Dielectric function

The dielectric function of a material $\epsilon (\omega )$ describes its optical properties at all energies $\hbar \omega$.

In the case of solids, the complex dielectric function is intimately connected to band structure. The primary quantities that characterize the electronic structure of any crystalline material are its critical-point energies. These are the energies, $E_{i}$, at which there are discontinuities or infinite first derivatives in the joint density of states or, in the absence of line broadening, in the probability of photon absorption and hence in the imaginary part of the optical dielectric function $\epsilon (\omega )$.