Slow waves in locally resonant metamaterials line defect waveguides

In the past decades, many efforts have been devoted to the temporal manipulation of waves, especially focusing on slowing down their propagation. In electromagnetism, from microwave to optics, as well as in acoustics or for elastic waves, slow wave propagation indeed largely benefits both applied and fundamental physics. It is for instance essential in analog signal computing through the design of components such as delay lines and buffers, and it is one of the prerequisite for increased wave/matter interactions. Despite the interest of a broad community, researches have mostly been conducted in optics along with the development of wavelength scaled structured composite media, that appear promising candidates for compact slow light components. Yet their minimum structural scale prevents them from being transposed to lower frequencies where wavelengths range from sub-millimeter to meters. In this article, we propose to overcome this limitation thanks to the deep sub-wavelength scale of locally resonant metamaterials. In our approach, implemented here in the microwave regime, we show that introducing coupled resonant defects in such composite media allows the creation of deep sub-wavelength waveguides. We experimentally demonstrate that waves, while propagating in such waveguides, exhibit largely reduced group velocities. We qualitatively explain the mechanism underlying this slow wave propagation and first experimentally demonstrate, then numerically verify, how it can be taken advantage of to tune the velocity, achieving group indices ng as high as 227 over relatively large bandwidths. We conclude by highlighting the three beneficial consequences of our line defect slow wave waveguides in locally resonant metamaterials: the deep sub-wavelength scale, the very large group indices and the fact that slow wave propagation does not occur at the expense of drastic bandwidth reductions

Métamatériaux localement résonants : cristaux photoniques et phononiques sub-longueur d’onde

This thesis deals with the control of the wave propagation at deep sub-wavelength scales in locally resonant metamaterials. Those composite media are composed of small resonators arranged on spatial scales much smaller than their typical wavelength at resonance. They are hence generally considered as homogeneous media and described with effective parameters. We here prove that, going beyond those homogenization approaches, the properties of most metamaterials can be reinterpreted at the light of a microscopic approach. The latter evidences that the wave propagation in metamaterials only results from phenomenon analog to what happens in photonic/phononic crystals: namely interferences and multiple scattering. We hence demonstrate that concepts developed for wave manipulation in photonic/phononic crystals can be transposed in metamaterials while taking advantage of the latter sub-wavelength spatial organization. For instance, locally modifying the medium, at the scale of the unit cell, creates cavities and waveguides confining and guiding waves on dimensions that are independent of the wavelength. We further study the possibility offered by those waveguides to both mold and slow down the flow of waves. We finally highlight the importance of the spatial subwavelength structuration of metamaterials due to the presence of multiple scattering. We prove that a so-called single negative metamaterial (presenting only one negative effective property) can be turned into a double negative one (hence presenting a negative index of refraction), simply by smartly organizing the building blocks of the metamaterial, at scales much smaller than the wavelength.Cette thèse traite du contrôle de la propagation des ondes, électromagnétiques et acoustiques, à l’échelle sub-longueur d’onde dans les métamatériaux localement résonants. Ces derniers sont des matériaux composites composés d’ensembles de résonateurs agencés sur des périodes très petites comparées aux longueurs d’ondes caractéristiques de résonance. Ils sont en général considérés comme des milieux homogènes aux propriétés effectives. Nous prouvons que, au-delà de ces approches communes d’homogénéisation, les propriétés de la plupart des métamatériaux peuvent être réinterprétées à lumière d’une approche microscopique. Celle-ci permet de mettre en évidence que la propagation des ondes dans ces métamatériaux résulte de phénomènes physiques analogues à ceux mis en jeu dans les cristaux photoniques/phononiques : des interférences et de la diffusion multiple. Nous prouvons alors que les concepts de manipulation des ondes développés dans les cristaux photoniques, sont transposables aux métamatériaux, bénéficiant alors des avantages de la structuration sub-longueur d’onde. Nous montrons que des modifications locales du milieu induisent la formation de cavité et guides d’ondes confinant et guidant le champ sur des dimensions arbitrairement plus petites que la longueur d’onde. Nous étudions la capacité de ces guides à manipuler le flux d’onde spatialement et temporellement. Nous soulignons enfin l’importance de la structure microscopique des métamatériaux, jusque-là toujours négligée. Nous prouvons qu’un métamatériau dit simplement négatif (avec une seule propriété effective négative) peut présenter un indice de réfraction négatif simplement en le structurant ingénieusement

Chiral Waveguides for Robust Waveguiding at the Deep Subwavelength Scale

Routing electromagnetic energy at a scale smaller than the wavelength is a highly sought functionality in a variety of applications, including compact lightweight satellite communications, slow-waves sensors, all-optical information processing, and energy harvesting. Unfortunately, strong field confinement at this scale requires the use of coupled subwavelength resonators, implying a large sensitivity to geometrical imperfections and disorder-induced backscattering. We propose a very unconventional solution to this problem by exploiting the interface modes occurring at the boundary between two chiral metamaterials composed of resonant metamolecules with opposite chirality. Our numerical and experimental results demonstrate the inherent robustness of these interface states to disorder in both the position and resonance frequency of the metamaterial’s meta-atoms. By computing transmission averages over many realizations of disorder, we quantitatively demonstrate the superiority of this form of subwavelength routing over previously proposed designs, including frequency-defect lines, symmetry-based topological edge modes, and Valley-Hall interface states

Soda Cans Metamaterial: A Subwavelength-Scaled Phononic Crystal

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