  We present a theoretical model for describing light scattering from randomly
distributed Au nanoparticles on a substrate, including the clustering effect.
By using the finite-element Green function method and spherical harmonic basis
functions, we are able to calculate the polarization-dependent reflectivity
spectra of the system (modeled by randomly distributed nanoparticles coupled
with clusters) efficiently and accurately. The calculated ellipsometric spectra
of the system with clusters can adequately describe the experimental data for
the whole frequency range. We find that the clustering effect leads to some
prominent features in the low frequency range of the ellipsometric spectra,
which are attributed to plasmonic resonances associated with the coupling of Au
nanoparticles and clusters.
