Photon-Electron Interaction, Crystals Without Fields

In the Maxwell equations, the property of matter is represented by a dielectric constant and a permeability. We are interested in materials for which only the dielectric constant, e,needs to be considered. The dielectric constant is a frequency dependent tensor quantity for crystalline solids. It reduces to a scalar quantity for crystals of cubic symmetry and for polycrystalline materials which may be regarded as isotropic. The dielectric constant depends also on the wave vector, \(\bar{K} \),in addition to the frequency and the polarization of the radiation field:\( \tilde{\varepsilon }\)(\( \bar{K}\) w). However, for optical radiation K is negligibly small on the scale of the Brillouin zone of the crystal, and the relevant quantity is \( \tilde{\varepsilon }\) (0, ω).