Perfect Resonant Absorption of Guided Water Waves by Autler-Townes Splitting.

The control of guided water wave propagation based on the Autler-Townes splitting resonance concept is demonstrated experimentally, numerically, and theoretically. Complete wave absorption is achieved using an asymmetric pointlike scatterer made of two closely spaced resonant side channels connected to a guide and designed so that its energy leakage is in perfect balance with the inherent viscous losses in the system. We demonstrate that the nature of the resonators and guide junction completely controls the positions of the wave numbers at the reflection and transmission zeros on the real axis; the asymmetry of the resonators completely controls their positions on the imaginary axis. Thus, by adjusting these two independent parameters, we obtain a zero reflection and transmission.

Hidden Symmetries in Acoustic Wave Systems.

Latent symmetries are hidden symmetries which become manifest by performing a reduction of a given discrete system into an effective lower-dimensional one. We show how latent symmetries can be leveraged for continuous wave setups in the form of acoustic networks. These are systematically designed to possess latent-symmetry induced pointwise amplitude parity between selected waveguide junctions for all low frequency eigenmodes. We develop a modular principle to interconnect latently symmetric networks to feature multiple latently symmetric junction pairs. By connecting such networks to a mirror symmetric subsystem, we design asymmetric setups featuring eigenmodes with domain-wise parity. Bridging the gap between discrete and continuous models, our work takes a pivotal step towards exploiting hidden geometrical symmetries in realistic wave setups.

Scattering by Finite Periodic PT-Symmetric Structures.

In this work, we study the transmission properties of one-dimensional finite periodic systems with PT symmetry. A simple closed-form expression is obtained for the total transmittance from a lattice of N cells, that allows us to describe the transmission minima (maxima) when the system is in the PT-unbroken (broken) phase. Utilizing this expression, we provide the necessary conditions, independent of the number of cells, for the occurrence of a coherent perfect absorber and laser for any finite PT-symmetric periodic potential. Under these conditions, we provide a recipe for building finite periodic structures with near perfect absorption and extremely large amplification.

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.

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.

Experimental realization of a water-wave metamaterial shifter.

We demonstrate by quantitative experimental measurements that metamaterials with anisotropic properties can be used in the context of water waves to produce a reflectionless bent waveguide. The anisotropic medium consists in a bathymetry with subwavelength layered structure that shifts the wave in the direction of the waveguide bending (10°, 20°, and 30°). The waveguide filled with such metamaterial is tested experimentally and compared to a reference empty bent waveguide. The experimental method used to characterize the wave field allows for space-time resolved measurements of water elevation. Results show the efficiency of the shifter. Modal treatment of the experimental data confirms that the metamaterial prevents higher modes from being excited in the waveguide.

Time reversal of water waves.

We present time reversal experiments demonstrating refocusing of gravity-capillary waves in a water tank cavity. Owing to the reverberating effect of the cavity, only a few channels are sufficient to reconstruct the surface wave at the point source, even if the absorption is not negligible. Space-time-resolved measurements of the waves during the refocusing allow us to quantitatively demonstrate that the quality of the refocusing increases linearly with the number of reemitting channels. Numerical simulations corresponding to water waves at larger scales, with negligible damping, indicate the possibility of very high quality refocusing.

Different regimes for water wave turbulence.

We present an experimental study on gravity capillary wave turbulence in water. By using space-time resolved Fourier transform profilometry, the behavior of the wave energy density |η(k,ω)|(2) in the 3D (k,ω) space is inspected for various forcing frequency bandwidths and forcing amplitudes. Depending on the bandwidth, the gravity spectral slope is found to be either forcing dependent, as classically observed in laboratory experiments, or forcing independent. In the latter case, the wave spectrum is consistent with the Zakharov-Filonenko cascade predicted within wave turbulence theory.

Phase-space analysis of acoustics fields and its application to waveguide.

