Surface plasmons are collective oscillations of electrons in metals or semiconductors that enable confinement and control of electromagnetic energy at subwavelength scales1, 2, 3, 4, 5. Rapid progress in plasmonics has largely relied on advances in device nano-fabrication5, 6, 7, whereas less attention has been paid to the tunable properties of plasmonic media. One such medium—graphene—is amenable to convenient tuning of its electronic and optical properties by varying the applied voltage8, 9, 10, 11. Here, using infrared nano-imaging, we show that common graphene/SiO2/Si back-gated structures support propagating surface plasmons. The wavelength of graphene plasmons is of the order of 200 nanometres at technologically relevant infrared frequencies, and they can propagate several times this distance. We have succeeded in altering both the amplitude and the wavelength of these plasmons by varying the gate voltage. Using plasmon interferometry, we investigated losses in graphene by exploring real-space profiles of plasmon standing waves formed between the tip of our nano-probe and the edges of the samples. Plasmon dissipation quantified through this analysis is linked to the exotic electrodynamics of graphene10. Standard plasmonic figures of merit of our tunable graphene devices surpass those of common metal-based structures.
Figures at a glance
Figure 1: Infrared nano-imaging experiment and results. 
a, Diagram of an infrared nano-imaging experiment at the surface of graphene (G) on SiO2. Green and blue arrows display the directions of incident and back-scattered light, respectively. Concentric red circles illustrate plasmon waves launched by the illuminated tip. b–e, Images of infrared amplitude s (ω = 892 cm−1) defined in the text taken at zero gate voltage. These images show a characteristic interference pattern close to graphene edges (blue dashed lines) and defects (green dashed lines and green dot), and at the boundary between single (G) and bilayer (BG) graphene (white dashed line). Additional features marked with arrows in e are analysed in refs 27 and 30. Locations of boundaries and defects were determined from AFM topography taken simultaneously with the near-field data. Scale bars, 100 nm. All data were acquired at ambient conditions.
Figure 2: Spatial variation of the electric field and near-field amplitude at the graphene edge. 
For all panels, graphene is present at L > 0, and SiO2 not covered by graphene is displayed at L < 0. a, Upper panels, illustration of interference between tip-launched plasmon waves (white) and their reflection (green) from the edge at L = 0. Solid and dashed lines correspond to positive and negative field maxima of the propagating plasmon, respectively. False colour plots of the absolute value of electric field |Ez| reveal standing waves formed between the tip and the edge. Left and right panels show snapshots of destructive (minimum signal) and constructive (maximum signal) interference underneath the tip, respectively. Scale bar, 0.5λp. Lower panels, profiles of |Ez| underneath the tip versus its distance to the edge. The blue circles and arrows mark the positions of the tip. b, Experimental (grey) and calculated (colour) s(ω) line profiles at zero gate voltage. Inset, G-peak positions inferred from micro-Raman data (squares) and the carrier density profile (red line) we used to model the plasmonic standing wave (in b). The Raman G-peak positions are associated with the variation of the local carrier density in graphene (n: right-hand scale)17, 18, 29.
Figure 3: Electrostatically tunable plasmons in back-gated graphene. 
ftp://mail.ihim.uran.ru/localfiles/nature11253.pdf
