Spatiotemporal Wave Front Shaping in a Microwave Cavity. Del Hougne, P., F. Lemoult, M. Fink, and G. Lerosey. Physical Review Letters 117, no. 13 (2016).


Exploiting spatiotemporal degrees of freedom for farfield subwavelength focusing using time reversal in fractals. Dupré, M., F. Lemoult, M. Fink, and G. Lerosey. Physical Review B – Condensed Matter and Materials Physics 93, no. 18 (2016).
Résumé: © 2016 American Physical Society. Materials which possess a high local density of states varying at a subwavelength scale theoretically permit the focusing of waves onto focal spots much smaller than the free space wavelength. To do so, metamaterials – manmade composite media exhibiting properties not available in nature – are usually considered. However, this approach is limited to narrow bandwidths due to their resonant nature. Here, we prove that it is possible to use a fractal resonator alongside time reversal to focus microwaves onto λ/15 subwavelength focal spots from the far field, on extremely wide bandwidths. We first numerically prove that this approach can be realized using a multiplechannel time reversal mirror that utilizes all the degrees of freedom offered by the fractal resonator. Then, we experimentally demonstrate that this approach can be drastically simplified by coupling the fractal resonator to a complex medium, here a cavity, that efficiently converts its spatial degrees of freedom into temporal ones. This makes it possible to achieve deep subwavelength focusing of microwave radiation by time reversing a single channel. Our method can be generalized to other systems coupling complex media and fractal resonators.


Negative refractive index and acoustic superlens from multiple scattering in single negative metamaterials. Kaina, N., F. Lemoult, M. Fink, and G. Lerosey. Nature 525, no. 7567 (2015): 77–81.


Acoustic double negativity induced by position correlations within a disordered set of monopolar resonators. Lanoy, M., J. H. Page, G. Lerosey, F. Lemoult, A. Tourin, and V. Leroy. Physical Review B 96, no. 22 (2017).
Résumé: © 2017 American Physical Society. Using a multiple scattering theory algorithm, we investigate numerically the transmission of ultrasonic waves through a disordered locally resonant metamaterial containing only monopolar resonators. By comparing the cases of a perfectly random medium with its pair correlated counterpart, we show that the introduction of short range correlation can substantially impact the effective parameters of the sample. We report, notably, the opening of an acoustic transparency window in the region of the hybridization band gap. Interestingly, the transparency window is found to be associated with negative values of both effective compressibility and density. Despite this feature being unexpected for a disordered medium of monopolar resonators, we show that it can be fully described analytically and that it gives rise to negative refraction of waves.


Subwavelength focusing in bubbly media using broadband time reversal. Lanoy, M., R. Pierrat, F. Lemoult, M. Fink, V. Leroy, and A. Tourin. Physical Review B 91, no. 22 (2015).


Soda cans metamaterial: A subwavelengthscaled phononic crystal. Lemoult, F., N. Kaina, M. Fink, and G. Lerosey. Crystals 6, no. 7 (2016).
Résumé: © 2016 by the authors; licensee MDPI, Basel, Switzerland.Photonic or phononic crystals and metamaterials, due to their very different typical spatial scales—wavelength and deep subwavelength—and underlying physical mechanisms—Bragg interferences or local resonances—, are often considered to be very different composite media. As such, while the former are commonly used to manipulate and control waves at the scale of the unit cell, i.e., wavelength, the latter are usually considered for their effective properties. Yet we have shown in the last few years that under some approximations, metamaterials can be used as photonic or phononic crystals, with the great advantage that they are much more compact. In this review, we will concentrate on metamaterials made out of soda cans, that is, Helmholtz resonators of deep subwavelength dimensions. We will first show that their properties can be understood, likewise phononic crystals, as resulting from interferences only, through multiple scattering effects and Fano interferences. Then, we will demonstrate that below the resonance frequency of its unit cell, a soda can metamaterial supports a band of subwavelength varying modes, which can be excited coherently using time reversal, in order to beat the diffraction limit from the far field. Above this frequency, the metamaterial supports a band gap, which we will use to demonstrate cavities and waveguides, very similar to those obtained in phononic crystals, albeit of deep subwavelength dimensions. We will finally show that multiple scattering can be taken advantage of in these metamaterials, by correctly structuring them. This allows to turn a metamaterial with a single negative effective property into a negative index metamaterial, which refracts waves negatively, hence acting as a superlens.
MotsClés: Acoustics; Metamaterial; Multiple scattering; Phononic crystals


Experimental Demonstration of Ordered and Disordered Multiresonant Metamaterials for Lamb Waves. Rupin, M., F. Lemoult, G. Lerosey, and P. Roux. Physical Review Letters 112, no. 23 (2014).


