Influence of nanoparticle–graphene separation on the localized surface plasmon resonances of metal nanoparticles

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