Articles 2023

Résumé: Elastic waves in anisotropic media can exhibit a power flux that is not collinear with the wave vector. This has notable consequences for waves guided in a plate. Through laser-ultrasonic experiments, we evidence remarkable phenomena due to slow waves in a single-crystal silicon wafer. Waves exhibiting power flux orthogonal to their wave vector are identified. A pulsed line source that excites these waves reveals a wave packet radiated parallel to the line. Furthermore, there exist precisely eight plane waves with zero power flux. These so-called zero-group-velocity modes are oriented along the crystal's principal axes. Time acts as a filter in the wave-vector domain that selects these modes. Thus, a point source leads to beating resonance patterns with moving nodal curves on the surface of the infinite plate. We observe this pattern as it emerges naturally after a pulsed excitation.

Résumé: 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.

Résumé: We report experimental and theoretical investigations of photon diffusion in a second-order-nonlinear disordered medium under conditions of strong nonlinearity. Experimentally, photons at the fundamental wavelength (λ=1064nm) are launched into the structure in the form of a cylindrical pellet, and the second-harmonic (λ=532nm) photons are temporally analyzed in transmission. For comparison, separate experiments are carried out with incident green light at λ=532nm. We observe that the second-harmonic light peaks earlier compared to the incident green photons. Next, the sideways spatial scattering of the fundamental as well as second-harmonic photons is recorded. The spatial diffusion profiles of second-harmonic photons are seen to peak deeper inside the medium in comparison to both the fundamental and incident green photons. In order to give more physical insights into the experimental results, a theoretical model is derived from first principles. It is based on the coupling of transport equations. Solved numerically using a Monte Carlo algorithm and experimentally estimated transport parameters at both wavelengths, it shows excellent semiquantitative agreement with the experiments for both fundamental and second-harmonic light.

Résumé: Imaging the structure of major fault zones is essential for our understanding of crustal deformations and their implications on seismic hazards. Investigating such complex regions presents several issues, including the variation of seismic velocity due to the diversity of geological units and the cumulative damage caused by earthquakes. Conventional migration techniques are in general strongly sensitive to the available velocity model. Here we apply a passive matrix imaging approach which is robust to the mismatch between this model and the real seismic velocity distribution. This method relies on the cross-correlation of ambient noise recorded by a geophone array. The resulting set of impulse responses form a reflection matrix that contains all the information about the subsurface. In particular, the reflected body waves can be leveraged to: (a) determine the transmission matrix between the Earth's surface and any point in the subsurface; (b) build a confocal image of the subsurface reflectivity with a transverse resolution only limited by diffraction. As a study case, we consider seismic noise (0.1–0.5 Hz) recorded by the Dense Array for Northern Anatolia that consists of 73 stations deployed for 18 months in the region of the 1999 Izmit earthquake. Passive matrix imaging reveals the scattering structure of the crust and upper mantle around the North Anatolian Fault zone over a depth range of 60 km. The results show that most of the scattering is associated with the Northern branch that passes throughout the crust and penetrates into the upper mantle.

Résumé: Matrix imaging paves the way towards a next revolution in wave physics. Based on the response matrix recorded between a set of sensors, it enables an optimized compensation of aberration phenomena and multiple scattering events that usually drastically hinder the focusing process in heterogeneous media. Although it gave rise to spectacular results in optical microscopy or seismic imaging, the success of matrix imaging has been so far relatively limited with ultrasonic waves because wave control is generally only performed with a linear array of transducers. In this paper, we extend ultrasound matrix imaging to a 3D geometry. Switching from a 1D to a 2D probe enables a much sharper estimation of the transmission matrix that links each transducer and each medium voxel. Here, we first present an experimental proof of concept on a tissue-mimicking phantom through ex-vivo tissues and then, show the potential of 3D matrix imaging for transcranial applications.

Résumé: This article deals with the optimization of resonant plasmonic metasurfaces through their surface-homogenized counterpart. The derivation of effective transition conditions that takes into account the spatially varying geometries is done using locally periodic surface homogenization. The resulting model reduces the numerical cost of simulating these metasurfaces, thus allowing to find their design using adjoint-based optimization methods. This new algorithm is presented in details, together with various numerical examples to asses its validity and compare its performance with the classical design based on local phase matching.

