Radiative and nonradiative decay rates of molecules adsorbed on clusters of small dielectric particles

In this work we shall develop a formalism which extends previous calculations of lifetimes of excited molecular states near planar dielectric surfaces and near single small dielectric particles to situations where the molecule is adsorbed on a cluster made of several dielectric spherical grains. The nonradiative relaxation rate is seen to be relatively weakly dependent on the cluster structure and, if the molecule is adsorbed on one of the grains, is well approximated by the single grain result. The radiative decay rate and hence the quantum yield are much more sensitive to the geometry of the cluster which determines the position (in frequency) of the dielectric resonances of the cluster. The formalism developed here may be used to evaluate local field intensities at different positions within a cluster of dielectric grains under the influence of an external incident field.