Random Matrix Theory Applied to Acoustic Backscattering and Imaging In Complex Media

Aubry, Alexandre; Derode, Arnaud

doi:10.1103/physrevlett.102.084301

Cited by 133 publications

(138 citation statements)

References 17 publications

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“…In optical experiments, the finite numerical aperture of the illumination and detection systems limits the angular coverage of the input and output channels [25]. In acoustics or electromagnetism, the spatial sampling of measurements has not been sufficient to have access to the full S−matrix so far [9,10,12].In this Letter, we present experimental measurements of the full S-matrix across a disordered elastic wave guide. To that aim, laser-ultrasonic techniques have been used in order to obtain a satisfying spatial sampling of the field at the input and output of the scattering medium.…”

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confidence: 98%

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Full transmission and reflection of waves propagating through a maze of disorder

Gérardin

Laurent

Derode

et al. 2016

Journal of the Acoustical Society of America

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Thirty years ago, theorists showed that a properly designed combination of incident waves could be fully transmitted through (or reflected by) a disordered medium, based on the existence of propagation channels which are essentially either closed or open (bimodal law). In this Letter, we study elastic waves in a disordered waveguide and present a direct experimental evidence of the bimodal law. Full transmission and reflection are achieved. The wave-field is monitored by laser interferometry and highlights the interference effects that take place within the scattering medium. PACS numbers: 42.25.Dd, 43.20.Gp, 42.25.Bs Light travelling through thick clouds, electrons conducting through metals or seismic waves in the earth crust are all examples of waves propagating through disordered materials. Energy transport by waves undergoing strong scattering is usually well described by diffusion theory. However, this classical picture neglects interference effects that may resist the influence of disorder. Interference is responsible for fascinating phenomena in mesoscopic physics. On the one hand, it can slow down and eventually stop the diffusion process, giving rise to Anderson localization [1,2]. On the other hand, it can also help waves to find a way through a maze of disorder [3]. Actually, a properly designed combination of incident waves can be completely transmitted through a strongly scattering medium, as suggested by Dorokhov and others more than twenty years ago [4][5][6][7]. This prediction has recently received a great deal of attention mostly due to the emergence of wave-front shaping techniques in optics [8].In order to address the open channels (i.e., to achieve full energy transmission) across a disordered wave guide, one has to perform a complete measurement of the scattering matrix S. The S-matrix relates the input and output of the medium [7]. It fully describes wave propagation across a scattering medium. It can be generally divided into blocks containing transmission and reflection matrices, t and r, with a certain number N of input and output channels. Initially, random matrix theory (RMT) has been successfully applied to the transport of electrons through chaotic systems and disordered wires [7]. However, the confrontation between theory and experiment has remained quite restrictive since specific input electron states cannot be addressed in practice. On the contrary, a coherent control of the incident wave-field is possible in classical wave physics. Several works have demontrated the ability of measuring the S-matrix, or at least some of its subspaces, in disordered media, whether it be in acoutics [9-11], electromagnetism [12,13] or optics [14][15][16][17].The existence of open channels has been revealed by investigating the eigenvalues T of the Hermitian matrix tt † . Theoretically, their distribution should follow a bimodal law [4,5,7], exhibiting two peaks. The highest one, around T ∼ 0, correspond to closed (i.e. strongly reflected) eigenchannels. At the other end of the spectrum (T ∼ 1)...

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Full transmission and reflection of waves propagating through a maze of disorder

Gérardin

Laurent

Derode

et al. 2016

Journal of the Acoustical Society of America

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“…A simple measurement of the scattering matrix (or a subpart of it) at neighboring frequencies [27] yields the time-delay matrix from which particle-like state inputs can be extracted. Such a measurement can be routinely performed through 3D scattering media whether it be in optics [6,12], in the microwave regime [13,35] or in acoustics [33,34]. As to the generation of particle-like wave packets, multi-element technology is a powerful tool for the coherent control of acoustic waves and electromagnetic waves [60].…”

Section: Discussionmentioning

confidence: 99%

“…This highly dimension S-matrix relates any arbitrary wave-field at the input to the output of the scattering medium, and in principle, allows the reconstruction or prediction of either. It fully describes wave propagation across a scattering medium and can meanwhile be routinely measured not only in acoustics [33,34], but also in microwave technology [13,35] and optics [6,12]. The sub-blocks of the scattering matrix contain the complex-valued transmission (t, t ) and reflection (r, r ) matrices with a certain number N of input and output channels, S = r t t r .…”

Section: Introductionmentioning

confidence: 99%

Particle-like wave packets in complex scattering systems

Gérardin

Laurent

Ambichl

et al. 2016

2016 URSI International Symposium on Electromagnetic Theory (EMTS)

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A wave packet undergoes a strong spatial and temporal dispersion while propagating through a complex medium. This wave scattering is often seen as a nightmare in wave physics whether it be for focusing, imaging or communication purposes. Controlling wave propagation through complex systems is thus of fundamental interest in many areas, ranging from optics or acoustics to medical imaging or telecommunications. Here, we study the propagation of elastic waves in a cavity and a disordered waveguide by means of laser interferometry. From the direct experimental access to the time-delay matrix of these systems, we demonstrate the existence of particle-like wave packets that remain focused in time and space throughout their complex trajectory. Due to their limited dispersion, their selective excitation will be crucially relevant for all applications involving selective wave focusing and efficient information transfer through complex media.

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“…The consequence is a decrease of imaging and characterization capabilities of classical ultrasonic techniques. To overcome these difficulties, Aubry et al [1] have developed a specific signal treatment to reduce the influence of the microstructure. This treatment is based on random matrix theory to separate single scattering and multiple scattering contributions.…”

Section: Introductionmentioning

confidence: 99%

Multiple scattering filter: Application to plane defect detection in a nickel alloy

Trottier¹,

Shahjhan²,

Schumm³

et al. 2016

AIP Conference Proceedings

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Random Matrix Theory Applied to Acoustic Backscattering and Imaging In Complex Media

Cited by 133 publications

References 17 publications

Full transmission and reflection of waves propagating through a maze of disorder

Full transmission and reflection of waves propagating through a maze of disorder

Particle-like wave packets in complex scattering systems

Multiple scattering filter: Application to plane defect detection in a nickel alloy

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