7.1 Introduction

In this chapter the analysis, given in the previous two chapters for a low coverage, will be extended to a higher coverage following Haarmans and Bedeaux [49], [50], [23]. In this case the electromagnetic interaction between different small particles lying on the substrate has to be taken into account. As in the two previous chapters the electric field is described using the Laplace equation for the potential. Retardation effects are neglected. On the one hand, because the size of the particles is small compared to the wavelength. On the other hand it is used, that the interaction between particles affects the polarization substantially only, if the particles are close together compared to the wavelength. For the low coverage limit considered in the two previous chapters the interaction may be neglected. If the coverage is increased it is at first sufficient to account only for the dipole interactions between the particles, because the range of the dipole interaction is longest. For high coverages one must take multipole interactions into account up to a rather high order to obtain accurate results. In order to make an explicit analysis possible the particles will all be assumed to be identical.

In the analysis in sections 7.2-7.6 of this chapter the islands are assumed to be spherically symmetric. A complete analysis to arbitrary order in the multipole expansion is given in sections 7.2-7.4. If the coverage is not too high it is usually sufficient to use the dipole or the quadrupole approximation to...