The Dielectric Function

Abstract

The dielectric function and the functions directly related to it are fundamental in solid-state spectroscopy. Their derivation is based on a very general description of the reaction of a system to an external force. As long as the reaction is linear, the response is obtained according to a linear response model and the relations describing the reactions are called the linear response functions. Thus, the linear response functions are properties of the solid-state system itself and are independent of the driving force. This concept is applicable to the whole spectral range from radio waves to γ rays as well as to spectroscopy with particles. The linear response is formulated in time and space. Since the response is, in general, frequency- and wave vector-dependent and since it is convenient to operate with harmonic functions, a discussion in Fourier space, both with respect to time and coordinates, is more appropriate. Thus, rather than studying the response function directly the linear relation between the Fourier transform of the driving force and the Fourier transform of the system response are considered. One of the most fundamental response functions is the electric susceptibility which describes the polarization P(q, w) generated by an incident electric field E(q, w).