Quantization of the electromagnetic field in uniaxial crystalline dielectric media: long-wave limit

Abstract

The derivation of the relative electric permittivity tensor from a fully classical model is known, and a calculation of this quantity from a semiclassical model in the first order of perturbation theory is familiar as well. In applications to commonly occurring uniaxial crystalline media without optical activity, the whole discrete lattice is represented by a single atomic oscillator. We calculate the relative electric permittivity tensor provided that the discrete lattice can be represented by a continuum of quantum harmonic oscillators.