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 multichannel symmetric disordered systems. We confirm that an EP of the parity-time (PT)-symmetric RL operator is obtained for two isolated quasinormal modes when the spacing between central frequencies is equal to the decay rate into incoming and outgoing channels. Finally, we leverage the transfer functions associated with RL and RL-EP states to implement first- and second-order analog differentiation.

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 because 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, generally, one has no precise control on the properties of the obtained topological modes, such as their frequency or localization length. In this work, a unique construction is proposed to couple acoustic resonators such that acoustic modes are mapped exactly to the eigenmodes of the Su-Schrieffer-Heeger (SSH) model. The relation between energy in the lattice model and the acoustic frequency is controlled by the characteristics of the resonators. In this way, SSH topological modes are obtained at any given frequency, for instance, in the subwavelength regime. The construction is also generalized to obtain well-controlled topological edge modes in alternative tunable configurations.

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.

Broadband-Enhanced Transmission through Symmetric Diffusive Slabs.

We report on a significant and broadband enhancement of the transmission through an opaque barrier, when placed between symmetric diffusive disordered slabs. The transmission enhancement is accompanied by a bimodal distribution of the transmission eigenvalues, and, for a given transmittance of the barrier, it finds an optimal value for a particular length of the disordered slabs. A simple model allows us to quantify the scalings between the parameters that show that the stronger the barrier, the stronger the maximum possible enhancement. The sensitivity to symmetry defects is also explored, displaying potential interest for wave based sensing.

Slow sound laser in lined flow ducts.

This work considers 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. This work analyzes 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 acts as a resonant cavity, and triggers a laser-like instability. This work shows that the instability is highly subwavelength. Besides, if the subsonic region is small enough, the instability is static. This work also analyzes the effect of a shear flow layer near the impedance wall. Although its presence significantly alters the instability, its main properties are maintained. This work points out the analogy between the present instability and a similar one in fluid analogues of black holes known as the black hole laser.

Non-reciprocal scattering in shear flow.

This work presents a study of scattering phenomena in shear flows and its application to impedance walls. These flows are described by a dimensionless shear layer thickness and a mean Mach number. Both transmission through a given shear layer and reflection on an acoustic treatment are studied. This paper shows that the dimensionless thickness of the shear layer may be an interesting tool to reach perfect absorption or large lateral displacement of a Gaussian beam.

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 an Eckart explicit expression initially derived for water waves, accurate explicit approximations are proposed for the wavenumber of the fundamental mode in lined ducts. While the Eckart expression is 5% accurate, some improved approximations can reach maximum relative errors of less than 10-8. The cases with small dissipation parts in the admittance of the liner and/or axisymmetric ducts are also considered.

PT-Symmetric Scattering in Flow Duct Acoustics.

We show theoretically and experimentally that the propagation of an acoustic wave in an airflow duct going through a pair of diaphragms, with equivalent amounts of mean-flow-induced effective gain and loss, displays all the features of a parity-time (PT) symmetric system. Using a scattering matrix formalism, we observe, experimentally, the properties which reflect the PT symmetry of the scattering acoustical system: the existence of spontaneous symmetry breaking with symmetry-broken pairs of scattering eigenstates showing amplification and reduction, and the existence of points with unidirectional invisibility.

Asymmetric Acoustic Propagation of Wave Packets Via the Self-Demodulation Effect.

This Letter presents the experimental characterization of nonreciprocal elastic wave transmission in a single-mode elastic waveguide. This asymmetric system is obtained by coupling a selection layer with a conversion layer: the selection component is provided by a phononic crystal, while the conversion is achieved by a nonlinear self-demodulation effect in a 3D unconsolidated granular medium. A quantitative experimental study of this acoustic rectifier indicates a high rectifying ratio, up to 10^{6}, with wide band (10 kHz) and an audible effect. Moreover, this system allows for wave-packet rectification and extends the future applications of asymmetric systems.

