Table of Contents
ISRN Mathematical Physics
Volume 2012, Article ID 983809, 25 pages
http://dx.doi.org/10.5402/2012/983809
Research Article

On Energy Conditions for Electromagnetic Diffraction by Apertures

1Beuth Hochschule für Technik Berlin, Fachbereich II-Mathematik-Physik-Chemie, Luxemburger Straβe 10, 13353 Berlin, Germany
2Institut für Analysis und Numerik, Otto-von-Guericke-Universität, Universitätsplatz 2, 39106 Magdeburg, Germany

Received 24 September 2011; Accepted 2 November 2011

Academic Editors: G. Ghirardi and V. Putkaradze

Copyright © 2012 Norbert Gorenflo and Matthias Kunik. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The diffraction of light is considered for a plane screen with an open bounded aperture. The corresponding solution behind the screen is given explicitly in terms of the Fourier transforms of the tangential components of the electric boundary field in the aperture. All components of the electric as well as the magnetic field vector are considered. We introduce solutions with global finite energy behind the screen and describe them in terms of two boundary potential functions. This new approach leads to a decoupling of the vectorial boundary equations in the aperture in the case of global finite energy. For the physically admissible solutions, that is, the solutions with local finite energy, we derive a characterisation in terms of the electric boundary fields.