- September 18, 2009 , Friday - 15h15 (Room P
3.10):
Some new
considerations about the diffraction of light
through an aperture in a plane screen
Matthias Kunik
(Otto-von-Guericke University of Magdeburg, Germany)
Abstract. 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.
Seminars take place in Lisbon, I.S.T. -
Post Graduation Building
Webpage: http://www.math.ist.utl.pt/funcional
