  This work analyses how impurities and vacancies on the surface of a graphene
sample affect its optical conductivity and plasmon excitations. The disorder is
analysed in the self-consistent Green's function formulation and nonlocal
effects are fully taken into account. It is shown that impurities modify the
linear spectrum and give rise to an impurity band whose position and width
depend on the two parameters of our model, the density and the strength of
impurities. The presence of the impurity band strongly influences the
electromagnetic response and the plasmon losses. Furthermore, we discuss how
the impurity-band position can be obtained experimentally from the plasmon
dispersion relation and discuss this in the context of sensing.
