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.

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.

Precise Localization of Multiple Noncooperative Objects in a Disordered Cavity by Wave Front Shaping.

Complicated multipath trajectories of waves in disordered cavities cause object localization to be very challenging with traditional ray-tracing approaches. Yet it is known that information about the object position is encoded in the Green's function. After a calibration step, traditional time-reversal approaches retrieve a source's location from a broadband impulse response measurement. Here, we show that a nonemitting object's scattering contribution to a reverberant medium suffices to localize the object. We demonstrate our finding in the microwave domain. Then, we further simplify the scheme by replacing the temporal degrees of freedom (d.o.f.) of the broadband measurement with spatial d.o.f. obtained from wave front shaping. A simple electronically reconfigurable reflectarray inside the cavity dynamically modulates parts of the cavity boundaries, thereby providing spatial d.o.f. The demonstrated ability to localize multiple noncooperative objects with a single-frequency scheme may have important applications for sensors in smart homes.

Intensity-only measurement of partially uncontrollable transmission matrix: demonstration with wave-field shaping in a microwave cavity.

Transmission matrices (TMs) have become a powerful and widely used tool to describe and control wave propagation in complex media. In certain scenarios the TM is partially uncontrollable, complicating its identification and use. In standard optical wavefront shaping experiments, uncontrollable reflections or imperfect illumination may be the cause; in reverberating cavities, uncontrollable reflections off the walls have that effect. Here we employ phase retrieval techniques to identify such a partially uncontrollable TM solely based on random intensity-only reference measurements. We demonstrate the feasibility of our method by focusing both on a single target as well as on multiple targets in a microwave cavity, using a phase-binary Spatial-Microwave-Modulator.

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.

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.

Retrieving time-dependent Green's functions in optics with low-coherence interferometry.

We report on the passive measurement of time-dependent Green's functions in the optical frequency domain with low-coherence interferometry. Inspired by previous studies in acoustics and seismology, we show how the correlations of a broadband and incoherent wave field can directly yield the Green's functions between scatterers of a complex medium. Both the ballistic and multiple scattering components of the Green's function are retrieved. This approach opens important perspectives for optical imaging and characterization in complex scattering media.

Hybridized resonances to design tunable binary phase metasurface unit cells.

The recent concept of metasurfaces is a powerful tool to shape waves by governing precisely the phase response of each constituting element through its resonance properties. While most efforts are devoted to realize reconfigurable metasurfaces that allow such complete phase control, for many applications a binary one is sufficient. Here, we propose and demonstrate through experiments and simulations a binary state tunable phase reflector based on the concept of hybridized resonators as unit cell for a possible metasurface. The concept presents the great advantages to be very general, scalable to all frequency domains and above all very robust to fluctuations induced by the tunable mechanism, as we prove it at microwave frequencies using electronically tunable patch reflectors.

Using subwavelength diffraction gratings to design open electromagnetic cavities.

In this Letter we propose to use subwavelength diffraction gratings as very good semitransparent mirrors for electromagnetic waves to design open cavities. To do so, we replace part of the walls of a cavity by such a grating. We numerically and analytically link the grating characteristics to the spectral properties of the realized open cavity. Then we demonstrate that the eigenmodes of the cavity can be transmitted perfectly through the grating to the exterior, thereby turning a point source inside the cavity into a very directive source. We investigate the effect of disorder, which leads to isotropic radiation patterns, and perform experiments in the microwave domain in order to support our claims. Finally, we present an example of application of the concept in fundamental physics, by measuring from outside the eigenmodes of a disordered microwave cavity.

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.

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.

Dynamic Metasurface Aperture as Smart Around-the-Corner Motion Detector.

Detecting and analysing motion is a key feature of Smart Homes and the connected sensor vision they embrace. At present, most motion sensors operate in line-of-sight Doppler shift schemes. Here, we propose an alternative approach suitable for indoor environments, which effectively constitute disordered cavities for radio frequency (RF) waves; we exploit the fundamental sensitivity of modes of such cavities to perturbations, caused here by moving objects. We establish experimentally three key features of our proposed system: (i) ability to capture the temporal variations of motion and discern information such as periodicity ("smart"), (ii) non line-of-sight motion detection, and (iii) single-frequency operation. Moreover, we explain theoretically and demonstrate experimentally that the use of dynamic metasurface apertures can substantially enhance the performance of RF motion detection. Potential applications include accurately detecting human presence and monitoring inhabitants' vital signs.

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.

Slow waves in locally resonant metamaterials line defect waveguides.

Many efforts have been devoted to wave slowing, as it is essential, for instance, in analog signal computing and is one prerequisite for increased wave/matter interactions. Despite the interest of many communities, researches have mostly been conducted in optics, where wavelength-scaled structured composite media are promising candidates for compact slow light components. Yet their structural scale prevents them from being transposed to lower frequencies. Here, we propose to overcome this limitation using the deep sub-wavelength scale of locally resonant metamaterials. We experimentally show, in the microwave regime, that introducing coupled resonant defects in such metamaterials creates sub-wavelength waveguides in which wave propagation exhibit reduced group velocities. We qualitatively explain the mechanism underlying this slow wave propagation and demonstrate how it can be used to tune the velocity, achieving group indices as high as 227. We conclude by highlighting the three beneficial consequences of our line defect slow wave waveguides: (1) the sub-wavelength scale making it a compact platform for low frequencies (2) the large group indices that together with the extreme field confinement enables efficient wave/matter interactions and (3) the fact that, contrarily to other approaches, slow wave propagation does not occur at the expense of drastic bandwidth reductions.

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.

Smart optical coherence tomography for ultra-deep imaging through highly scattering media.

Multiple scattering of waves in disordered media is a nightmare whether it is for detection or imaging purposes. So far, the best approach to get rid of multiple scattering is optical coherence tomography. This basically combines confocal microscopy and coherence time gating to discriminate ballistic photons from a predominant multiple scattering background. Nevertheless, the imaging-depth range remains limited to 1 mm at best in human soft tissues because of aberrations and multiple scattering. We propose a matrix approach of optical imaging to push back this fundamental limit. By combining a matrix discrimination of ballistic waves and iterative time reversal, we show, both theoretically and experimentally, an extension of the imaging-depth limit by at least a factor of 2 compared to optical coherence tomography. In particular, the reported experiment demonstrates imaging through a strongly scattering layer from which only 1 reflected photon out of 1000 billion is ballistic. This approach opens a new route toward ultra-deep tissue imaging.

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.