Electromagnetic wave interactions with a conducting medium: A graphic illustration of dispersive properties

Electromagnetic wave behavior in a conducting medium is a thought-provoking subject for a graduate-level electrodynamics course. Here, we focus on electromagnetic waves incident upon a conductor and highlight how the same dispersion relation, spanning 20 orders of magnitude in frequency, transforms the conductor from a perfectly reflecting to a perfectly transparent medium according to the classical free-electron model. We show that the spectral responses of the conductor can be divided into three radically different regimes. This article presents a graphic illustration of wave reflection, transmission, and penetration properties for copper in these regimes, along with physical interpretations and a brief discussion on the limitations of the free-electron model.