Empirical mode decomposition profilometry: small-scale capabilities and comparison to Fourier transform profilometry.

We present the empirical mode decomposition profilometry (EMDP) for the analysis of fringe projection profilometry (FPP) images. It is based on an iterative filter, using empirical mode decomposition, which is free of spatial filtering and adapted for surfaces characterized by a broadband spectrum of deformation. Its performances are compared to Fourier transform profilometry, the benchmark of FPP. We show both numerically and experimentally that using EMDP improves strongly the profilometry small-scale capabilities. Moreover, the height reconstruction distortion is much lower: the reconstructed height field is now both spectrally and statistically accurate. EMDP is thus particularly suited to quantitative experiments.

Slow sound in lined flow ducts.

The acoustic propagation in lined flow duct with purely reactive impedance at the wall is considered. This reacting liner has the capability to reduce the speed of sound, and thus to enhance the interaction between the acoustic propagation and the low Mach number flow ( M≃0.3). At the lower frequencies, there are typically four acoustic or hydrodynamic propagating modes, with three of them propagating in the direction of the flow. Above a critical frequency, there are only two propagating modes that all propagate in the direction of the flow. From the exact two-dimensional formulation an approximate one-dimensional model is developed to study the scattering of acoustic waves in a straight duct with varying wall impedance. This simple system, with a uniform flow and with non-uniform liner impedance at the wall, permits to study the scattering between regions with different wave characteristics. Several situations are characterized to show the importance of negative energy waves, strong interactions between acoustic and hydrodynamic modes, or asymmetric scattering.

Low frequency acoustic resonances in urban courtyards.

Urban courtyards can be regarded as open cavities in the urban area, in which resonances can be excited by waves generated in the neighboring streets. The aim of the present work is to experimentally and numerically investigate low frequency resonance phenomena in these configurations. Experiments are carried out in a scale model and a numerical study is performed with a coupled modal-finite elements method. The method enables the three-dimensional modeling of the acoustic field and thus to take into account the interactions between the courtyard and the street canyon that occur above the roof level, a particular characteristic of wave propagation in urban areas. The attention is focused on two aspects, the amplification of the sound level inside the courtyard and the acoustic attenuation in the street due to resonances. Experimental and numerical results are in good agreement and show a strong resonant behavior of these configurations.

Tunneling of electromagnetic energy in multiple connected leads using ε-near-zero materials.

A realization of a reflectionless power splitter is proposed by use of a metamaterial junction. To design the junction, the electromagnetic wave transmission in multiple connected leads is investigated theoretically and numerically. A closed analytical form is derived for the scattering matrix of any geometry of the interconnected leads. We show that the use of a junction made of ϵ-near-zero (ENZ) material allows production of perfect transmission. This can be achieved by reducing the area of the ENZ junction (squeezing effect) and by tuning the widths of the output leads with respect to the input lead. It is also shown that the same effect is obtained without squeezed junction by using a match impedance zero index material (MIZIM junction).

Higher-order mode filtering by a resistive layer.

A method for filtering higher-order acoustic modes using a resistive layer is proposed and applied to a two-dimensional rectangular waveguide with a quiescent fluid. An analogue of Cremer's criterion is discussed and used to obtain the optimal modal attenuation of the non-planar waves while the plane wave is preserved. Numerical validation of the concept is performed for a straight waveguide and an abrupt expansion in a waveguide.

Frozen sound: An ultra-low frequency and ultra-broadband non-reciprocal acoustic absorber.

The absorption of airborne sound is still a subject of active research, and even more since the emergence of acoustic metamaterials. Although being subwavelength, the screen barriers developed so far cannot absorb more than 50% of an incident wave at very low frequencies (<100 Hz). Here, we explore the design of a subwavelength and broadband absorbing screen based on thermoacoustic energy conversion. The system consists of a porous layer kept at room temperature on one side while the other side is cooled down to a very low temperature using liquid nitrogen. At the absorbing screen, the sound wave experiences both a pressure jump caused by viscous drag, and a velocity jump caused by thermoacoustic energy conversion breaking reciprocity and allowing a one-sided absorption up to 95 % even in the infrasound regime. By overcoming the ordinary low frequency absorption limit, thermoacoustic effects open the door to the design of innovative devices.

