  We develop a theory to model the interaction of graphene substrate with
localized plasmon resonances in metallic nanoparticles. The influence of a
graphene substrate on the surface plasmon resonances is described using an
effective background permittivity that is derived from a pseudoparticle concept
using the electrostatic method. For this purpose, the interaction of metal
nanoparticle with graphene sheet is studied to obtain the optical spectrum of
gold nanoparticles deposited on a graphene substrate. Then, we introduce a
factor based on dipole approximation to predict the influence of the separation
of nanoparticles and graphene on the spectral position of the localized plasmon
resonance of the nanoparticles. We applied the theory for a 4 nm radius gold
nanosphere placed near 1.5 nm graphene layer. It is shown that a blue shift is
emerged in the position of plasmon resonance when the nanoparticle moves away
from graphene.
