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

$blub$

Incident field:
Herglotz function

$blub$

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 $H$ .

Dr. Sven Heumann

Research

Chirality

Maxwell's equations

Poster