A coupled modal-finite element method for the wave propagation modeling in irregular open waveguides.

In modeling the wave propagation within a street canyon, particular attention must be paid to the description of both the multiple reflections of the wave on the building facades and the radiation in the free space above the street. The street canyon being considered as an open waveguide with a discontinuously varying cross-section, a coupled modal-finite element formulation is proposed to solve the three-dimensional wave equation within. The originally open configuration-the street canyon open in the sky above-is artificially turned into a close waveguiding structure by using perfectly matched layers that truncate the infinite sky without introducing numerical reflection. Then the eigenmodes of the resulting waveguide are determined by a finite element method computation in the cross-section. The eigensolutions can finally be used in a multimodal formulation of the wave propagation along the canyon, given its geometry and the end conditions at its extremities: initial field condition at the entrance and radiation condition at the output.

Flower patterns in drop impact on thin liquid films.

We describe experimentally the formation of a pattern for drop impacts on thin liquid films for a large range of impact parameters. Using the shallow-water approximation, we are able to explain the main mechanisms leading to these patterns: it consists in the linear instability of the self-similar axisymmetric radial solution of the equations. Agreement between the experiments and the theory is remarkably good, leading, in particular, to the prediction that the most unstable fold number scales like (We/h∞)2/7.

Sensitivity to losses and defects of the symmetry-induced transmission enhancement through diffusive slabs.

We inspect the robustness to absorption and to symmetry defects of the symmetry-induced broadband enhancement through opaque barriers in disordered slabs. The sensitivity of this phenomenon to symmetry defects is found to be strongly related to the distance from to barrier to the nearest defect, and, following, we propose a probabilistic model to estimate the conductance of a medium with an arbitrary number of randomly distributed defects. Also, the conductance enhancement is shown to be robust to absorption in the disordered medium, though being of course weakened. For sufficiently opaque barriers, the conditions of an optimal enhancement are mainly driven by the absorption length of the medium.

Space-time resolved wave turbulence in a vibrating plate.

Wave turbulence in a thin elastic plate is experimentally investigated. By using a Fourier transform profilometry technique, the deformation field of the plate surface is measured simultaneously in time and space. This enables us to compute the wave-vector-frequency (k, omega) Fourier spectrum of the full space-time deformation velocity. In the 3D (k, omega) space, we show that the energy of the motion is concentrated on a 2D surface that represents a nonlinear dispersion relation. This nonlinear dispersion relation is close to the linear dispersion relation. This validates the usual wave-number-frequency change of variables used in many experimental studies of wave turbulence. The deviation from the linear dispersion, which increases with the input power of the forcing, is attributed to weak nonlinear effects. Our technique opens the way for many new extensive quantitative comparisons between theory and experiments of wave turbulence.

Experimental and theoretical inspection of the phase-to-height relation in Fourier transform profilometry.

The measurement of an object's shape using projected fringe patterns needs a relation between the measured phase and the object's height. Among various methods, the Fourier transform profilometry proposed by Takeda and Mutoh [Appl. Opt.22, 3977-3982 (1983)] is widely used in the literature. Rajoub et al. have shown that the reference relation given by Takeda is erroneous [J. Opt. A. Pure Appl. Opt.9, 66-75 (2007)]. This paper follows from Rajoub's study. Our results for the phase agree with Rajoub's results for both parallel- and crossed-optical-axes geometries and for either collimated or noncollimated projection. Our two main results are: (i) we show experimental evidence of the error in Takeda's formula and (ii) we explain the error in Takeda's derivation and we show that Rajoub's argument concerning Takeda's error is not correct.