  Experiments have shown strong effects of some substrates on the localized
plasmons of metallic nano particles but they are inconclusive on the affecting
parameters. Here we have used Discrete Dipole Approximation in conjunction with
Sommerfeld integral relations to explain the effect of the substrates as a
function of the parameters of incident radiation. The radiative coupling can
both quench and enhance the resonance and its dependence on the angle and
polarization of incident radiation with respect to the surface is shown.
Non-radiative interaction with the substrate enhances the plasmon resonance of
the particles and can shift the resonances from their free-space energies
significantly. The non-radiative interaction of the substrate is sensitive to
the shape of particles and polarization of incident radiation with respect to
substrate. Our results show that plasmon resonances in coupled and single
particles can be significantly altered from their free-space resonances and are
quenched or enhanced by the choice of substrate and polarization of incident
radiation.
