Photonic crystal for graphene plasmons

Abstract

Photonic crystals are commonly implemented in media with periodically varying optical properties. Photonic crystals enable exquisite control of light propagation in integrated optical circuits, and also emulate advanced physical concepts. However, common photonic crystals are unfit for in-operando on/off controls. We overcome this limitation and demonstrate a broadly tunable two-dimensional photonic crystal for surface plasmon polaritons. Our platform consists of a continuous graphene monolayer integrated in a back-gated platform with nano-structured gate insulators. Infrared nano-imaging reveals the formation of a photonic bandgap and strong modulation of the local plasmonic density of states that can be turned on/off or gradually tuned by the applied gate voltage. We also implement an artificial domain wall which supports highly confined one-dimensional plasmonic modes. Our electrostatically-tunable photonic crystals are derived from standard metal oxide semiconductor field effect transistor technology and pave a way for practical on-chip light manipulation.

Fig. 1

Graphene photonic crystal. a Schematic of a photonic crystal comprised of a graphene monolayer fully-encapsulated by hexagonal boron nitride on top of an array of SiO₂ pillars. Inset, simulated carrier density map n_s(r) at average carrier density ${\overline{n}}_{\mathrm{s}}=4.5\times 10^{12}{\mathrm{cm}}^{-2}$, showing two hexagonal-patterned domains separated by an artificial lattice dislocation (domain wall). The lattice periodicity a = 80 nm. The photonic crystal unit cell is marked by a white dashed hexagon. b Calculated plasmonic band structure as a function of wave-vector k and average carrier density ${\overline{n}}_{\mathrm{s}}$. A vertical cut parallel to the $\omega -\mathbf{k}$ plane (back panel) generates the plasmonic band structure at fixed carrier density ${\overline{n}}_{\mathrm{s}}=5.5\times 10^{12}{\mathrm{cm}}^{-2}$. The dashed lines mark the range of a complete plasmonic bandgap. A horizontal cut parallel to ${\overline{n}}_{\mathrm{s}}-\mathbf{k}$ plane (bottom panel) generates the plasmonic dispersion as a function of average carrier density ${\overline{n}}_{\mathrm{s}}$ and wave-vector k, at laser frequency ω = 904 cm⁻¹; a complete bandgap is evident for carrier density around ${\overline{n}}_{\mathrm{s}}=5.5\times 10^{12}{\mathrm{cm}}^{-2}$

Fig. 2

Gate-tunable plasmonic response of a graphene-based photonic crystal. a Schematic of the photonic crystal structure with an engineered domain wall in the middle, highlighted in orange. Color contrast represents carrier density modulation n_1,2 in graphene. A gold antenna in the left serves as a plasmon launcher. The scanned area in panel c is marked with a dashed box. K/M directions in BZ are marked with arrows. b Simulated LDOS maps for upper and lower plasmonic bands. c Experimental near-field images s(r,ω) acquired at different gate voltages at T = 60 K and laser frequency ω = 904 cm⁻¹. At V_g = −40 V, only faint plasmonic fringes are observed. At V_g = −60 V, a hexagonal pattern of dark spots emerges. At V_g = −70 V, a 1D domain wall state appears in the middle of the image. At V_g = −90 V, propagating plasmons are launched by the gold antenna on the left. This latter image also reveals a hexagonal pattern of bright spots. Black solid line marks the location of the line profiles in panel d. Scale bar: 400 nm. d Line profiles s(r,ω) taken in the photonic crystal region away from the domain wall. Dotted lines display the corresponding line profiles in un-patterned region. The systematic increase of SPP wavelength λ_p with carrier density n_s matches the expected scaling: ${\lambda }_{\mathrm{p}}\propto \frac{v_{\mathrm{F}}\sqrt{n_{\mathrm{s}}}}{ϵ{\omega }^2}$

Fig. 3

Gate dependence of the 1D plasmonic domain wall state. a Stacked near-field images (analogous to Fig. 2c) and detailed voltage-dependent contrast across the artificial domain wall (vertical panel) collected at ω = 904 cm⁻¹. Scale bar: 400 nm. b The same data as panel a vertical panel, displayed in 2D false color map of near-field signal s as a function of gate voltages V_g and position x across the domain wall. c Simulated voltage-dependent measurement based on point dipole model. ${\overline{n}}_{\mathrm{s}}$ is the averaged carrier density. The position of the domain wall is marked by an arrow. The lattice periodicity a = 80 nm. d 1D plasmonic dispersion simulation for the structure shown in Fig. 2a. Gray region corresponds to 2D plasmonic modes. The blue solid line highlights the 1D domain wall state