Functional Analysis and Applications Seminar 

18/09/2009, 15:15 — 16:15 — Room P3.10, Mathematics Building
Matthias Kunik, Otto-von-Guericke University of Magdeburg, Germany

Some new considerations about the diffraction of light through an aperture in a plane screen

In the first part of my talk I present a new method in order to obtain mapping properties of the boundary operators for slit diffraction occurring in Sommerfeld’s diffraction theory, covering two different cases of the polarisation of the light. This theory is entirely developed in the context of the boundary operators with a Hankel kernel and not based on the corresponding mixed boundary value problem for the Helmholtz equation. For a logarithmic approximation of the Hankel kernel we obtain explicit solutions together with certain regularity results. In the second part of my talk I use the Fourier method in order to present the boundary equations for the more general diffraction of light through an aperture in a plane screen. In this way we also obtain the solution of the diffraction problem behind the screen in terms of the Fourier transforms of the electrical boundary fields. However, these electrical boundary fields have to be determined from the singular boundary equations mentioned above. This is a common work with Dr. Norbert Gorenflo of the Beuth Hochschule für Technik Berlin, Germany.