Symmetry issues in the hybridization of multimode waves with resonators: An example with Lamb waves metamaterial. Rupin, M., P. Roux, G. Lerosey, and F. Lemoult. Scientific Reports 5 (2015).
Résumé: 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 crosssections. 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 A 0 and S 0 Lamb waves that propagate in a thin plate are good candidates for this study, as they are either antisymmetric 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 A 0/S 0 modes of the freeplate. 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.


Measuring Dirac Cones in a Subwavelength Metamaterial. Yves, S., T. Berthelot, M. Fink, G. Lerosey, and F. Lemoult. Physical Review Letters 121, no. 26 (2018).
Résumé: © 2018 American Physical Society. 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 tightbinding 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 solidstate physics offer.


Lefthanded band in an electromagnetic metamaterial induced by subwavelength multiple scattering. Yves, S., T. Berthelot, M. Fink, G. Lerosey, and F. Lemoult. Applied Physics Letters 114, no. 11 (2019).
Résumé: © 2019 Author(s). Due to the deep subwavelength unit cell in metamaterials, the quasistatic approximation is usually employed to describe the propagation. By making pairs of resonators, we highlight that multiple scattering also occurs at this scale and results in the existence of a dipolar resonance, which leads to a negative index of refraction when we consider several resonators. We experimentally verify the possibility of obtaining a negative index of refraction in periodic metamaterials in two different ways and eventually demonstrate the subwavelength recovery of several point sources in both cases.


Crystalline metamaterials for topological properties at subwavelength scales. Yves, S., R. Fleury, T. Berthelot, M. Fink, F. Lemoult, and G. Lerosey. Nature Communications 8 (2017).
Résumé: The exciting discovery of topological condensed matter systems has lately triggered a search for their photonic analogues, motivated by the possibility of robust backscatteringimmune 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.


Topological acoustic polaritons: Robust sound manipulation at the subwavelength scale. Yves, S., R. Fleury, F. Lemoult, M. Fink, and G. Lerosey. New Journal of Physics 19, no. 7 (2017).
Résumé: © 2017 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. Topological insulators, a hallmark of condensed matter physics, have recently reached the classical realm of acoustic waves. A remarkable property of timereversal invariant topological insulators is the presence of unidirectional spinpolarized propagation along their edges, a property that could lead to a wealth of new opportunities in the ability to guide and manipulate sound. Here, we demonstrate and study the possibility to induce topologically nontrivial acoustic states at the deep subwavelength scale, in a structured twodimensional metamaterial composed of Helmholtz resonators. Radically different from previous designs based on nonresonant sonic crystals, our proposal enables robust sound manipulation on a surface along predefined, subwavelength pathways of arbitrary shapes.
MotsClés: acoustic metamaterials; polaritons; quantum spin Hall effect; topological insulators


Crystalline Soda Can Metamaterial exhibiting Graphenelike Dispersion at subwavelength scale. Yves, S., F. Lemoult, M. Fink, and G. Lerosey. Scientific Reports 7, no. 1 (2017).
Résumé: © 2017 The Author(s). Graphene, a honeycomb lattice of carbon atoms ruled by tightbinding 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 sublattice generates a bandgap at low frequency, which induces a tightbinding coupling between the resonant defects of the second honeycomb one, hence allowing us to obtain a graphenelike 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 solidstate physics phenomena with classical waves.


WaveField Shaping in Cavities: Waves Trapped in a Box with Controllable Boundaries. Dupré, M., P. Del Hougne, M. Fink, F. Lemoult, and G. Lerosey. Physical Review Letters 115 (2015): 017701.


