Hermitian formulation of multiple scattering induced topological phases in metamaterial crystals

In this article we develop an analog to the SSH model in tight-binding chains of resonators and an innovative Hermitian matrix formulation to describe the topological phases induced by multiple scattering at subwavelength scales in one-dimensional structured and locally resonant metamaterial crystals. We first start from a set of coupled dipole equations capturing the nature of the wave-matter interactions, i.e., hybridization between locally dispersive resonances and a continuum as well as infinite long range multiple scattering coupling, to analytically derive a matrix operator H MS , which is found to be Hermitian when evaluated on propagative bands. This new operator straightforwardly highlights how the composition, structure, scattering resonance, and Bloch periodicity together set in the chain macroscopic properties, in particular its topology. We analytically confirm the existence of a structure based topological transition in chiral-symmetric biperiodic metamaterial crystal chains, characterized by a winding number. We further demonstrate that chiral symmetry breaking in metamaterial crystal chains prevents us from defining a proper topological invariant. We finally numerically confirm, in the microwave domain, the existence of the topological transition in a chiral symmetric metamaterial crystal chain through the study of topological interface modes and their robustness to disorder.

Exploiting the leaky-wave properties of transmission-line metamaterials for single-microphone direction finding

Sami Driss Karkar, Hervé Lissek, Juan Ramon Mosig, Seyyed Hussein Seyyed Esfahlani

A transmission-line acoustic metamaterial is an engineered, periodic arrangement of relatively small unit-cells, the acoustic properties of which can be manipulated to achieve anomalous physical behaviours. These exotic properties open the door to practical applications, such as an acoustic leaky-wave antenna, through the implementation of radiating channels along the metamaterial. In the transmitting mode, such a leaky-wave antenna is capable of steering sound waves in frequency-dependent directions. Used in reverse, the antenna presents a well defined direction-frequency behaviour. In this paper, an acoustic leaky-wave structure is presented in the receiving mode. It is shown that it behaves as a sound source direction-finding device using only one sensor. After a general introduction of the acoustic leaky-wave antenna concept, its radiation pattern and radiation efficiency are expressed in closed form. Then, numerical simulations and experimental assessments of the proposed transmission-line based structure, implementing only one sensor at one termination, are presented. It is shown that such a structure is capable of finding the direction of an incoming sound wave, from backward to forward, based on received sound power spectra. This introduces the concept of sound source localization without resorting to beam-steering techniques based on multiple sensors.

2016

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

Vladimir Dorodnitsyn

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.

EPFL2016

Chiral Metamaterials for a Robust Waveguiding Scheme

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).