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Journal Articles Inverse Problems Year : 2015

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

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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Dates and versions

hal-01109534 , version 1 (26-01-2015)

Identifiers

  • HAL Id : hal-01109534 , version 1

Cite

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, 2015. ⟨hal-01109534⟩
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