  The plasmon modes of pristine and impurity doped graphene are calculated,
using a real-space theory which determines the non-local dielectric response
within the random phase approximation. A full diagonalization of the
polarization operator is performed, allowing the extraction of all its poles.
It is demonstrated how impurities induce the formation of localized modes which
are absent in pristine graphene. The dependence of the spatial modulations over
few lattice sites and frequencies of the localized plasmons on the electronic
filling and impurity strength is discussed. Furthermore, it is shown that the
chemical potential and impurity strength can be tuned to control target
features of the localized modes. These predictions can be tested by scanning
tunneling microscopy experiments.
