arXiv subjects

Vincent Pagneux

Publications and source records attributed to Vincent Pagneux.

At least 37 records · Page 2Linked to original sources

arXiv2022

Acoustic Su-Schrieffer-Heeger lattice: Direct mapping of acoustic waveguides to Su-Schrieffer-Heeger model

Topological physics strongly relies on prototypical lattice model with particular symmetries. We report here on a theoretical and experimental work on acoustic waveguides that is directly mapped to the one-dimensional Su-Schrieffer-Heeger chiral model. Starting from the continuous two dimensional wave equation we use a combination of monomadal approximation and the condition of equal length tube segments to arrive at the wanted discrete equations. It is shown that open or closed boundary conditions topological leads automatically to the existence of edge modes. We illustrate by graphical construction how the edge modes appear naturally owing to a quarter-wavelength condition and the conservation of flux. Furthermore, the transparent chirality of our system, which is ensured by the geometrical constraints allows us to study chiral disorder numerically and experimentally. Our experimental results in the audible regime demonstrate the predicted robustness of the topological edge modes.

cond-mat.mes-hall↗

arXiv2021

Subwavelength Su-Schrieffer-Heeger topological modes in acoustic waveguides

Topological systems furnish a powerful way of localizing wave energy at edges of a structured material. Usually this relies on Bragg scattering to obtain bandgaps with nontrivial topological structures. However, this limits their applicability to low frequencies since that would require very large structures. A standard approach to address the problem is to add resonating elements inside the material to open gaps in the subwavelength regime. Unfortunately, one usually has no precise control on the properties of the obtained topological modes, such as their frequency or localization length. In this work, we propose a new construction to couple acoustic resonators such that acoustic modes are mapped exactly to the eigenmodes of the Su-Schrieffer-Heeger model. The relation between energy in the lattice model and the acoustic frequency is controlled by the characteristics of the resonators. This allows us to obtain Su-Schrieffer-Heeger topological modes at any given frequency, for instance in the subwavelength regime. We also generalize the construction to obtain well-controlled topological edge modes in alternative tunable configurations.

physics.class-ph↗

arXiv2021

Experimental characterization of rigid scatterer hyperuniform distributions for audible acoustics

Two-dimensional stealthy hyperuniform distributions of rigid scatterers embedded in a waveguide are experimentally characterized the wave transport properties for scalar waves in airborne audible acoustics. The non resonant nature of the scatterers allows us to directly links the these properties to the geometric distribution of points through the structure factor. The transport properties are analyzed as a function of the stealthiness $χ$ of their hyperuniform point pattern and compared to those of a disordered material in the diffusive regime, which are characterized by the Ohm's law through the mean free path. Different scattering regimes are theoretically and numerically identified showing transparent regions, isotropic band gaps, and anisotropic scattering depending on $χ$. The robustness of these scattering regimes to losses which are unavoidable in audible acoustics is experimentally unvealed.

cond-mat.dis-nn↗

arXiv2021

Experimental evidence of enhanced broadband transmission in disordered systems with mirror symmetry

We demonstrate in microwave measurements the broadband enhancement of transmission through an opaque barrier due to mirror symmetry. This enhancement relies on constructive interference between mirror scattering paths resulting from strong internal reflections at the left and right interfaces of a multichannel cavity. We observe a strong sensitivity of the conductance to a shift of the barrier from the center of the cavity. Remarkably, the impact of mirror symmetry can be further increased by tuning the degree of disorder within the cavity. We report an additional enhancement of the conductance found by symmetrically placing randomly located scatterers. Our results illuminate the impact of symmetry and disorder correlation on transmission through complex systems.

cond-mat.dis-nn↗

arXiv2021

Exceptional points of PT-symmetric reflectionless states in complex scattering systems

We investigate experimentally and analytically the coalescence of reflectionless (RL) states in symmetric complex wave-scattering systems. We observe RL-exceptional points (EPs), first, with a conventional Fabry-Perot system for which the scattering strength within the system is tuned symmetrically, and then with single- and multi-channel symmetric disordered systems. We identify that an EP of the parity-time (PT)-symmetric RL-operator is obtained when the spacing between central frequencies of two natural resonances of the system is equal to the decay rate into incoming and outgoing channels. Finally, we leverage the transfer functions associated with RL and RL-EPs states to implement first- and second-order analog differentiation.

physics.class-ph↗

arXiv2021

Effect of symmetry defect on the edge resonance of semi-infinite FGM plates

The effect of asymmetric functionally graded material on the edge resonance and the Fano resonance in semi-infinite FGM plates are reported in this work. The edge resonance is weakened by the material perturbation and the complete mode conversion is illustrated with incident $S_0$ mode. The Fano resonance occurs on the reflected $A_0$ mode as a result of interference between the resonance and direct scattering with incident $A_0$ mode. A hybrid analytical model based on the collocation discretization and the modal decomposition of the elastic field is developed to analyze the scattering properties of the semi-infinite plates. The Fano line-shape is discussed in detail. The results show that the Fano line shape is sensitive to the volume fraction, which is beneficial for the quantitative guided wave application.