A description of two-dimensional acoustic fields by means of a joint "space-wave number" representation is discussed. A function defined in the phase-space domain (x,y,k(x),k(y)) is associated with a signal which is a function of spatial coordinates (x,y). This paper presents two methods to realize it. The first is to associate with each point (x,y) of the wave field a two-dimensional wave number spectrum (k(x),k(y)), called local spectrum. The second is to process by other coordinates the wave field along an arbitrary direction, introduced in quantum mechanics for the study of classical billiards, and provided by the Birkhoff variables (s,cos phi). Phase-space diagrams are given by quadratic phase-space distributions. Simulations are presented for wave fields in a 2D planar waveguide for a pedagogical point of view with Gaussian beam or point-source excitation, and nonuniform waveguides as a sudden area expansion chamber and an open billiard with a single incoming mode at the entrance of each of them. In these problems, local spectrum and Birkhoff analysis are used in order to identify the structures hidden in the field. The result is the contribution of different wave vectors which contribute to the field value at the analysis point or at a certain section of the boundary, and show complicated structure of the acoustic field like whispering gallery or diffracted waves.

Multiple scattering of acoustic waves and porous absorbing media.

Porous media like air-saturated polymer foams with open cells, have a nontrivial frequency-dependent absorption that arises due to viscous and thermal effects at the scale of the rigid frame microstructure. In order to produce multiple scattering at ultrasonic frequencies, mesoscale scatterers are introduced in the porous medium host. The effective wave number of such a multiscale medium should take into account the peculiar absorption at the microscale and the multiple scattering at the mesoscale to describe precisely the propagation of a coherent acoustic wave. For this purpose, a simple model is developed. First, an equivalent fluid model, derived from a homogenization method, is used to describe the acoustic propagation in the host porous medium itself. Second, the scattering by the inclusions is described with a multiple scattering approximation (independent scattering approximation). This simple model allows to obtain the total effective wave number of the porous medium with mesoscale scatterers. After some validating results on the multiple scattering by an array of rigid cylinders in air, experiments on the multiple scattering by rigid cylinders embedded in a porous medium are presented and compared to the developed simple model. Incidentally, it appears that for the host medium itself, the equivalent fluid model is not capable to describe the high-frequency behavior whilst a multiple scattering approach with (thin) viscous and thermal boundary layers around the scatterers is accurate in the whole frequency range.

Determination of Lamb mode eigenvalues.

An original method is presented to determine the complex Lamb wave spectrum by using a numerical spectral method applied to the elasticity equations. This method presents the advantage to directly determine complex wave numbers for a given frequency via a classical matricial eigenvalue problem, and allows the wave numbers to be determined at relatively high frequencies (i.e., corresponding to many propagating modes). It does not need initial guess values for the wave numbers, contrary to the usual method of root finding of the Rayleigh-Lamb frequency equations (dispersion relation) in the complex plane. Results are presented and the method is discussed.

Sound propagation in rigid bends: a multimodal approach.

The sound propagation in a waveguide with bend of finite constant curvature is analyzed using multimodal decomposition. Two infinite first-order differential equations are constructed for the pressure and velocity in the bend, projected on the local transverse modes. A Riccati equation for the impedance matrix is then derived, which can be numerically integrated after truncation at a sufficient number of modes. An example of validation is considered and results show the accuracy of the method and its suitability for the formulation of radiation conditions. Reflection and transmission coefficients are also computed, showing the importance of higher order mode generation at the junction between the bend and the straight ducts. The case of varying cross-section curved ducts is also considered using multimodal decomposition.

Irregular scattering of acoustic rays by vortices.

The scattering of high-frequency sound wave, under geometrical acoustic approximation, by three stationary vortices in two dimensions is investigated. For a sufficiently high Mach number of the vortex flow, the scattering of sound rays becomes irregular, displaying a new example of chaotic scattering for a time-reversal breaking system. The fractal dimension, as well as the unstable and stable manifolds of the scattering dynamics, is presented.