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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.
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).
Consider the time harmonic case with frequency . Then wave propagation in chiral media is governed by the following equations with electric permittivity , magnetic permeability and chirality :
The difference to the achiral case is in the parameter , which adds links between the electric induction and the curl of the electric field and between the magnetic induction and the curl of the magnetic field .