A more comprehensive treatment of the general problem of reflection and refraction at oblique incidence on a dielectric-metallic interface has been given from the viewpoint of classical electromagnetic theory for which the media involved are homogeneous and isotropic and have arbitrary values for the dielectric constant, permeability, and conductivity. Particular stress has been placed on determining the amplitudes, absolute phases, wave forms, and the time averages of the energy flow in the incident, reflected, and refracted electromagnetic waves. The fractions of the time average of the incident radiant flux contained in the reflected and refracted electromagnetic waves are also evaluated and show that the energy flow is continuous across the boundary. The general approach of Konig has been used in which the properties of inhomogeneous waves are first discussed and then utilized in determining the forms of the incident, reflected, and refracted electromagnetic waves. For the two initial planes of polarization of the electric vector, the refracted electromagnetic wave may be elliptical in either E or H, and the metallic medium is found to have a refractive index and extinction coefficient which are functions of the material constants and the angle of incidence. Two different laws of refraction become necessary when considering the directions of the energy flow in the refracting medium for the two initial planes of polarization of the electric vector.
A. I. MAHAN, "Reflection and Refraction at Oblique Incidence on a Dielectric-Metallic Interface as a Boundary Value Problem in Electromagnetic Theory," J. Opt. Soc. Am. 46, 913-914 (1956)