Ultra small mode volume defect cavities in spatially ordered and disordered metamaterials. Kaina, N., F. Lemoult, M. Fink, and G. Lerosey. Applied Physics Letters 102, no. 14 (2013).
Résumé: In this letter, we study metamaterials made out of resonant electric wires arranged on a spatial scale much smaller than the free space wavelength, and we show that they present a hybridization band that is insensible to positional disorder. We experimentally demonstrate defect cavities in disordered and ordered samples and prove that, analogous to those designed in photonic crystals, those cavities can present very high quality factors. In addition, we show that they display mode volumes much smaller than a wavelength cube, owing to the deep subwavelength nature of the unit cell. We underline that this type of structure can be shrunk down to a period close of a few skin depth. Our approach paves the way towards the confinement and manipulation of waves at deep subwavelength scales in both ordered and disordered metamaterials. © 2013 AIP Publishing LLC.
MotsClés: Defect cavity; Display modes; Freespace wavelengths; High quality factors; Positional disorder; Spatial scale; Subwavelength; Subwavelength scale; Defects; Metamaterials


Acoustic resonators for farfield control of sound on a subwavelength scale. Lemoult, F., M. Fink, and G. Lerosey. Physical Review Letters 107, no. 6 (2011).
Résumé: 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 diffractionlimited 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. © 2011 American Physical Society.
MotsClés: Acoustic pressures; Diffraction limited; Farfield; Focal spot; Helmholtz resonators; Sensors and actuators; Strong enhancement; Subdiffraction; Subwavelength; Subwavelength scale; Visual experiments; Acoustic fields; Resonators; Acoustic resonators


Farfield subwavelength imaging and focusing using a wire medium based resonant metalens. Lemoult, F., M. Fink, and G. Lerosey. Waves in Random and Complex Media 21, no. 4 (2011): 614–627.
Résumé: This is the second article in a series of two dealing with the concept of a 'resonant metalens' we introduced recently. This is a new type of lens capable of coding in time and radiating efficiently in the farfield region subdiffraction information about an object. A proof of the concept of such a lens is performed in the microwave range, using a medium made out of a square lattice of parallel conducting wires with finite length. We investigate a subwavelength focusing scheme with time reversal and demonstrate experimentally spots with focal widths of λ /25. Through a crosscorrelation based imaging procedure we show an image reconstruction with a resolution of λ/80. Eventually we discuss the limitations of such a lens which reside essentially in losses. © 2011 Taylor & Francis.
MotsClés: Conducting wire; Cross correlations; Farfield; Farfield region; Finite length; MetaLens; Square lattices; Subdiffraction; Subwavelength; Time reversal; Wire medium; Image reconstruction; Wire; Focusing


Revisiting the wire medium: An ideal resonant metalens. Lemoult, F., M. Fink, and G. Lerosey. Waves in Random and Complex Media 21, no. 4 (2011): 591–613.
Résumé: This article is the first one in a series of two dealing with the concept of a 'resonant metalens' we introduced recently. Here, we focus on the physics of a medium with finite dimensions consisting of a square lattice of parallel conducting wires arranged on a subwavelength scale. This medium supports electromagnetic fields that vary much faster than the operating wavelength. We show that such modes are dispersive due to the finiteness of the medium. Their dispersion relation is established in a simple way, a link with designer plasmons is made, and the canalization phenomenon is reinterpreted in the light of our model. We explain how to take advantage of this dispersion in order to code subwavelength wavefields in time. Finally, we show that the resonant nature of the medium ensures an efficient coupling of these modes with free space propagating waves and, thanks to the Purcell effect, with a source placed in the near field of the medium. © 2011 Taylor & Francis.
MotsClés: Conducting wire; Dispersion relations; Efficient coupling; Finite dimensions; Free space; MetaLens; Near fields; Operating wavelength; Purcell effect; Square lattices; Subwavelength; Wavefields; Wire medium; Electromagnetic fields; Wire; Dispersion (waves)


A polychromatic approach to farfield superlensing at visible wavelengths. Lemoult, F., M. Fink, and G. Lerosey. Nature Communications 3 (2012).
Résumé: Breaking the diffraction barrier in the visible part of the electromagnetic spectrum is of fundamental importance. Farfield subwavelength focusing of light could, for instance, drastically broaden the possibilities available in nanolithography, lightmatter 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. © 2012 Macmillan Publishers Limited. All rights reserved.
MotsClés: nanomaterial; nanorod; article; diffraction; electromagnetic field; electromagnetic radiation; imaging system; lens; light; polychromatic light; spectral sensitivity


