5.1 Introduction

Very thin films are in many cases discontinuous, see for instance [29], [30], [4] and references therein. The film material is then distributed in the form of islands on the surface of the substrate. The size of the islands is small compared to the wavelength. As a consequence retardation effects are unimportant for the fields inside and around the islands. The electric field is then described using the Laplace equation for the potential

In this chapter only non-magnetic systems will be considered. If one considers a single island surrounded by the ambient the electro-magnetic response may be characterized by dipole, quadrupole and higher order multipole polarizabilities [26]. If this particle is brought close to the substrate the (multipole) polarizabilities are modified, due to an induced charge distribution on the surface of the substrate, and become dependent on the distance to the substrate. The presence of other islands along the substrate in the neighborhood of the original island also changes the polarizabilities of the island. Both the interaction with the images and the interaction with the other islands result in polarizabilities parallel and orthogonal to the surface which are unequal, even if the islands are spherical. As a consequence the film is anisotropic in its reaction to fields parallel versus fields normal to the surface. If the islands are not symmetric, this may also contribute to the anisotropy, in particular, if the orientation of the island and the direction of the normal are correlated due to, for instance, the...