physics.class-ph↗

arXiv2021

Topological two-dimensional Su-Schrieffer-Heeger analogue acoustic networks: Total reflection at corners and corner induced modes

In this work, we investigate some aspects of an acoustic analogue of the two-dimensional Su-Schrieffer-Heeger model. The system is composed of alternating cross-section tubes connected in a square network, which in the limit of narrow tubes is described by a discrete model coinciding with the two-dimensional Su-Schrieffer-Heeger model. This model is known to host topological edge waves, and we develop a scattering theory to analyze how these waves scatter on edge structure changes. We show that these edge waves undergo a perfect reflection when scattering on a corner, incidentally leading to a new way of constructing corner modes. It is shown that reflection is high for a broad class of edge changes such as steps or defects. We then study consequences of this high reflectivity on finite networks. Globally, it appears that each straight part of edges, separated by corners or defects, hosts localized edge modes isolated from their neighbourhood.

cond-mat.mes-hall↗

arXiv2020

Robustness of topological corner modes against disorder and application to acoustic networks

We study the two-dimensional extension of the Su-Schrieffer-Heeger model in its higher order topological insulator phase, which is known to host corner states. Using the separability of the model into a product of one-dimensional Su-Schrieffer-Heeger chains, we analytically describe the eigen-modes, and specifically the zero-energy level, which includes states localized in corners. We then consider networks with disordered hopping coefficients that preserve the chiral (sublattice) symmetry of the model. We show that the corner mode and its localization properties are robust against disorder if the hopping coefficients have a vanishing flux on appropriately defined super plaquettes. We then show how this model with disorder can be realised using an acoustic network of air channels, and confirm the presence and robustness of corner modes.

cond-mat.mes-hall↗

arXiv2020

Spatial transient behavior in waveguides with lossy impedance boundary conditions

Attenuation in acoustic waveguides with lossy impedance boundary conditions are associated with non-Hermitian and non-normal operators. This subject has been extensively studied in fundamental and engineering research, and it has been traditionally assumed that the attenuation behavior of total sound power can be totally captured by considering the decay of each transverse mode individually. One of the classical tools in this context is the Cremer optimum concept that aims to maximize the attenuation of the least attenuated mode. However, a typical sound field may be a superposition of a large number of transverse modes which are nonorthogonal, and the individual mode attenuation may have little to do with the total sound power attenuation. By using singular value decomposition, we link the least attenuated total sound power to the maximum singular value of the non-normal propagator. The behaviors of the least attenuated total sound power depend only on the lossy boundary conditions and frequency, but are independent of sources. The sound may be almost non-decaying along the waveguide transition region for any lossy impedance boundary conditions although all modes attenuate exponentially. This spatial transient appears particularly strongly if the impedance is close to an exceptional point of the propagator, at which a pair of adjacent modes achieve maximum attenuation predicted by Cremer optimum concept. These results are confirmed using non-modal numerical calculations and a two-by-two toy model.

physics.class-ph↗

arXiv2020

Anomalous transmission through periodic resistive sheets

This work investigates anomalous transmission effects in periodic dissipative media, which is identified as an acoustic analogue of the Borrmann effect. For this, the scattering of acoustic waves on a set of equidistant resistive sheets is considered. It is shown both theoretically and experimentally that at the Bragg frequency of the system, the transmission coefficient is significantly higher than at other frequencies. The optimal conditions are identified: one needs a large number of sheets, which induce a very narrow peak, and the resistive sheets must be very thin compared to the wavelength, which gives the highest maximal transmission. Using the transfer matrix formalism, it is shown that this effect occurs when the two eigenvalues of the transfer matrix coalesce, i.e. at an exceptional point. Exploiting this algebraic condition, it is possible to obtain similar anomalous transmission peaks in more general periodic media. In particular, the system can be tuned to show a peak at an arbitrary long wavelength.

physics.class-ph↗

arXiv2020

Slow sound laser in lined flow ducts

We consider the propagation of sound in a waveguide with an impedance wall. In the low frequency regime, the first effect of the impedance is to decrease the propagation speed of acoustic waves. Therefore, a flow in the duct can exceed the wave propagation speed at low Mach numbers, making it effectively supersonic. We analyze a setup where the impedance along the wall varies such that the duct is supersonic then subsonic in a finite region and supersonic again. In this specific configuration, the subsonic region act as a resonant cavity, and triggers a laser-like instability. We show that the instability is highly subwavelength. Besides, if the subsonic region is small enough, the instability is static. We also analyze the effect of a shear flow layer near the impedance wall. Although its presence significantly alter the instability, its main properties are maintained.

physics.class-ph↗

arXiv2019

Observation of edge waves in a two-dimensional Su-Schrieffer-Heeger acoustic network

