Diffraction of electromagnetic waves caused by apertures in absorbing plane screens

The perturbation field caused by holes in a plane, infinitely thin screen of arbitrary material on which electromagnetic radiation is incident, can be split up in two fields, one of which is symmetrical in the tangential components of the electric, the other in those of the magnetic vector. Both fields satisfy equations within the holes which are generalizations of Bethe´s conditions for the perfectly conducting screen and which can be used to derive approximate solutions of Kirchhoff type. The solution for a screen which absorbs practically all of the incident radiation is essentially different from Kirchhoff´s result for scalar radiation incident on a so-called perfectly absorbing screen.