Zur Reflexion und Transmission elektromagnetischer Wellen bei senkrechtem Einfall auf ebene Grenzflächen zwischen unterschiedlich absorbierenden Medien

On Reflection and Transmission of Electromagnetic Waves Propagating Perpendicular to Plane Surfaces between Different Absorbing Media Born and Ladenburg already in 1911 pointed out that to describe reflection and transmission of electromagnetic waves through a plane surface between two different absorbing media in addition to the usual Poynting vectors of the running waves the so called “mixed” Poynting vector is necessary to maintain the balance of energy on the boundary plane. The flow of energy connected with this vector always points toward the region of maximal wastage of this energy and is closely related to the spatial modulation of the energy consumption within the partially standing interference pattern between the incoming and the reflected wave. In almost all substances the energy absorption is caused by the electric field whereas practically a direct contribution from the magnetic field can be neglected. But taking account of these magnetic effects we may get a better understanding of the mixed Poynting vector. To that end we add to the second of the Maxwell equations a quantity analogous to the electric current term in the first Maxwell equation. The amplitude of the “mixed” Poynting vector then turns out to depend essentially on the ratio of the energy absorption by the electric and the magnetic field. To confirm this fact we consider a medium, which shows in addition to the usual electric losses also magnetic ones of comparable magnitudes. In such materials the resultant energy consumption is distributed more similar to the spatial distribution of the fieldenergy. As a result the amplitude of the mixed Poynting vector disappears if the percentage of energy absorption by the electric and the magnetic field and their energy densities themselves are made equal to each other.