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Publication# Acoustic metamaterial properties of a 2D closed cellular solid with entrained fluid

Résumé

Metamaterials are often defined as artificial compositions designed to exhibit desired physical properties. These materials attract a lot of research attention due to unusual behavior that may not yet have been seen in nature. Although there is no commonly accepted definition for metamaterials, they are typically associated with peculiar macroscale properties resulting from their substructure. The electromagnetic metamaterial concept was first developed in 1968. As the wave theory is similar in every field, the achievements in optics were reflected in acoustics several decades later. This allowed developing acoustic metamaterials with such extraordinary properties as negative refractive index, negative bulk modulus and mass density, acoustic lensing, sound wave spectral decomposition, and acoustic bandgaps. All of those features are not only attractive scientifically, but are of interest for plenty of potential applications, including sound and vibration insulation, waveguiding, audible and high-frequency filtering, and even seismic absorption. On the other hand, cellular solids and saturated porous media have been studied for a long time. These media are abundant in nature as granular soils, wood, rocks, bones, and foams. Wave analysis in such environments typically requires some crucial assumptions which do not allow extending a theory to other configurations. An example of such a constraint is the openness of the cells in a medium. Many porous media applications are found in geophysics - particularly gas and oil extractions - the permeability of the cells plays an important role. The ad-hoc dynamic models for such media operate only with open-cell configuration. Moreover, the study is limited to the low-frequency analysis, omitting the influence of wave scattering. The latter, however, is the key source of dispersion in acoustic metamaterials. Scattering may have two origins, geometrical or resonant. Bragg's scattering is determined by the geometrical configuration, such that constructive interference occurs only when the incident wave matches the characteristic size of a unit cell. This makes such systems practically inconvenient. The concept of resonant scattering, introduced about a decade ago, has much fewer limitations and is mostly determined by the dynamics of matrix inclusions. In this thesis, a closed-cell cellular solid with thin vibrating walls and fluid-filled cells is proposed as a new class of acoustic metamaterials. First, the dynamics of a prototypical square cell is investigated numerically considering periodic boundary conditions and taking into account fluid-structure interaction. The results are compared to Biot's theory of saturated porous media in the limit of a closed-cells system. The proposed configuration is studied with respect to dispersion sources, showing the presence of local resonant behavior for different combinations of relative density and entrained fluid. Surprisingly, semi-analytical models can be used to provide a bottom-up explanation of the structure's dynamic behavior. The presence of two pressure waves, slow and fast, is confirmed numerically and analytically. Finally, an experimental proof-of-concept was carried out. Periodic cellular solids represent a versatile acoustic metamaterial platform characterized by low cost, simple, scalable design, which makes possible achieving the desired macroscopic behavior using different types of fluids and bulk materials.

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Publications associées (19)

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Romain Christophe Rémy Fleury, Nadège Sihame Kaïna, Bakhtiyar Orazbayev

Recent advances in the field of metamaterials have shown that waves can be efficiently manipulated at the subwavelength scale through the interactions with an ensemble of resonant inclusions, opening new horizons in overcoming the size limits of devices which are often tied to the wavelength of operation [1]. Such size limit is crucial for many applications where the overall dimensions are required to be as small as possible, for instance cost-eﬃcient devices for satellite communications. Unfortunately, the resonant inclusions of these artificial media result in a large sensitivity of the propagation to geometrical imperfections and disorder-induced backscattering, reducing their performance. More recently, it has been demonstrated that the topological concepts which originated in solid-state physics can be transferred to not only to photonic crystals [3,4], which still scale with the operating wavelength, but also to locally-resonant crystalline metamaterials, which can have a deeply subwavelength structure [5]. However, since the topological properties in such time-reversal invariant designs heavily rely on the lattice structure of the media and frequency dispersion of the metamaterial, they are inevitably sensitive to any disruption of the lattice symmetries that can couple time-reversed modes. Moreover, since most of disorders (in the location or in resonance frequency of the resonant inclusions) will most likely break the lattice symmetry and disrupt the wave propagation, these time-reversal invariant topological designs are also in principle sensitive to defects. In this talk, we will show that a chiral metamaterial [6,7] can be exploited to create a robust-to-disorder subwavelength waveguide and we will demonstrate this possibility experimentally in the microwave regime. Moreover, we will quantitatively demonstrate the superior robustness of the proposed design to both spatial or frequency disorders by performing ensemble averages on disorder realizations along the path of the guided wave, and comparing them with previously proposed subwavelength waveguide designs: frequency defect lines, symmetry-based topological edge modes and valley interface states. [1] J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, Princeton, 2008), 2nd ed. [2] N. Kaina, F. Lemoult, M. Fink, and G. Lerosey, Negative Refractive Index and Acoustic Superlens from Multiple Scattering in Single Negative Metamaterials, Nature, 525, 77 (2015). [3] S. Raghu and F. D. M. Haldane, Analogs of Quantum-Hall-Effect Edge States in Photonic Crystals, Phys. Rev. A - At. Mol. Opt. Phys., 78, 1 (2008). [4] Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, Observation of Unidirectional Backscattering-Immune Topological Electromagnetic States., Nature, 461, 772 (2009). [5] S. Yves, R. Fleury, T. Berthelot, M. Fink, F. Lemoult, and G. Lerosey, Crystalline Metamaterials for Topological Properties at Subwavelength Scales, Nat. Commun., 8, 16023 (2017). [6] M. Goryachev and M. E. Tobar, Reconfigurable Microwave Photonic Topological Insulator, Phys. Rev. Appl., 6, 1 (2016). [7] J. E. Vázquez-Lozano and A. Martínez, Optical Chirality in Dispersive and Lossy Media, Phys. Rev. Lett., 121, 43901 (2018).

