Electromagnetic propagation across a metal: the causal propagator

Abstract

The very general expression of the Schwinger–Feynman causal propagator is explicitly derived for the transmission of a photon through a metal from air, as a generalization of our earlier work dealing with dielectrics. In a very general context, the corresponding transition amplitudes for crossing through the metal of a polarized or unpolarized photon are obtained. Inspired by Feynman’s intuitive and well-publicized non-technical treatment, we consider, from a quantum viewpoint, the fate of a red and a blue photon in determining their transmission probabilities, as an application, through a thin layer of silver whose complex dielectric function, in particular, has been experimentally carefully determined in recent years. Particular emphasis is also put in assessing the accuracy of the phenomenological expression of exponential damping used in considering transmissions through metals in comparison to the exact expressions obtained in the bulk of the paper.

Keywords:

• Propagator theory
• photons moving across a metal
• computations in electrodynamics and boundary conditions
• quantum probability