Flexural pulse wave velocity in blood vessels.

Arteriosclerosis is a major risk factor for cardiovascular disease and results in arterial vessel stiffening. Velocity estimation of the pulse wave sent by the heart and propagating into the arteries is a widely accepted biomarker. This symmetrical pulse wave propagates at a speed which is related to the Young's modulus through the Moens Korteweg (MK) equation. Recently, an antisymmetric flexural wave has been observed in vivo. Unlike the symmetrical wave, it is highly dispersive. This property offers promising applications for monitoring arterial stiffness and early detection of atheromatous plaque. However, as far as it is known, no equivalent of the MK equation exists for flexural pulse waves. To bridge this gap, a beam based theory was developed, and approximate analytical solutions were reached. An experiment in soft polymer artery phantoms was built to observe the dispersion of flexural waves. A good agreement was found between the analytical expression derived from beam theory and experiments. Moreover, numerical simulations validated wave speed dependence on the elastic and geometric parameters at low frequencies. Clinical applications, such as arterial age estimation and arterial pressure measurement, are foreseen.

Dynamic structured illumination for confocal microscopy.

Structured illumination enables the tailoring of an imaging device's optical transfer function to enhance resolution. We propose the incorporation of a temporal periodic modulation, specifically a rotating mask, to encode multiple transfer functions in the temporal domain. This approach is demonstrated using a confocal microscope configuration. At each scanning position, a temporal periodic signal is recorded. By filtering around each harmonic of the rotation frequency, multiple images of the same object can be constructed. The image carried by the nth harmonic is a convolution of the object with a phase vortex of topological charge n, similar to the outcome when using a vortex phase plate as an illumination. This enables the collection of chosen high spatial frequencies from the sample, thereby enhancing the spatial resolution of the confocal microscope.

Viscoelastic dynamics of a soft strip subject to a large deformation.

To produce sounds, we adjust the tension of our vocal folds to shape their properties and control the pitch. This efficient mechanism offers inspiration for designing reconfigurable materials and adaptable soft robots. However, understanding how flexible structures respond to a significant static strain is not straightforward. This complexity also limits the precision of medical imaging when applied to tensioned organs like muscles, tendons, ligaments and blood vessels among others. In this article, we experimentally and theoretically explore the dynamics of a soft strip subject to a substantial static extension, up to 180%. Our observations reveal a few intriguing effects, such as the resilience of certain vibrational modes to a static deformation. These observations are supported by a model based on the incremental displacement theory. This has promising practical implications for characterizing soft materials but also for scenarios where external actions can be used to tune properties.

Soft elastomers: A playground for guided waves.

Mechanical waves propagating in soft materials play an important role in physiology. They can be natural, such as the cochlear wave in the inner ear of mammalians, or controlled, such as in elastography in the context of medical imaging. In a recent study, Lanoy, Lemoult, Eddi, and Prada [Proc. Natl. Acad. Sci. U.S.A. 117(48), 30186-30190 (2020)] implemented an experimental tabletop platform that allows direct observation of in-plane guided waves in a soft strip. Here, a detailed description of the setup and signal processing steps is presented as well as the theoretical framework supporting them. One motivation is to propose a tutorial experiment for visualizing the propagation of guided elastic waves. Last, the versatility of the experimental platform is exploited to illustrate experimentally original features of wave physics, such as backward modes, stationary modes, and Dirac cones.

Cloaking, trapping and superlensing of lamb waves with negative refraction.

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.

Dirac cones and chiral selection of elastic waves in a soft strip.

We study the propagation of in-plane elastic waves in a soft thin strip, a specific geometrical and mechanical hybrid framework which we expect to exhibit a Dirac-like cone. We separate the low frequencies guided modes (typically 100 Hz for a 1-cm-wide strip) and obtain experimentally the full dispersion diagram. Dirac cones are evidenced together with other remarkable wave phenomena such as negative wave velocity or pseudo-zero group velocity (ZGV). Our measurements are convincingly supported by a model (and numerical simulation) for both Neumann and Dirichlet boundary conditions. Finally, we perform one-way chiral selection by carefully setting the source position and polarization. Therefore, we show that soft materials support atypical wave-based phenomena, which is all of the more interesting as they make most of the biological tissues.

Measuring Dirac Cones in a Subwavelength Metamaterial.

The exciting discovery of bidimensional systems in condensed matter physics has triggered the search of their photonic analogues. In this Letter, we describe a general scheme to reproduce some of the systems ruled by a tight-binding Hamiltonian in a locally resonant metamaterial; by specifically controlling the structure and the composition it is possible to engineer the band structure at will. We numerically and experimentally demonstrate this assertion in the microwave domain by reproducing the band structure of graphene, the most famous example of those 2D systems, and by accurately extracting the Dirac cones. This is direct evidence that opting for a crystalline description of those subwavelength scaled systems, as opposed to the usual description in terms of effective parameters, makes them a really convenient tabletop platform to investigate the tantalizing challenges that solid-state physics offer.

Crystalline Soda Can Metamaterial exhibiting Graphene-like Dispersion at subwavelength scale.

