Radiative lifetimes of nano-plasmonic states

The strongly localized quasi-static eigenstates (also known as surface-plasmon resonances) which are found in a small nanometric cluster of spherical inclusions can form the basis for some interesting potential applications such as SPASER and nanolens. In a SPASER, a strong coherent electric field, oscillating at a frequency ω in the visible or infra-red spectral range, can be excited in a spatial region whose linear dimensions are much smaller than the wavelength appropriate to that frequency. In a nanolens an incident electromagnetic field, oscillating at such a frequency, can be focused to a spot whose size is much less than the relevant wavelength. An important property of such resonances is their finite radiative lifetime, which is infinite in the strict quasi-static limit. One needs to solve the full Maxwell's equations in order to find the radiative decay rate, and consequently the lifetime, of such an eigenstate. We develop a method for calculating such lifetimes for clusters of closely spaced spherical inclusions. We also discuss how symmetry properties of such a cluster can be exploited to ensure that certain eigenstates have especially long radiative lifetimes.