The polarizability of a spheroidal particle on a substrate

A general method is developed to calculate the polarizability of a spheroidal particle on a substrate. The axis of revolution of the particle is assumed to be normal to the substrate and its linear dimensions are supposed to be much smaller than the wavelength of the incident light. As in earlier work a multipole method is employed with multipoles located at the centre of the particle and “image multipoles” at the image of this centre with respect to the surface of the substrate. To adapt the method to the specific geometry of the particle spheroidal multipoles are used. The special cases of a disk and a needle are considered. The spheroidal dipole approximation is compared with the conventional spherical dipole approximation. The method is applied to a transmission experiment with a square lattice of gold particles on sapphire.