INRIA Sophia Antipolis, team Factas, and LEAT, team Isa, spring-summer 2018.

Advisors: Juliette Leblond, Fabien Seyfert (Inria, Factas, juliette.leblond@inria.fr, fabien.seyfert@inria.fr) together with Iannis Aliferis, Jean-Yves Dauvignac, Claire Migliaccio (LEAT, Isa).

Electrical characteristics, namely the dielectric constant and the electrical conductivity, are crucial quantities used to model materials involved in microwave systems. These quantities, that appear in Maxwell’s equation [1, 3],

vary with the frequency and call for a characterization procedure for each frequency range of interest.

The approach that we consider here, makes use of inverse scattering techniques [2] in a cylindrical setting. More precisely, a cylinder made of the specific material is enlighted by a planar electromagnetic (EM) wave, while the scattered field is measured on a surrounding circular section.

As solutions to Helmholtz equations, the involved EM elds can be modeled by expansions on suitable basis functions (Bessel, Hankel). The coefficients of such expansions depend on the electrical charateristics that are to be

recovered. Therefore, in principle at least, the dielectric constant and the electrical conductivity can be estimated from available measurements of the incident and scattered fields. This is a typical inverse problem.

The internship will begin with the analysis of the model and a bibliographical study. Based on existing codes developed at LEAT, the goal is to set up and to implement an estimation procedure. The latter will be tested against

synthetic data as well as on actual measurements obtained at the LEAT laboratory and concerning various materials.

The internship topic requires skills in software development, computational mathematics and modelization, together with a pronounced taste for practical applications.

References

[1] C. A. Balanis. Advanced Engineering Electromagnetics. J. Wiley & Sons, 2nd edition, 2012 (1st edition, 1989).

[2] D. Colton, R. Kress. Inverse Acoustic and Electromagnetic Scattering Theory. Springer, 2013.

[3] J. D. Jackson. Classical Electrodynamics. J. Wiley & Sons, 3rd edition, 1998.