Graphene, a honeycomb lattice of carbon atoms ruled by tight-binding interaction, exhibits extraordinary electronic properties due to the presence of Dirac cones within its band structure. These intriguing singularities have naturally motivated the discovery of their classical analogues. In this work, we present a general and direct procedure to reproduce the peculiar physics of graphene within a very simple acoustic metamaterial: a double lattice of soda cans resonating at two different frequencies. The first triangular sub-lattice generates a bandgap at low frequency, which induces a tight-binding coupling between the resonant defects of the second honeycomb one, hence allowing us to obtain a graphene-like band structure. We prove the relevance of this approach by showing that both numerical and experimental dispersion relations exhibit the requested Dirac cone. We also demonstrate the straightforward monitoring of the coupling strength within the crystal of resonant defects. This work shows that crystalline metamaterials are very promising candidates to investigate tantalizing solid-state physics phenomena with classical waves.

Crystalline metamaterials for topological properties at subwavelength scales.

The exciting discovery of topological condensed matter systems has lately triggered a search for their photonic analogues, motivated by the possibility of robust backscattering-immune light transport. However, topological photonic phases have so far only been observed in photonic crystals and waveguide arrays, which are inherently physically wavelength scaled, hindering their application in compact subwavelength systems. In this letter, we tackle this problem by patterning the deep subwavelength resonant elements of metamaterials onto specific lattices, and create crystalline metamaterials that can develop complex nonlocal properties due to multiple scattering, despite their very subwavelength spatial scale that usually implies to disregard their structure. These spatially dispersive systems can support subwavelength topological phases, as we demonstrate at microwaves by direct field mapping. Our approach gives a straightforward tabletop platform for the study of photonic topological phases, and allows to envision applications benefiting the compactness of metamaterials and the amazing potential of topological insulators.

Spatiotemporal Wave Front Shaping in a Microwave Cavity.

Controlling waves in complex media has become a major topic of interest, notably through the concepts of time reversal and wave front shaping. Recently, it was shown that spatial light modulators can counterintuitively focus waves both in space and time through multiple scattering media when illuminated with optical pulses. In this Letter, we transpose the concept to a microwave cavity using flat arrays of electronically tunable resonators. We prove that maximizing the Green's function between two antennas at a chosen time yields diffraction limited spatiotemporal focusing. Then, changing the photons' dwell time inside the cavity, we modify the relative distribution of the spatial and temporal degrees of freedom (DOF), and we demonstrate that it has no impact on the field enhancement: wave front shaping makes use of all available DOF, irrespective of their spatial or temporal nature. Our results prove that wave front shaping using simple electronically reconfigurable arrays of reflectors is a viable approach to the spatiotemporal control of microwaves, with potential applications in medical imaging, therapy, telecommunications, radar, or sensing. They also offer new fundamental insights regarding the coupling of spatial and temporal DOF in complex media.

Negative refractive index and acoustic superlens from multiple scattering in single negative metamaterials.

Metamaterials, man-made composite media structured on a scale much smaller than a wavelength, offer surprising possibilities for engineering the propagation of waves. One of the most interesting of these is the ability to achieve superlensing--that is, to focus or image beyond the diffraction limit. This originates from the left-handed behavior--the property of refracting waves negatively--that is typical of negative index metamaterials. Yet reaching this goal requires the design of 'double negative' metamaterials, which act simultaneously on the permittivity and permeability in electromagnetics, or on the density and compressibility in acoustics; this generally implies the use of two different kinds of building blocks or specific particles presenting multiple overlapping resonances. Such a requirement limits the applicability of double negative metamaterials, and has, for example, hampered any demonstration of subwavelength focusing using left-handed acoustic metamaterials. Here we show that these strict conditions can be largely relaxed by relying on media that consist of only one type of single resonant unit cell. Specifically, we show with a simple yet general semi-analytical model that judiciously breaking the symmetry of a single negative metamaterial is sufficient to turn it into a double negative one. We then demonstrate that this occurs solely because of multiple scattering of waves off the metamaterial resonant elements, a phenomenon often disregarded in these media owing to their subwavelength patterning. We apply our approach to acoustics and verify through numerical simulations that it allows the realization of negative index acoustic metamaterials based on Helmholtz resonators only. Finally, we demonstrate the operation of a negative index acoustic superlens, achieving subwavelength focusing and imaging with spot width and resolution 7 and 3.5 times better than the diffraction limit, respectively. Our findings have profound implications for the physics of metamaterials, highlighting the role of their subwavelength crystalline structure, and hence entering the realm of metamaterial crystals. This widens the scope of possibilities for designing composite media with novel properties in a much simpler way than has been possible so far.

Symmetry issues in the hybridization of multi-mode waves with resonators: an example with Lamb waves metamaterial.

