We present an approach for subwavelength focusing of microwaves using both a time-reversal mirror placed in the far field and a random distribution of scatterers placed in the near field of the focusing point. The far-field time-reversal mirror is used to build the time-reversed wave field, which interacts with the random medium to regenerate not only the propagating waves but also the evanescent waves required to refocus below the diffraction limit. Focal spots as small as one-thirtieth of a wavelength are described. We present one example of an application to telecommunications, which shows enhancement of the information transmission rate by a factor of 3.

We report the first experimental demonstration of time-reversal focusing with electromagnetic waves. An antenna transmits a 1-micros electromagnetic pulse at a central frequency of 2.45 GHz in a high-Q cavity. Another antenna records the strongly reverberated signal. The time-reversed wave is built and transmitted back by the same antenna acting now as a time-reversal mirror. The wave is found to converge to its initial source and is compressed in time. The quality of focusing is determined by the frequency bandwidth and the spectral correlations of the field within the cavity.

The possibility of recovering the Green's function from the field-field correlations of coda waves in an open multiple scattering medium is investigated. The argument is based on fundamental symmetries of reciprocity, time-reversal invariance, and the Helmholtz-Kirchhoff theorem. A criterion is defined, indicating how sources should be placed inside an open medium in order to recover the Green's function between two passive receivers. The case of noise sources is also discussed. Numerical experiments of ultrasonic wave propagation in a multiple scattering medium are presented to support the argument.Wave propagation in a multiple scattering or reverberating environment has been a subject of interest in a wide variety of domains ranging from solid state physics to optics or acoustics. Ultrasound is particularly interesting because it allows a direct measurement of the field fluctuations, both in amplitude and in phase. In connection with this, a remarkable work by Weaver and Lobkis 1-3 recently showed that the Green's function between two points could be recovered from the field-field correlation of a diffuse ultrasonic field. This amounts to doing ''ultrasonics without a source'' since they showed that thermal noise could be used instead of a direct pulse/echo measurement between the two points. The experiment was carried out in an aluminum block, and the theoretical analysis was based on discrete modal expansion of the field, with random modal amplitudes. Applications are promising: it would be possible to recover the Green's function of a complex medium just by correlating diffuse fields received on passive sensors ͑application to shallow water ocean acoustics, where the field is not diffuse but propagates in a wave guide, was also evoked 4 ͒.However, the basic assumption in the theoretical analysis is that the medium is closed and free of absorption. In a real medium, absorption will tend to cut out the longest scattering ͑or reverberating͒ paths, and discrete modes will not be resolved any more. Similar problems are expected if the medium is open rather than closed ͑actually, in an open medium, the fluctuation-dissipation theorem 3 establishes the result, as long as the field is diffuse in the thermal sense͒. The aim of this letter is to examine whether the Green's function can still be recovered from the correlations of an ultrasonic wave field in an open scattering medium, when a discrete expansion on orthogonal modes is no longer relevant and the field is not thermally diffuse.To that end, we present 2-D numerical experiments of acoustic scattering on rigid inclusions randomly located either in a closed cavity or in a open medium. The wave equation is solved by a finite differences simulation ͑centered scheme͒; the boundary conditions is implemented following Collino's work. 5 Naturally, a finite difference scheme shows numerical dispersion. However, the essential point is that the fundamental symmetries of reciprocity and time reversal still hold in the numerical experiments.To begin with, let us consider...