Selective focusing on small scatterers in acoustic waveguides using time reversal mirrors

International audienceWe investigate the acoustic selective focusing properties of time reversal in a two-dimensional acoustic waveguide. A far-field model of the problem is proposed in the time-harmonic case. In order to tackle the question of selective focusing, we derive an asymptotic model for small scatterers. We show that in the framework of this limit problem, approximate eigenvectors of the time reversal operator can be obtained when the number of propagating modes of the waveguide is large enough. This result provides, in particular, a mathematical justification of the selective focusing properties observed experimentally. Some numerical experiments on selective focusing are presented

Two numerical methods for recovering small inclusions from the scattering amplitude at a fixed frequency

International audienceIn this paper two noniterative algorithms for locating small electromagnetic inclusions from the scattering amplitude at a fixed frequency are developed. In particular, a variety of numerical results is presented to highlight their potential and their limitations