  Graphene has raised high expectations as a low-loss plasmonic material in
which the plasmon properties can be controlled via electrostatic doping. Here,
we analyze realistic configurations, which produce inhomogeneous doping, in
contrast to what has been so far assumed in the study of plasmons in
nanostructured graphene. Specifically, we investigate backgated ribbons,
co-planar ribbon pairs placed at opposite potentials, and individual ribbons
subject to a uniform electric field. Plasmons in backgated ribbons and ribbon
pairs are similar to those of uniformly doped ribbons, provided the Fermi
energy is appropriately scaled to compensate for finite-size effects such as
the divergence of the carrier density at the edges. In contrast, the plasmons
of a ribbon exposed to a uniform field exhibit distinct dispersion and spatial
profiles that considerably differ from uniformly doped ribbons. Our results
provide a road map to understand graphene plasmons under realistic
electrostatic doping conditions.
