Anderson Mobility Gap Probed by Dynamic Coherent Backscattering.

We use dynamic coherent backscattering to study one of the Anderson mobility gaps in the vibrational spectrum of strongly disordered three-dimensional mesoglasses. Comparison of experimental results with the self-consistent theory of localization allows us to estimate the localization (correlation) length as a function of frequency in a wide spectral range covering bands of diffuse transport and a mobility gap delimited by two mobility edges. The results are corroborated by transmission measurements on one of our samples.

Experimental observation of ultrasound fast and slow waves through three-dimensional printed trabecular bone phantoms.

In this paper, ultrasound measurements of 1:1 scale three-dimensional (3D) printed trabecular bone phantoms are reported. The micro-structure of a trabecular horse bone sample was obtained via synchrotron x-ray microtomography, converted to a 3D binary data set, and successfully 3D-printed at scale 1:1. Ultrasound through-transmission experiments were also performed through a highly anisotropic version of this structure, obtained by elongating the digitized structure prior to 3D printing. As in real anisotropic trabecular bone, both the fast and slow waves were observed. This illustrates the potential of stereolithography and the relevance of such bone phantoms for the study of ultrasound propagation in bone.

Recurrent scattering and memory effect at the Anderson localization transition.

We report on ultrasonic measurements of the propagation operator in a strongly scattering mesoglass. The backscattered field is shown to display a deterministic spatial coherence due to a remarkably large memory effect induced by long recurrent trajectories. Investigation of the recurrent scattering contribution directly yields the probability for a wave to come back close to its starting spot. The decay of this quantity with time is shown to change dramatically near the Anderson localization transition. The singular value decomposition of the propagation operator reveals the dominance of very intense recurrent scattering paths near the mobility edge.

Random multiple scattering of ultrasound. I. Coherent and ballistic waves.

This is the first article in a series of two dealing with the statistical moments of ultrasonic waves transmitted through a disordered medium with resonant multiple scattering. Only the first-order moment is considered here. An ultrasonic pulsed wave is transmitted from a point source to a 128-element receiving array through two-dimensional samples with various thicknesses. The samples consist of random collections of parallel steel rods immersed in water. Experimental results show that the ensemble-averaged transmitted wave forms ("coherent wave") exhibit a time-dependent frequency spectrum. Within the independent scattering approximation, this is well explained by individual resonances of the scatterers. The coherent wave only appears after ensemble averaging and has to be distinguished from the "ballistic wave," i.e., the first well-defined pulse that crosses the sample, which can be measured on every realization of disorder. A physical interpretation is given, which is based on the separation of the coherent wave between a rigid and a resonant contribution.

Random multiple scattering of ultrasound. II. Is time reversal a self-averaging process?

This is the second article in a series of two dealing with the statistical moments of ultrasonic waves transmitted through a disordered medium with resonant multiple scattering. Second-order moments in time and space are considered here. An ultrasonic pulsed wave is transmitted from a point source to a 128-element receiving array through two-dimensional samples with various thicknesses. The samples consist of random collections of parallel steel rods immersed in water. The scattered waves are recorded, time reversed, and sent back into the medium. The time-reversed waves are converging back to their source and the quality of spatial and temporal focusing on the source is related to the second-order moments of the scattered wave (correlation) in time and in space. Experimental results show that it is possible to obtain a robust estimation on a single realization of disorder, taking advantage of the wide frequency bandwidth. The spatial resolution of the system is only limited by the correlation length of the scattered field, and no longer by the array aperture. As the sample thickness is increased, the quality of focusing saturates, which we believe is linked to the Thouless factor g. In the thickest sample, g approximately 30, which is still well above the localization threshold.

Limits of time-reversal focusing through multiple scattering: long-range correlation

Experimental results of time-reversal focusing in a high-order multiple scattering medium are presented and compared to theoretical predictions based on a statistical model. The medium consists of a random collection of parallel steel rods. An ultrasonic source (3.2 MHz) transmits a pulse that undergoes multiple scattering and is recorded on an array. The time-reversed waves are sent by the array back to the source through the scattering medium. The quality of temporal focusing is very well predicted by a simple statistical model. However, for thicker samples, persistent temporal side-lobes appear. We interpret these side-lobes as a consequence of the growing number of crossing paths in the sample due to high-order multiple scattering. As to spatial focusing, the resolution is practically independent from the array's aperture. With a 16-element array, the resolution was found to be 30 times finer than in a homogeneous medium. Resolutions of the order of the wavelength (0.5 mm) were attained. These results are discussed in relation with the statistical properties of time-reversal mirrors in a random medium.

