Electromagnetic Waves in Absorbing Media

Abstract

Specific Intensities of Radiation in Two Media in Thermal Equilibrium.---If the media are transparent, the specific intensity of radiation $K$ is proportional to the square of the index of refraction, as was shown by Kirchhoff. In dealing with absorbing media Planck assumes that $K$ is proportional to the square of the real part of the complex index. Laue has questioned the validity of this assumption and has published an investigation of the problem purporting to show that $K$ is proportional to the square of the modulus of the index of refraction. Laue, however, has treated incident and reflected waves in an absorbing medium as separate entities in computing energy fluxes, a method which is not legitimate when a change in phase occurs at reflection. The mathematical investigation of the problem given in this paper confirms Planck's assumed proportionality in the case of moderately absorbing media. In intensely absorbing media it is doubtful if it is legitimate to substitute trains of plane waves of equal intensity moving in all directions for the irregular fluxes due to emission and absorption in the medium.Energy Flux for Homogeneous Plane Waves Incident on the Plane Surface of an Absorbing Medium.---Equations are derived for the energy reflected and the energy transmitted. On account of the difference in phase between incident and reflected waves the rate of absorption near the surface varies with the phase; in fact, it is negative for part of each period.