Electrodynamic Interaction Between Point Dipoles: Local Fields
In near-field electrodynamics, it is of central importance to study electromagnetic field variations on a length scale (much) shorter than the wavelengths which characterize the given problem. Macroscopic field calculations must therefore be replaced by so-called local-field analyses. Although, in general, quantum physics is required to determine local fields in both macroscopic and mesoscopic media, it is nevertheless of some interest to study such fields on the basis of the classical point-particle model. The importance of the local field cannot be overestimated since a knowledge of this field allows one to predict all electrodynamic properties of the medium under study. Local fields can of course only be calculated approximately, even within the framework of the naive classical point-particle picture. In this chapter, we shall see how local fields emerge from multiple scattering among polarizable point-particles occupying fixed positions in space, and we shall begin to understand that the eigenmode concept in electrodynamics in its widest sense is a manifestation of resonance in the local field.