Selective Acoustic Focusing Using Time-Harmonic Reversal Mirrors

Christophe Hazard 1 Karim Ramdani 2, 3
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 CORIDA - Robust control of infinite dimensional systems and applications
IECN - Institut Élie Cartan de Nancy, LMAM - Laboratoire de Mathématiques et Applications de Metz, Inria Nancy - Grand Est
Abstract : A mathematical study of the focusing properties of acoustic fields obtained by a time-reversal process is presented. The case of time-harmonic waves propagating in a nondissipative medium containing sound-soft obstacles is considered. In this context, the so-called D.O.R.T. method (decomposition of the time-reversal operator in French) was recently proposed to achieve selective focusing by computing the eigenelements of the time-reversal operator. The present paper describes a justification of this technique in the framework of the far field model, i.e., for an ideal time-reversal mirror able to reverse the far field of a scattered wave. Both cases of closed and open mirrors, that is, surrounding completely or partially the scatterers, are dealt with. Selective focusing properties are established by an asymptotic analysis for small and distant obstacles.
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Christophe Hazard, Karim Ramdani. Selective Acoustic Focusing Using Time-Harmonic Reversal Mirrors. SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2004, 64 (3), pp.1057-1076. ⟨10.1137/S0036139903428732⟩. ⟨hal-00794524⟩

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