  Shifting of the surface plasmon resonance wavelength induced by the variation
of the thickness of insulating spacer between single layer graphene and Au
nanoparticles is studied. The system demonstrates a blue shift of 29 nm as the
thickness of the spacer layer increases from 0 to 15 nm. This is due to the
electromagnetic coupling between the localized surface plasmons excited in the
nanoparticles and the graphene film. The strength of the coupling decays
exponentially with a decay length of d/R=0.36, where d is the spacer layer
thickness and R is the diameter of the Au nanoparticles. The result agrees
qualitatively well with the plasmon ruler equation. Interestingly, a further
increment of the spacer layer thickness induces a red shift of 17 nm in the
resonance wavelength and the shift saturates when the thickness of the spacer
layer increases above 20 nm.
