No abstract

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)...

This paper provides a theoretical investigation of negative refraction and focusing of elastic guided waves in a free-standing plate with a step-like thickness change. Under certain conditions, a positive phase velocity (forward) Lamb mode can be converted into a negative phase velocity (backward) mode at such interface, giving rise to negative refraction. A semi-analytical model is developed in order to study the influence of various parameters such as the material Poisson's coefficient, the steplike thickness, the frequency and the incidence angle. To this end, all the Lamb and shear horizontal propagating modes, but also a large number of their inhomogeneous and evanescent counterpart,s are taken into account. The boundary conditions applied to the stress-displacement fields at the thickness step yields an equation system. Its inversion provides the transmission and reflection coefficients between each mode at the interface. The step-like thickness and Poisson's ratio are shown to be key parameters to optimize the negative refraction process. In terms of material, Duralumin is found to be optimal as it leads to a nearly perfect conversion between forward and backward modes over broad frequency and angular ranges. An excellent focusing ability is thus predicted for a flat lens made of two symmetric thickness steps. Theoretical results are confirmed by a numerical FDTD simulation and experimental measurements made on an optimized Duralumin flat lens by means of laser interferometry. This theoretical study paves the way towards the optimization of elastic devices based on negative refraction, in particular for cloaking or super-focusing purposes.

The paper studies the interaction of Lamb waves with the free edge of a plate. The reflection coefficients of a Lamb mode at a plate free edge are calculated using a semi-analytical method, as a function of frequency and angle of incidence. The conversion between forward and backward Lamb modes is thoroughly investigated. It is shown that, at the zero-group velocity (ZGV) frequency, the forward S1 Lamb mode fully converts into the backward S 2b Lamb mode at normal incidence. Besides, this conversion is very efficient over most of the angular spectrum and remains dominant at frequencies just above the ZGV-point. This effect is observed experimentally on a Duralumin plate. Firstly, the S1 Lamb mode is selectively generated using a transducer array, secondly the S 2b mode is excited using a single circular transducer. The normal displacement field is probed with an interferometer. The free edge is shown to retro-focus the incident wave at different depths depending on the wave number mismatch between the forward and backward propagating modes. In the vicinity of the ZGV-point, wave numbers coincide and the wave is retro-reflected on the source. In this frequency range, the free edge acts as a perfect phase conjugating mirror.

The propagation of waves in complex media can be harnessed either by taming the incident wave-field impinging on the medium or by forcing waves along desired paths through its careful design. These two alternative strategies have given rise to fascinating concepts such as time reversal or negative refraction. Here, we show how these two processes are intimately linked through the negative reflection phenomenon. A negative reflecting mirror converts a wave of positive phase velocity into its negative counterpart and vice versa. In this article, we experimentally demonstrate this phenomenon with elastic waves in a 2D billiard and in a disordered plate by means of laser interferometry. Despite the complexity of such configurations, the negatively reflected wave field focuses back towards the initial source location, thereby mimicking a phase conjugation operation while being a fully passive process. The super-focusing capability of negative reflection is also highlighted in a monochromatic regime. The negative reflection phenomenon is not restricted to guided elastic waves since it can occur in zero-gap systems such as photonic crystals, chiral metamaterials or graphene. Negative reflection can thus become a tool of choice for the control of waves in all fields of wave physics.

We report on experimental and numerical implementations of devices based on the negative refraction of elastic guided waves, the so-called Lamb waves. Consisting in plates of varying thickness, these devices rely on the concept of complementary media, where a particular layout of negative index media can cloak an object with its anti-object or trap waves around a negative corner. The diffraction cancellation operated by negative refraction is investigated by means of laser ultrasound experiments. However, unlike original theoretical predictions, these intriguing wave phenomena remain, nevertheless, limited to the propagating component of the wave-field. To go beyond the diffraction limit, negative refraction is combined with the concept of metalens, a device converting the evanescent components of an object into propagating waves. The transport of an evanescent wave-field is then possible from an object plane to a far-field imaging plane. Twenty years after Pendry’s initial proposal, this work thus paves the way towards an elastic superlens.

No abstract

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.