Nano-imaging of graphene plasmons

Graphene plasmonics provides strong and wavelength-tunable spatial confinement of electromagnetic fields at mid-infrared frequencies. Near-field imaging of standing wave surface plasmon polariton (SPP) spatial distributions has been recently achieved by scattering-type scanning near-field optical microscopy ($s$-SNOM). The spatial patterns are a result of the interference of plasmons launched by the sharp scanning probe tip with counter-propagating plasmons reflected from graphene edges. We present a full phase and amplitude resolved near-field characterization of SPP propagation and reflection off edges, defects, and grain boundaries.~Using mid-infrared excitation at $\lambda_{\mathrm{exc}} =$ 10.8$\mu $m, we measure deep sub-wavelength periodicity in the spatial distribution of the near-field~with plasmon wavelength on the order of~$\lambda_{\mathrm{p}} =$ 250 nm. The standing amplitude and phase patterns can be fully described based on a simple near-field SPP cavity model.