In this work, we experimentally report the acoustic realization the two-dimensional (2D) Su-Schrieffer-Heeger (SSH) model in a simple network of air channels. We analytically study the steady state dynamics of the system using a set of discrete equations for the acoustic pressure, leading to the 2D SSH Hamiltonian matrix without using tight binding approximation. By building an acoustic network operating in audible regime, we experimentally demonstrate the existence of topological band gap. More supremely, within this band gap we observe the associated edge waves even though the system is open to free space. Our results not only experimentally demonstrate topological edge waves in a zero Berry curvature system but also provide a flexible platform for the study of topological properties of sound waves.

physics.class-ph↗

arXiv2018

From zero transmission to trapped modes in waveguides

We consider the time-harmonic scattering wave problem in a 2D waveguide at wavenumber $k$ such that one mode is propagating in the far field. In a first step, for a given $k$, playing with one scattering branch of finite length, we demonstrate how to construct geometries with zero transmission. The main novelty in this result is that the symmetry of the geometry is not needed: the proof relies on the unitary structure of the scattering matrix. Then, in a second step, from a waveguide with zero transmission, we show how to build geometries supporting trapped modes associated with eigenvalues embedded in the continuous spectrum. For this second construction, using the augmented scattering matrix and its unitarity, we play both with the geometry and the wavenumber. Finally, the mathematical analysis is supplemented by numerical illustrations of the results.

math.AP↗

arXiv2018

Perfect absorption of water waves by linear or nonlinear critical coupling

We report on experiments of perfect absorption for surface gravity waves impinging a wall structured by a subwavelength resonator. By tuning the geometry of the resonator, a balance is achieved between the radiation damping and the intrinsic viscous damping, resulting in perfect absorption by critical coupling. Besides, it is shown that the resistance of the resonator, hence the intrinsic damping, can be controlled by the wave amplitude, which provides a way for perfect absorption tuned by nonlinear mechanisms. The perfect absorber that we propose, without moving parts or added material, is simple, robust and it presents a deeply subwavelength ratio wavelength/size $\simeq 18$.

physics.flu-dyn↗

arXiv2018

Using liner surface modes in ducts to make obstacles reflectionless

Acoustic cloaking for the suppression of backscattering inside ducts is proposed in the audible range where plane waves are curved around the object using the surface modes of the liner. It is numerically shown that a slowly varying resonant liner (e. g. based on an array of tubes) creates a zone of silence in which an object of arbitrary shape can be acoustically hidden for a wide range of frequencies. And then, a resonant liner has deflecting properties without reflection of the wavefront, which are close to an ideal invisibility cloak. This kind of cloaking is effective in a wide frequency band and the cloaking band is a function of the impedance and height of the obstacle relative to the conduit. For smooth shaped obstacles, there is an ability of the object to help hide itself, which increases the cloaking frequency band (self-cloaking). Dispersion effects lead to slow sounds and distortion of the wave phase.

physics.app-ph↗

arXiv2018

Acoustic Propagation in lined ducts with varying cross-section using a Mild-Slope approximation

A modelling of low-frequency sound propagation in slowly varying ducts with smoothly varying lining is proposed leading to an acoustic mild-slope equation analogue to the with mild-slope equation for water waves. This simple 1D Mild Slope Equation is derived by direct application of the Galerkin method. It is shown that the acoustic mild-slope equation can serve as a good alternative to computationally expensive Helmholtz equations to solve such kind of problem. The results from this equation agrees well with FEM based solutions of Helmholtz equation.

physics.flu-dyn↗

arXiv2018

Explicit approximation of the wavenumber for lined ducts

For acoustic waves in lined ducts, at given frequencies, the dispersion relation leads to a transcendental equation for the wavenumber that has to be solved by numerical methods. Based on Eckart explicit expression initially derived for water waves, accurate explicit approximations are proposed for the wavenumber of the fundamental mode in lined ducts. While Eckart expression is 5 % accurate, some improved approximations can reach maximum relative error of less than 10 raised to -8. The cases with small dissipation part in the admittance of the liner and/or axisymmetric ducts are also considered.

physics.flu-dyn↗

arXiv2018

Invisibility and perfect reflectivity in waveguides with finite length branches

We consider a time-harmonic wave problem, appearing for example in water-waves and in acoustics, in a setting such that the analysis reduces to the study of a 2D waveguide problem with a Neumann boundary condition. The geometry is symmetric with respect to an axis orthogonal to the direction of propagation of waves. Moreover, the waveguide contains one branch of finite length. We analyse the behaviour of the complex scattering coefficients $\mathcal{R}$, $\mathcal{T}$ as the length of the branch increases and we show how to design geometries where non reflectivity ($\mathcal{R}=0$, $|\mathcal{T}|=1$), perfect reflectivity ($|\mathcal{R}|=1$, $\mathcal{T}=0$) or perfect invisibility ($\mathcal{R}=0$, $\mathcal{T}=1$) hold. Numerical experiments illustrate the different results.

math.AP↗