Locally resonant metamaterials derive their effective properties from hybridization between their resonant unit cells and the incoming wave. This phenomenon is well understood in the case of plane waves that propagate in media where the unit cell respects the symmetry of the incident field. However, in many systems, several modes with orthogonal symmetries can coexist at a given frequency, while the resonant unit cells themselves can have asymmetric scattering cross-sections. In this paper we are interested in the influence of symmetry breaking on the hybridization of a wave field that includes multiple propagative modes. The A0 and S0 Lamb waves that propagate in a thin plate are good candidates for this study, as they are either anti-symmetric or symmetric. First we designed an experimental setup with an asymmetric metamaterial made of long rods glued to one side of a metallic plate. We show that the flexural resonances of the rods induce a break of the orthogonality between the A0/S0 modes of the free-plate. Finally, based on numerical simulations we show that the orthogonality is preserved in the case of a symmetric metamaterial leading to the presence of two independent polariton curves in the dispersion relation.

Wave-Field Shaping in Cavities: Waves Trapped in a Box with Controllable Boundaries.

Electromagnetic cavities are used in numerous domains of applied and fundamental physics, from microwave ovens and electromagnetic compatibility to masers, quantum electrodynamics (QED), and quantum chaos. The wave fields established in cavities are statically fixed by their geometry, which are usually modified by using mechanical parts like mode stirrers in reverberation chambers or screws in masers and QED. Nevertheless, thanks to integral theorems, tailoring the cavity boundaries theoretically permits us to design at will the wave fields they support. Here, we show in the microwave domain that it is achievable dynamically simply by using electronically tunable metasurfaces that locally modify the boundaries, switching them in real time from Dirichlet to Neumann conditions. We prove that at a high modal density, counterintuitively, it permits us to create wave patterns presenting hot spots of intense energy. We explain and model the physical mechanism underlying the concept, which allows us to find a criterion ensuring that modifying parts of a cavity's boundaries turn it into a completely different one. We finally prove that this approach even permits us, in the limiting case where the cavity supports only well-separated resonances, to choose the frequencies at which the latter occur.

Experimental demonstration of ordered and disordered multiresonant metamaterials for lamb waves.

We demonstrate the experimental realization of a multiresonant metamaterial for Lamb waves, i.e., elastic waves propagating in plates. The metamaterial effect comes from the resonances of long aluminum rods that are attached to an aluminum plate. Using time-dependent measurements, we experimentally prove that this metamaterial exhibits wide band gaps as well as sub- and suprawavelength modes for both a periodic and a random arrangement of the resonators. The dispersion curve inside the metamaterial is predicted through hybridizations between flexural and compressional resonances in the rods and slow and fast Lamb modes in the plate. We finally underline how the various degrees of freedom of such system paves the way to the design of metamaterials for the control of Lamb waves in unprecedented ways.

A polychromatic approach to far-field superlensing at visible wavelengths.

Breaking the diffraction barrier in the visible part of the electromagnetic spectrum is of fundamental importance. Far-field subwavelength focusing of light could, for instance, drastically broaden the possibilities available in nanolithography, light-matter interactions and sensing at the nanoscale. Similarly, imaging with a nanometric resolution could result in incredible breakthroughs in soft matter and biology. There have been numerous proposals in this regard based on metamaterials, structured illumination methods or diffractive optical components. The common denominator of all these approaches resides in their monochromatic nature. Here we show that using polychromatic light in dispersive metamaterials allows us to circumvent many limitations associated with previous monochromatic approaches. We design a plasmonic metalens based on metallic nanorods that, when used with broadband light fields, can beat the diffraction limit for imaging and focusing from the far field.

Acoustic resonators for far-field control of sound on a subwavelength scale.

We prove experimentally that broadband sounds can be controlled and focused at will on a subwavelength scale by using acoustic resonators. We demonstrate our approach in the audible range with soda cans, that is, Helmholtz resonators, and commercial computer speakers. We show that diffraction-limited sound fields convert efficiently into subdiffraction modes in the collection of cans that can be controlled coherently in order to obtain focal spots as thin as 1/25 of a wavelength in air. We establish that subwavelength acoustic pressure spots are responsible for a strong enhancement of the acoustic displacement at focus, which permits us to conclude with a visual experiment exemplifying the interest of our concept for subwavelength sensors and actuators.

Resonant metalenses for breaking the diffraction barrier.

We introduce the resonant metalens, a cluster of coupled subwavelength resonators. Dispersion allows the conversion of subwavelength wave fields into temporal signatures while the Purcell effect permits an efficient radiation of this information in the far field. The study of an array of resonant wires using microwaves provides a physical understanding of the underlying mechanism. We experimentally demonstrate imaging and focusing from the far field with resolutions far below the diffraction limit. This concept is realizable at any frequency where subwavelength resonators can be designed.

Manipulating spatiotemporal degrees of freedom of waves in random media.

We show that all the spatiotemporal degrees of freedom available in a complex medium can be harnessed and converted into spatial ones. This is demonstrated experimentally through an instantaneous spatial inversion, using broadband ultrasonic waves in a multiple scattering sample. We show theoretically that the inversion convergence is governed by the total number of degrees of freedom available in the medium for a fixed bandwidth and demonstrate experimentally its use for complex media investigation. We believe our approach has potential in sensing, imagery, focusing, and telecommunication.