Quantification du champ électromagnétique au voisinage d'un miroir plan métallique

Abstract

We quantify the electromagnetic field in a half-space bounded by a perfect mirror. By analogy with the quantization near a dielectric, by Carniglia and Mandel, we use doublet modes obtained by superposition of incident and reflected waves satisfying Fresnel's conditions. These functions form a complete basis in the space of the field states. By expanding the electromagnetic field in terms of these doublet modes, the energy and the impulsion parallel to the mirror reduce to the sum of the contributions of independent harmonic oscillators. It is therefore possible to quantify as in a free field. We use successively Maxwell–Minkowski's tensor and de Broglie's. With the latter, the calculus is more straightforward and easier than with the former. The interest in quantum formalism of doublet modes is that interactions with the electromagnetic field near a mirror can be studied as in a free field.