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Research Group on Inverse Problems

Secretariat
Allianz-Gebäude (05.20)
Room 4C-20.2

Address
Kaiserstr. 93
Institut für Algebra und Geometrie
76128 Karlsruhe

Office hours:
Mo. - Fr., 11:00 - 12:00 Uhr und 13.00 - 15.00 Uhr

Tel.: +49 721 608 42051

Fax.: +49 721 608 46968

Photo of Sven Heumann Dr. Sven Heumann

Office hour for students: Mittwoch, 15:00 - 16:30 Uhr und nach Vereinbarung
Room: 4C-02 Allianz-Gebäude (05.20)
Tel.: 0721 608-46469
Email: sven.heumann@kit.edu

Kaiserstraße 89-93
76133 Karlsruhe

Welcome to my homepage!







Research

I'm interested in inverse scattering problems for electromagnetic waves in chiral media. This includes the solvability study of the direct problem: An incoming wave hits a chiral scatterer. As result a scattered field is produced. The inverse problem I'm dealing with consists in reconstructing the scatterer from the far field data. In order to solve this inverse problem I want to adapt the factorization method.

blub

Kite shaped
scattering object

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Incident field:
Herglotz function

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Reconstruction

Chirality

In geometry, a figure is chiral if it cannot be mapped to its mirror image by rotations and translations alone. In chemistry, chirality usually refers to molecules. Two mirror images of a chiral molecule are called enantiomers.

The two enantiomers of a generic amino acid

Chiral material is optically active: It rotates plane polarized light and left- and right-circularly polarized waves propagate with different phase velocities. Wave propagation in chiral media is governed by Maxwell's equations and the Drude-Born-Fedorov equations (constitutive relations).

Maxwell's equations

Consider the time harmonic case with frequency \omega. Then wave propagation in chiral media is governed by the following equations with electric permittivity \varepsilon, magnetic permeability \mu and chirality \beta:

$\begin{array}{rcl}\text{curl }H&=&-i\omega D\\\text{curl }E&=&i\omega B\\D&=&\varepsilon(E+\beta\,\text{curl }E)\\B&=&\mu(H+\beta\,\text{curl }H)\end{array}$

The difference to the achiral case is in the parameter \beta, which adds links between the electric induction D and the curl of the electric field E and between the magnetic induction B and the curl of the magnetic field H.

Poster