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Pré-Publication, Document De Travail Année : 2016

Perfect transmission invisibility for waveguides with sound hard walls

Résumé

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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Dates et versions

hal-01371163 , version 1 (24-09-2016)
hal-01371163 , version 2 (18-09-2017)

Identifiants

  • HAL Id : hal-01371163 , version 1

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Anne-Sophie Bonnet-Ben Dhia, Lucas Chesnel, Sergei Nazarov. Perfect transmission invisibility for waveguides with sound hard walls. 2016. ⟨hal-01371163v1⟩
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