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Perfect transmission invisibility for waveguides with sound hard walls

Anne-Sophie Bonnet-Ben Dhia 1 Lucas Chesnel 2, 3, * Sergei Nazarov 4, 5
* Corresponding author
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
2 DeFI - Shape reconstruction and identification
Inria Saclay - Ile de France, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
Abstract : We are interested in a time harmonic acoustic problem in a waveguide with locally perturbed sound hard walls. We consider a setting where an observer generates incident plane waves at −∞ and probes the resulting scattered field at −∞ and +∞. Practically, this is equivalent to measure the reflection and transmission coefficients respectively denoted R and T. In [9], a technique has been proposed to construct waveguides with smooth walls such that R = 0 and |T | = 1 (non reflection). However the approach fails to ensure T = 1 (perfect transmission without phase shift). In this work, first we establish a result explaining this observation. More precisely, we prove that for wavenumbers smaller than a given bound k depending on the geometry, we cannot have T = 1 so that the observer can detect the presence of the defect if he/she is able to measure the phase at +∞. In particular, if the perturbation is smooth and small (in amplitude and in width), k is very close to the threshold wavenumber. Then, in a second step, we change the point of view and, for a given wavenumber, working with singular perturbations of the domain, we show how to obtain T = 1. In this case, the scattered field is exponentially decaying both at −∞ and +∞. We implement numerically the method to provide examples of such undetectable defects.
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Submitted on : Monday, September 18, 2017 - 4:52:26 PM
Last modification on : Thursday, May 27, 2021 - 2:14:06 PM


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  • HAL Id : hal-01371163, version 2


Anne-Sophie Bonnet-Ben Dhia, Lucas Chesnel, Sergei Nazarov. Perfect transmission invisibility for waveguides with sound hard walls. Journal de Mathématiques Pures et Appliquées, Elsevier, 2018. ⟨hal-01371163v2⟩



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