Imaging the full optical response of graphene surface plasmon polaritons

The full realization of electronic devices based on graphene requires the complete characterization of defects and their effect on local electronic properties. Using infrared scattering-type scanning near-field optical microscopy (IR \emph{s}-SNOM) surface plasmon polariton propagation in graphene can be imaged with nanometer spatial resolution, providing information on the local electronic properties. Here we use \emph{s}-SNOM imaging to provide full infrared optical characterization of graphene SPPs by studying both the amplitude and phase of the near-field scattered light. We develop a simple phenomenological model based on SPP reflection from boundaries and defects that provides semi-quantitative agreement for both amplitude and phase simultaneously. These results provide insight into nanometer scale variations in the electronic structure of graphene and thus inform future device development.