Résumé: Quantifying the effect of external forcings like seismicity or rain on slope destabilization is a long-standing and challenging issue. To investigate the respective roles of these forcings, we analyze an unprecedented 10-year long catalog of rockfalls occurring in the crater of the Piton de la Fournaise volcano (La Reunion Island), using statistical tools originally developed for earthquakes. Our analysis reveals the predominant effect of low amplitude repetitive seismicity in the triggering of rockfalls located at a few kilometers from the source, due to progressive damaging of the slope. Moreover, we show that the efficiency and time-delay of this dynamic triggering is controlled by the stability state of the slope, i.e. its closeness to the failure, as observed with lab-experiments on metastable granular slopes. Our results show the need to account for long-term swarm-type seismic activity that can affect the stability of geological structures like slopes and faults, but also buildings.

Résumé: The mesencephalic locomotor region (MLR) is a brain stem area whose stimulation triggers graded forward locomotion. How MLR neurons recruit downstream vsx2 + (V2a) reticulospinal neurons (RSNs) is poorly understood. Here, to overcome this challenge, we uncovered the locus of MLR in transparent larval zebrafish and show that the MLR locus is distinct from the nucleus of the medial longitudinal fasciculus. MLR stimulations reliably elicit forward locomotion of controlled duration and frequency. MLR neurons recruit V2a RSNs via projections onto somata in pontine and retropontine areas, and onto dendrites in the medulla. High-speed volumetric imaging of neuronal activity reveals that strongly MLR-coupled RSNs are active for steering or forward swimming, whereas weakly MLR-coupled medullary RSNs encode the duration and frequency of the forward component. Our study demonstrates how MLR neurons recruit specific V2a RSNs to control the kinematics of forward locomotion and suggests conservation of the motor functions of V2a RSNs across vertebrates.

Résumé: Dynamic full-field optical coherence tomography (D-FFOCT) has recently emerged as a label-free imaging tool, capable of resolving cell types and organelles within 3D live samples, whilst monitoring their activity at tens of milliseconds resolution. Here, a D-FFOCT module design is presented which can be coupled to a commercial microscope with a stage top incubator, allowing non-invasive label-free longitudinal imaging over periods of minutes to weeks on the same sample. Long term volumetric imaging on human induced pluripotent stem cell-derived retinal organoids is demonstrated, highlighting tissue and cell organization processes such as rosette formation and mitosis as well as cell shape and motility. Imaging on retinal explants highlights single 3D cone and rod structures. An optimal workflow for data acquisition, postprocessing and saving is demonstrated, resulting in a time gain factor of 10 compared to prior state of the art. Finally, a method to increase D-FFOCT signal-to-noise ratio is demonstrated, allowing rapid organoid screening.

Résumé: We present numerical and analytical predictions of mucociliary clearance based on the continuum description of a viscoelastic mucus film, where momentum transfer from the beating cilia is represented via a Navier-slip boundary condition introduced by Bottier et al. (PLoS Comput. Biol., vol. 13, issue 7, 2017a, e1005552). Mucus viscoelasticity is represented via the Oldroyd-B model, where the relaxation time and the viscosity ratio have been fitted to experimental data for the storage and loss moduli of different types of real mucus, ranging from healthy to diseased conditions. We solve numerically the fully nonlinear governing equations for inertialess flow, and develop analytical solutions via asymptotic expansion in two limits: (i) weak viscoelasticity, i.e. low Deborah number; (ii) low cilia beat amplitude (CBA). All our approaches predict a drop in the mucus flow rate in relation to the Newtonian reference value, as the cilia beat frequency is increased. This relative drop increases with decreasing CBA and slip length. In diseased conditions, e.g. mucus properties characteristic of cystic fibrosis, the drop reaches 30% in the physiological frequency range. In the case of healthy mucus, no significant drop is observed, even at very high frequency. This contrasts with the deterioration of microorganism propulsion predicted by the low-amplitude theory of Lauga (Phys. Fluids, vol. 19, issue 8, 2007, 083104), and is due to the larger beat amplitude and slip length associated with mucociliary clearance. In the physiological range of the cilia beat frequency, the low-amplitude prediction is accurate for both healthy and diseased conditions. Finally, we find that shear-thinning, modelled via a multi-mode Giesekus model, does not significantly alter our weakly viscoelastic and low-amplitude predictions based on the Oldroyd-B model.

