Non-scattering wavenumbers and far field invisibility for a finite set of incident/scattering directions

Anne-Sophie Bonnet-Ben Dhia 1 Lucas Chesnel 2, 3 Sergei Nazarov 4, 5
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
3 DeFI - Shape reconstruction and identification
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, Polytechnique - X, CNRS - Centre National de la Recherche Scientifique : UMR7641
Abstract : We investigate a time harmonic acoustic scattering problem by a penetrable inclusion with compact support embedded in the free space. We consider cases where an observer can produce inci-dent plane waves and measure the far field pattern of the resulting scattered field only in a finite set of directions. In this context, we say that a wavenumber is a non-scattering wavenumber if the associated relative scattering matrix has a non trivial kernel. Under certain assumptions on the physical coeffi-cients of the inclusion, we show that the non-scattering wavenumbers form a (possibly empty) discrete set. Then, in a second step, for a given real wavenumber and a given domain D, we present a construc-tive technique to prove that there exist inclusions supported in D for which the corresponding relative scattering matrix is null. These inclusions have the important property to be impossible to detect from far field measurements. The approach leads to a numerical algorithm which is described at the end of the paper and which allows to provide examples of (approximated) invisible inclusions.
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Inverse Problems, IOP Publishing, 2015
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Anne-Sophie Bonnet-Ben Dhia, Lucas Chesnel, Sergei Nazarov. Non-scattering wavenumbers and far field invisibility for a finite set of incident/scattering directions. Inverse Problems, IOP Publishing, 2015. 〈hal-01109534〉

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