2019Romain Christophe Rémy Fleury, Ali Momeni, Mahdi Safari

We propose a bianisotropic hybrid metal-dielectric structure comprising dielectric and metallic cylindrical wedges wherein the composite metacylinder enables advanced control of electric, magnetic, and magnetoelectric resonances. We establish a theoretical framework in which the electromagnetic response of this meta-atom is described through the electric and magnetic multipole moments. The complete dynamic polarizability tensor, expressed in a compact form, is derived as a function of the Mie-scattering coefficients. Further, the constitutive parameters—determined analytically—illustrate the tunability of the structure’s frequency and strength of resonances in light of its high degree of geometric freedom. Flexibility in the design makes the proposed metacylinder a viable candidate for various applications in the microscopic (single meta-atom) and macroscopic (metasurface) levels. We show that the highly versatile bianisotropic meta-atom is amenable to being designed for the desired electromagnetic response, such as electric dipole-free and zero or near-zero (backward and forward) scattering at the microscopic level. In addition, we show that the azimuthal asymmetry gives rise to normal polarizability components, which are vital elements in synthesizing asymmetric optical transfer function at the macroscopic level. We conduct a precise inspection, from the microscopic to the macroscopic level, of the metasurface synthesis for emphasizing on the role of normal polarizability components for spatial optical signal processing. It is shown that this simple two-dimensional asymmetric meta-atom can perform first-order differentiation and edge detection at normal illumination. The results reported herein contribute toward improving the physical understanding of wave interaction with artificial materials composed of asymmetric elongated metal-dielectric inclusions and open the potential of its application in spatial signal and image processing.

2021Metamaterials (MTMs) are broadly defined as artificial composite materials specifically engineered to produce desired unusual electromagnetic properties not readily available in nature. The most interesting unusual property achievable with MTMs is probably negative refraction, which is achieved when both the permittivity and the permeability of a medium are negative. Such structures are also referred to as left-handed media (LHM). From the first evidences in the early 2000's showing that materials with a negative refractive index were indeed physically realizable, numerous entirely new devices or improvements of existing devices have been reported in the microwave and antenna fields. In this context, the objective of this thesis is to contribute to the development of new characterization techniques for practical implementations of MTMs, aiming at determining a set of relevant equivalent medium parameters describing the structure from a macroscopic point of view. For this purpose, analysis techniques were developed based on the theory of wave propagation in periodic structures, and tested on selected existing or entirely new MTM structures of the two main reported categories: arrays of resonant particles and loaded transmission lines. In the first part of the work, an improved retrieval procedure which allows the determination of equivalent dyadic permittivity and permeability of MTMs from reflection and transmission coefficients obtained for several incidences was developed and tested, thereby extending current techniques which only dealt with normal incidence. The main achievement obtained with this technique is the ability to evaluate to which extent a given MTM slab can be considered as an equivalent homogeneous medium obeying some specific constitutive relations. This technique was tested on various structures, including a novel highly isotropic artificial magnetic material which was shown to exhibit a negative permeability in the three dimensions. In a second step, MTMs based on the transmission line approach have been investigated. In this context, the theory of the so-called composite right/left-handed transmission line (CRLH TL) has been revisited, and several planar implementations of this structure in various technologies were designed and realized. Subsequently, a volumetric LHM obtained by layering several planar artificial TLs of the CRLH type was proposed and fully characterized. This volumetric structure was shown to support left-handed propagation over a quite large bandwidth, compared to other resonant LHM made of split-ring resonators and wires. We provided an extensive experimental assessment of potential applications of this structure as an exotic substrate for microstrip patch antennas. An important contribution here consisted in the assessment of the ability of such a volumetric structure based on the TL approach to behave as a material filling in this type of configurations. The next part presents an enhanced analysis technique for periodic structures which allows accurately characterizing MTMs exhibiting higher order coupling phenomena between successive cells. This technique also allows an accurate and complete description of more elaborated structures such as periodically loaded multiconductor TLs. The main idea of this technique is to model the periodic structure with an equivalent multiconductor TL, a model which provides all the parameters needed to describe the phase response (dispersion) and terminations (excitation and matching) of finite size periodic structures. In the last part, we introduced and analyzed a novel unit cell topology for the CRLH TL which employs a lattice network in place of the conventional ladder-type topology. This new CRLH TL was shown to exhibit a more wideband behaviour than its conventional counterpart, both in terms of impedance and phase. These performances were numerically and experimentally demonstrated on several practical implementations. The possibilities of using this unit cell to reduce the beam squinting in leaky-wave antennas and in series-fed arrays were highlighted. It is foreseen that this new CRLH TL can be potentially used to improve the performances of many of the well-known CRLH TL applications.