Wave propagation control at the deep subwavelength scale in metamaterials. Lemoult, F., N. Kaina, M. Fink, and G. Lerosey. Nature Physics 9, no. 1 (2013): 55–60.
Résumé: The ability to control wave propagation is of fundamental interest in many areas of physics. Photonic crystals proved very useful for this purpose but, because they are based on Bragg interferences, these artificial media require structures with large dimensions. Metamaterials, on the other hand, can exhibit very deep subwavelength spatial scales. In general they are studied for their bulk effective properties that lead to effects such as negative refraction. Here we go beyond this effective medium paradigm and we use a microscopic approach to study metamaterials based on resonant unit cells. We show that we can tailor unit cells locally to shape the flow of waves at deep subwavelength scales. We validate our approach in experiments with both electromagnetic and acoustic waves in the metre range demonstrating cavities, waveguides, corners and splitters with centimetrescale dimensions, an order of magnitude smaller than previous proposals. © 2013 Macmillan Publishers Limited.


Manipulating Spatiotemporal Degrees of Freedom of Waves in Random Media. Lemoult, F., G. Lerosey, J. De Rosny, and M. Fink. Physical Review Letters 103, no. 17 (2009).
Résumé: 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. © 2009 The American Physical Society.
MotsClés: Complex media; Complex medium; Degrees of freedom; Number of degrees of freedom; Waves in random media; Ultrasonics; Mechanics


Resonant metalenses for breaking the diffraction barrier. Lemoult, F., G. Lerosey, J. De Rosny, and M. Fink. Physical Review Letters 104, no. 20 (2010).
Résumé: 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. © 2010 The American Physical Society.
MotsClés: Diffraction barrier; Diffraction limits; Far field; MetaLens; Purcell effect; Subwavelength; Subwavelength resonators; Temporal signatures; Underlying mechanism; Wavefields; Resonators


Time reversal in subwavelengthscaled resonant media: Beating the diffraction limit. Lemoult, F., A. Ourir, J. De Rosny, A. Tourin, M. Fink, and G. Lerosey. International Journal of Microwave Science and Technology (2011).
Résumé: Time reversal is a physical concept that can focus waves both spatially and temporally regardless of the complexity of the propagation medium. Time reversal mirrors have been demonstrated first in acoustics, then with electromagnetic waves, and are being intensively studied in many fields ranging from underwater communications to sensing. In this paper, we will review the principles of time reversal and in particular its ability to focus waves in complex media. We will show that this focusing effect depends on the complexity of the propagation medium rather than on the time reversal mirror itself. A modal approach will be utilized to explain the physical mechanism underlying the concept. A particular focus will be given on the possibility to break the diffraction barrier from the far field using time reversal. We will show that finite size media made out of coupled subwavelength resonators support modes which can radiate efficiently in the far field spatial information of the near field of a source. We will show through various examples that such a process, due to reversibility, permits to beat the diffraction limit using far field time reversal, and especially that this result occurs owing to the broadband inherent nature of time reversal. © 2011 Fabrice Lemoult et al.


Superabsorption of acoustic waves with bubble metascreens. Leroy, V., A. Strybulevych, M. Lanoy, F. Lemoult, A. Tourin, and J. H. Page. Physical Review B 91 (2015): 020301.
Résumé: A bubble metascreen, i.e., a single layer of gas inclusions in a soft solid, can be modeled as an acoustic open resonator, whose behavior is well captured by a simple analytical expression. We show that by tuning the parameters of the metascreen, acoustic superabsorption can be achieved over a broad frequency range, which is confirmed by finite element simulations and experiments. Bubble metascreens can thus be used as ultrathin coatings for turning acoustic reflectors into perfect absorbers.


Far field subwavelength imaging of magnetic patterns. Ourir, A., G. Lerosey, F. Lemoult, M. Fink, and J. De Rosny. Applied Physics Letters 101, no. 11 (2012).
Résumé: Far field imaging of subwavelength magnetic objects in real time is a very challenging issue. We propose an original solution based on a planar array of closely spaced split ring resonators. Hybridization between the resonators of such metalens induces subwavelength modes with different frequencies. Thanks to these high Q resonating modes, Purcell like effect allows an evanescent source, close to the metalens, to emit waves that can be collected efficiently in the far field. We present the first microwave experimental demonstration of such metalens to image of a subwavelength magnetic pattern. Numerical simulation shows that this approach is still valid at THz frequencies. © 2012 American Institute of Physics.
MotsClés: Different frequency; Far field; Farfield imaging; Magnetic patterns; MetaLens; Planar arrays; Real time; Split ring resonator; Subwavelength; Subwavelength imaging; THz frequencies; Physical properties; Physics

