Bloch polaritons.

(A) Schematic of a back-gated graphene polaritonic crystal. Gold launchers excite Bloch polaritons propagating along designated directions controlled by the gate voltage V_g. Inset shows the carrier density distribution in the graphene layer with average carrier density ${\overline{n}}_s=4.5\times {10}^{12}\mathrm{c}{\mathrm{m}}^{-2}$. (B) Simulated polaritonic band structure at ${\overline{n}}_s=3.6\times {10}^{12}\mathrm{c}{\mathrm{m}}^{-2}$. Dashed line corresponds to ω = 890 cm⁻¹. (C) Simulated equi-energy contours at ${\overline{n}}_s=3.6\times {10}^{12}\mathrm{c}{\mathrm{m}}^{-2}$ and ω = 890 cm⁻¹, showing the polaritonic pockets around M points. (D) Simulated electric field Re(E_z) of polaritons excited by a point source at ${\overline{\mathit{n}}}_{\mathit{s}}=3.6\times {10}^{12}\mathrm{c}{\mathrm{m}}^{-2}$ and ω = 890 cm⁻¹. Bloch polaritons propagate predominantly along $\hat{M}=\mathrm{\langle }-11\mathrm{\rangle }$directions. Inset shows an enlarged real-space lattice pattern. (E) to (G), (H) to (J), same as (B) to (D) at ${\overline{n}}_s=4.8\times {10}^{12}\mathrm{c}{\mathrm{m}}^{-2}$ and ${\overline{n}}_s=6.0\times {10}^{12}\mathrm{c}{\mathrm{m}}^{-2}$, respectively. At ${\overline{n}}_s=4.8\times {10}^{12}\mathrm{c}{\mathrm{m}}^{-2}$, Bloch polaritons reside in the lower band (E), emerge in the K pockets (F), and propagate along $\widehat{\mathit{K}}=\langle 10\rangle$ directions (G). At ${\overline{\mathit{n}}}_{\mathit{s}}=6.0\times {10}^{12}\mathrm{c}{\mathrm{m}}^{-2}$, Bloch polaritons reside entirely in the lower band (H), exhibit circular equi-energy contours (I) and propagate isotropically in all directions (J). Inset of (I) shows the first BZ marked with symmetry points.