Transport parameters for an ultrasonic pulsed wave propagating in a multiple scattering medium

A set of ultrasonic experimental methods was developed to characterize a multiple scattering medium in terms of l(s), l*, l(a), respectively, the elastic, transport, and absorption mean free paths and D the diffusion constant. Actually, these quantities are the key parameters for a wave propagating in a disordered medium. Although they are widely used in optics, they are less common in acoustics. The underlying model is based on the expansion of the average solution for the heterogeneous Green's function equation. To validate this theoretical approach, a sample made of randomly located steel rods was used as a prototype. Through time-resolved measurements of the transmitted amplitude, the difference between the ballistic and the coherent wave is highlighted. In varying the sample thickness, l(s) is determined, the coherent and diffusive regime are distinguished, and the transition from one to the other is followed. Furthermore, as a limit to a description of the average intensity based on the diffusion approximation, the existence of a coherent backscattering effect is shown. This latter gives a method to estimate D and l*. These quantities being determined, it becomes possible to infer l(a) using average time-resolved intensity measurements. Finally, some applications to coarse-grain stainless steels are discussed.

Spatial coherence of ultrasonic speckle in composites.

Pulsed echography in a scattering medium generates speckle noise. Its random nature implies a statistical processing of the backscattered signal. The second-order statistics, such as autocorrelation, can provide information about the structure of the medium and help detect a possible defect. The spatial autocorrelation function is related to the spatial coherence of the backscattered waves, which determines the speckle noise level. Specifically, this spatial coherence approach is applied to anisotropic fiber-reinforced composites. The authors present theoretical as well as experimental results and show how the autocorrelation function changes with the orientation of the layers inside the composite, thus pointing out its anisotropy.

Comparison between experimental and 2-D numerical studies of multiple scattering in Inconel600 by means of array probes.

Ultrasonic non-destructive testing of polycrystalline structures can be disturbed by scattering at grain boundaries. Understanding and modeling this so-called "structural noise" is crucial for characterization as well as detection purposes. Structural noise can be considered as a fingerprint of the material under investigation, since it contains information about its microstructure. The interpretation of experimental data necessitates an accurate comprehension of complex phenomena that occur in multiple scattering media and thus robust scattering models. In particular, numerical models can offer the opportunity to realize parametrical studies on controlled microstructures. However, the ability of the model to simulate wave propagation in complex media must be validated. In that perspective, the main objective of the present work is to evaluate the ability of the finite-element code ATHENA 2D to reproduce typical features of multiple wave scattering in the context of ultrasonic non-destructive evaluation, with an array of sources and receivers. Experiments were carried out with a 64-element array, around 2 MHz. The sample was a mock-up of Inconel600 exhibiting a coarse grain structure with a known grain size distribution. The numerical model of this microstructure is based on Voronoi diagrams. Two physical parameters were used to compare numerical and experimental data: the coherent backscattering peak, and the singular value distribution of the array response matrix. Though the simulations are 2-D, a good agreement was found between simulated and experimental data.

Sensitivity to perturbations of a time-reversed acoustic wave in a multiple scattering medium.

We present experimental results on the robustness of acoustic time-reversal focusing in a multiple scattering medium undergoing perturbations. Time reversal in such a medium can be viewed as a correlation technique, analogous to diffusive wave spectroscopy. Moreover, the recent introduction of telecommunication techniques based on time reversal in changeable media naturally raises the question of sensitivity to a perturbation of the medium. We consider the situation where the reversibility of an acoustic wave generated by a linelike source is gradually destroyed when a perturbation is added, either locally (by removing scatterers) or globally (by changing the temperature) to the multiple scattering medium.

Acoustical imaging through a multiple scattering medium using a time-reversal mirror.

Acoustical imaging is based on the ability to focus an acoustic beam inside the zone of interest. This remains an issue through a high-order multiple scattering medium because the electronic delay lines that enable one to focus through a multiple scattering medium are a priori unknown. Using time-reversal principles, we show that images can be obtained through a very disordered medium. Surprisingly, the images are better than those obtained in a homogeneous medium with a classical imaging device.

Time reversal of electromagnetic waves.

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.