Selective Acoustic Focusing Using Time-Harmonic Reversal Mirrors

Christophe Hazard (1) , Karim Ramdani (2, 3)

1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
2 CORIDA - Robust control of infinite dimensional systems and applications
3 IECN - Institut Élie Cartan de Nancy

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.

Keywords: acoustic scattering; time-reversal; far field operator; small obstacles

Domains: Analysis of PDEs [math.AP]

Christophe Hazard, Karim Ramdani. Selective Acoustic Focusing Using Time-Harmonic Reversal Mirrors. SIAM Journal on Applied Mathematics, 2004, 64 (3), pp.1057-1076. ⟨10.1137/S0036139903428732⟩. ⟨hal-00794524⟩