II - Electromagnetic potentials and polarization

Summary

IN the preceding chapter the effect of matter on an electromagnetic field was expressed in terms of a number of macroscopic constants. These have only a limited range of validity and are in fact inadequate to describe certain processes, such as the emission, absorption and dispersion of light. A full account of these phenomena would involve an extensive study of the atomistic theory and lies therefore outside the scope of this book.

It is possible, however, to describe the interaction of field and matter by means of a simple model which is entirely adequate for most branches of optics. For this purpose each of the vectors D and B is expressed as the sum of two terms. Of these one is taken to be the vacuum field and the other is regarded as arising from the influence of matter. Thus one is led to the introduction of two new vectors for describing the effects of matter: the electric polarization (P) and the magnetic polarization or magnetization (M). Instead of the material equations (10) and (11) in §1.1 connecting D and B with E and H, we now have equations connecting P and M with E and H. These new equations have a more direct physical meaning and lead to the following conception of the propagation of an electromagnetic field in matter:

An electromagnetic field produces at a given volume element certain amounts of polarization P and M which, in the first approximation, are proportional to the field, the constant of proportionality being a measure of the reaction of the field.