Dielectric and conductive properties of solids: classical versus extended electrodynamics

Abstract

We study the behavior of electromagnetic waves near the interface between two media: a dielectric medium and a conducting medium. Solving this problem within the framework of classical electrodynamics, we obtain results that coincide with the known ones, namely: (1) By comparison of the solution to this problem—when obtained within the framework of classical electrodynamics—with experimental data shows that using the values of electrical conductivity of metals given in physics reference books (the values of the so-called static electrical conductivity), we cannot achieve satisfactory agreement between theory and experiment. (2) We can achieve satisfactory agreement between experimental data and the predictions of classical electrodynamics only if we use values of the so-called optical conductivity that differ by two orders of magnitude from the values of the static conductivity. In addition, we propose a re-evaluation of some well-known facts, namely: (1) According to many literary sources, the permittivity of metals changes by several orders of magnitude depending on frequency and becomes negative at frequencies below the plasma frequency. It turns out that when applying Maxwell’s equations in different frequency ranges, it is necessary to use parameters that differ by two orders of magnitude. (2) At the same time, experimentalists interpret optical experiments by using formulae derived from Maxwell’s equations under the assumption that all parameters are constants. In our opinion, if we interpret experimental data using equations with constant coefficients and as a result we see that the coefficients depend significantly on frequency, we should think about using more complex equations to interpret the experimental data. (3) In this paper, we propose a new approach to interpretation of the experimental data. The novelty is that we use the equations of extended electrodynamics, which are three-dimensional analogues of Kirchhoff’s laws for electrical circuits. We show that extended electrodynamics allows us to describe experimental data using handbook values of conductivity and frequency-independent values of permittivity. Thus, we conclude that extended electrodynamics describes experimental data for metals more accurately than classical electrodynamics.