TABLE OF CONTENTS In section 5.6 of the previous chapter the relatively simple spherical model for an island film was treated. It will be clear that this model only provides a reasonable description of the optical properties of such film, if the islands do not deviate too much in shape from spheres.
A more general model system, describing island films, in which the particles are flattened, but still (more or less) symmetric for rotation around an axis normal to the substrate, consists of oblate spheroids, touching this substrate. (The axis of rotation of an oblate spheroid is the short axis.) The attractiveness of this model is again, that the polarizabilities, given by eq. (5.50), can be calculated to any order of accuracy. The reason for this is the fact, that a complete set of eigenfunctions of the Laplace equation (5.1) can be found for this form of particles. This is also the case for prolate spheroids, of which the axis of rotation is the long axis. The model will therefore be extended, in this section, to include oblate and, in the next section, to include prolate spheroidal particles. The axis of rotation of the spheroids is normal to the surface of the (flat) substrate.
Consider a homogeneous oblate spheroid with a dielectric constant ?, embedded in a homogeneous medium with dielectric constant ? a, far from the substrate. Both ? and ? a may be frequency dependent. The origin of the Cartesian...
