Olivier Richoux

Perfect and broadband acoustic absorption by critically coupled sub-wavelength resonators

Perfect absorption is an interdisciplinary topic with a large number of applications, the challenge of which consists of broadening its inherently narrow frequency-band performance. We experimentally and analytically report perfect and broadband absorption for audible sound, by the mechanism of critical coupling, with a sub-wavelength multi-resonant scatterer (SMRS) made of a plate-resonator/closed waveguide structure. In order to introduce the role of the key parameters, we first present the case of a single resonant scatterer (SRS) made of a Helmholtz resonator/closed waveguide structure. In both cases the controlled balance between the energy leakage of the several resonances and the inherent losses of the system leads to perfect absorption peaks. In the case of the SMRS we show that systems with large inherent losses can be critically coupled using resonances with large leakage. In particular, we show that in the SMRS system, with a thickness of λ/12 and diameter of λ/7, several perfect absorption peaks overlap to produce absorption bigger than 93% for frequencies that extend over a factor of 2 in audible frequencies. The reported concepts and methodology provide guidelines for the design of broadband perfect absorbers which could contribute to solve the major issue of noise reduction.

Experiments on metasurface carpet cloaking for audible acoustics

We present experiments on acoustic carpet cloaking by using a metasurface made of graded Helmholtz resonators. The thin metasurface, placed over the object to hide, is designed such that the reflection phase shifts of the resonators at the resonance frequency are tuned to compensate the shape of the object to cloak. Experimental as well as numerical results show the efficiency of the cloak at the resonance frequency. The reflection of a short pulse is also reported to inspect the broadband character of the cloak.

Control of acoustic absorption in one-dimensional scattering by resonant scatterers

We experimentally report perfect acoustic absorption through the interplay of the inherent losses and transparent modes with high Q factor. These modes are generated in a two-port, one-dimensional waveguide, which is side-loaded by isolated resonators of moderate Q factor. In symmetric structures, we show that in the presence of small inherent losses, these modes lead to coherent perfect absorption associated with one-sided absorption slightly larger than 0.5. In asymmetric structures, near perfect one-sided absorption is possible (96%) with a deep sub-wavelength sample ( λ/28, where λ is the wavelength of the sound wave in the air). The control of strong absorption by the proper tuning of the radiation leakage of few resonators with weak losses will open possibilities in various wave-control devices.

Limits of slow sound propagation and transparency in lossy, locally resonant periodic structures

We investigate sound propagation in lossy, locally resonant periodic structures by studying an air-filled tube periodically loaded with Helmholtz resonators and taking into account the intrinsic viscothermal losses. In particular, by tuning the resonator with the Bragg gap in this prototypical locally resonant structure, we study the limits and various characteristics of slow sound propagation. While in the lossless case the overlapping of the gaps results in slow-sound-induced transparency of a narrow frequency band surrounded by a strong and broadband gap, the inclusion of the unavoidable losses imposes limits to the slowdown factor and the maximum transmission. Experiments, theory, and finite element simulations have been used for the characterization of acoustic wave propagation by tuning the Helmholtz/Bragg frequencies and the total amount of loss both for infinite and finite lattices. This study contributes to the field of locally resonant acoustic metamaterials and slow sound applications.

Use of complex frequency plane to design broadband and sub-wavelength absorbers

The reflection of sound of frequency below 1 kHz, by a rigid-backed structure that contains sub-wavelength resonators is studied in this work. In particular, only single mode reflected waves are considered, an approximation which is accurate in this low frequency regime. A method of analysis of absorption that uses the structure of the reflection coefficient in the complex frequency plane is proposed. In the absence of losses, the reflection coefficient supports pairs of poles and zeros that are complex conjugate and which have imaginary parts linked to the energy leakage by radiation. When losses are introduced and balanced to the leakage, the critical coupling condition is satisfied and total absorption is obtained. Examples of a slot resonator and of multiple Helmholtz resonators are analyzed to obtain both narrow and broadband total absorption.

Experimental demonstrations in audible frequency range of band gap tunability and negative refraction in two-dimensional sonic crystal

The propagation of audible acoustic waves in two-dimensional square lattice tunable sonic crystals (SC) made of square cross-section infinitely rigid rods embedded in air is investigated experimentally. The band structure is calculated with the plane wave expansion (PWE) method and compared with experimental measurements carried out on a finite extend structure of 200 cm width, 70 cm depth and 15 cm height. The structure is made of square inclusions of 5 cm side with a periodicity of L = 7.5 cm placed inbetween two rigid plates. The existence of tunable complete band gaps in the audible frequency range is demonstrated experimentally by rotating the scatterers around their vertical axis. Negative refraction is then analyzed by use of the anisotropy of the equi-frequency surface (EFS) in the first band and of a finite difference time domain (FDTD) method. Experimental results finally show negative refraction in the audible frequency range.

Tunable acoustic waveguides in periodic arrays made of rigid square-rod scatterers: theory and experimental realization

The tunable and the engineering possibilities of waveguides in periodic arrays made of rigid square-rod scatterers are theoretically and experimentally reported in this work. Due to the square shape of the scatterers, the control of their orientation with respect to the direction of the incident wave can be used for moulding the propagating acoustic waves inside the periodic structure. On the one hand, the plane wave expansion with supercell approximation is used to obtain the band structure of the periodic system. On the other hand, the scattering of waves in finite periodic arrays is analysed using the finite elements method. Experimentally, a prototype made of rigid square-rod scatterers is used to validate the theoretical predictions. A spatial-frequency filter and some applications in waveguiding for audible sound are discussed in this work. Good agreement between theory and experiments and the high tunability of the system are demonstrated. (Some figures may appear in colour only in the online journal)

Acoustic characterization of the Hofstadter butterfly with resonant scatterers

We are interested in the experimental characterization of the Hofstadter butterfly by means of acoustical waves. The transmission of an acoustic pulse through an array of 60 variable and resonant scatterers periodically distributed along a waveguide is studied. An arbitrary scattering arrangement is realized by using the variable length of each resonator cavity. For a periodic modulation, the structures of forbidden bands of the transmission reproduce the Hofstadter butterfly. We compare experimental, analytical, and computational realizations of the Hofstadter butterfly and we show the influence of the resonances of the scatterers on the structure of the butterfly.

Laser Doppler Velocimetry for Joint Measurements of Acoustic and Mean Flow Velocities: LMS-Based Algorithm and CRB Calculation

This paper presents a least-mean-square (LMS) algorithm for the joint estimation of acoustic and mean flow velocities from laser Doppler velocimetry (LDV) measurements. The usual algorithms used for measuring with LDV purely acoustic velocity or mean flow velocity may not be used when the acoustic field is disturbed by a mean flow component. The LMS-based algorithm allows accurate estimations of both acoustic and mean flow velocities. The Cramer-Rao bound (CRB) of the associated problem is determined. The variance of the estimators of both acoustic and mean flow velocities is also given. Simulation results of this algorithm are compared with the CRB, and the comparison leads us to validate this estimator.

Non-Hermitian acoustic metamaterials: Role of exceptional points in sound absorption

Effective non-Hermitian Hamiltonians are obtained to describe coherent perfect absorbing and lasing boundary conditions. PT -symmetry of the Hamiltonians enables to design configurations which perfectly absorb at multiple frequencies. Broadened and flat perfect absorption is predicted at the exceptional point of PT -symmetry breaking while, for a particular case, absorption is enhanced with the use of gain. The aforementioned phenomena are illustrated for acoustic scattering through Helmholtz resonators revealing how tailoring the non-Hermiticity of acoustic metamaterials leads to novel mechanisms for enhanced absorption.