Reflection and refraction of an electromagnetic wave by a superconductor

Abstract

A rigorous treatment of the reflection and transmission of an electromagnetic wave by a superconductor in its ground state is reported. Starting from Maxwell’s equations, a calculation on the reflection and refraction at the interface between a metallic and superconducting plate is made. For the metal, a complex conductivity \(\sigma ^{\textrm{Re}} + i\sigma ^{\textrm{Im}}\) derived from the Drude-Zener treatment of the conduction electrons, while for the superconductor the London equation is incorporated into the equations. Thereafter, we consider the case when the first medium is either helium atmosphere or vacuum by setting the dielectric constant and magnetic permeability to unity, and by taking the limit \(\sigma ^{\textrm{Re}} \rightarrow 0\) and \(\sigma ^{\textrm{Im}} \rightarrow 0\). The reflection and transmission coefficients thus obtained are, 1.00 and 2.00, respectively over a wide frequency range from 10 GHz to 1 THz for the case when the magnetic field of the wave \({\varvec{H}}\) is perpendicular to the plane of incidence. The coefficients when \({\varvec{H}}\) lies in the plane of incidence are also calculated. These findings are discussed in relation to total reflection.