Résumé: Liquid-crystal (LC) optically addressable spatial light modulators (OASLMs) allow control of the phase and amplitude of optical beams. By performing wave mixing in an OASLM, we show that coherent phase detection can be achieved for light beams passing through highly scattering media, such as foam layers with several cm thicknesses. Thanks to the adaptive response of our OASLM, the phase information on the speckle signal is transferred at the output of the OASLM to the plane wave reference beam, allowing the cleaning of optical distortions and the direct measurement of amplitude phase modulations with a small diameter single photodiode. A good signal-to-noise ratio (SNR) is demonstrated for foam thickness up to 3 cm. These properties, together with the recently demonstrated sub-ms response time of our OASLM, make the method compatible with foreseen applications for imaging in biomedical tissues and turbid media.

Résumé: The diagnosis of cutaneous manifestations of deep mycoses relies on both histopathological and direct examinations. Yet, the current diagnostic criteria cannot prevent missed cases, including invasive aspergillosis, which requires the development of a novel diagnostic approach and imaging tools. We recently introduced the use of dynamic full-field optical coherence tomography (D-FF-OCT) in fungal diagnostics with a definition approaching that of conventional microscopy and the ability to return metabolic information regarding different fungal species. The present work focuses on subcellular dynamics and live-cell imaging of Aspergillus fumigatus with D-FF-OCT to follow the fungal growth stages

Résumé: Viruses have a profound influence on all forms of life, motivating the development of rapid and minimally invasive methods for virus detection. In this study, we present a novel methodology that enables quantitative measurement of the interaction between individual biotic nanoparticles and antibodies in solution. Our approach employs a label-free, full-field common-path interferometric technique to detect and track biotic nanoparticles and their interactions with antibodies. It is based on the interferometric detection of light scattered by viruses in aqueous samples for the detection of individual viruses. We employ single-particle tracking analysis to characterize the size and properties of the detected nanoparticles, and to monitor the changes in their diffusive mobility resulting from interactions. To validate the sensitivity of our detection approach, we distinguish between particles having identical diffusion coefficients but different scattering signals, using DNA-loaded and DNA-devoid capsids of the Escherichia coli T5 virus phage. In addition, we have been able to monitor, in real time, the interaction between the bacteriophage T5 and purified antibodies targeting its major capsid protein pb8, as well as between the phage SPP1 and nonpurified anti-SPP1 antibodies present in rabbit serum. Interestingly, these virus-antibody interactions are observed within minutes. Finally, by estimating the number of viral particles interacting with antibodies at different concentrations, we successfully quantify the dissociation constant Kd of the virus-antibody reaction using single-particle tracking analysis.

Résumé: This work compares two tomographic imaging technologies, time-domain fullfield optical coherence tomography (FFOCT) working in reflection and optical transmission tomography (OTT), using a new optical setup that combines both. We show that, due to forward-scattering properties, the axial sectioning and contrast in OTT can be optimized by tuning illumination. The influence of sample scattering and thickness are discussed. We illustrate the comparison of the two methods in static (morphology) and dynamic (metabolic contrast) regimes using cell cultures, tissues and entire organisms emphasizing the advantages of both approaches.

Résumé: Dynamic full-field optical coherence tomography (D-FFOCT) has recently emerged as an invaluable live label-free and non-invasive imaging modality able to image subcellular biological structures and their metabolic activity within complex 3D samples. However, D-FFOCT suffers from fringe artefacts when imaging near reflective surfaces and is highly sensitive to vibrations. Here, we present interface Self-Referenced (iSR) D-FFOCT, an alternative configuration to D-FFOCT that takes advantage of the presence of the sample coverslip in between the sample and the objective by using it as a defocused reference arm, thus avoiding the aforementioned artefacts. We demonstrate the ability of iSR D-FFOCT to image 2D fibroblast cell cultures, which are among the flattest mammalian cells.

Résumé: Light-matter interactions are often considered governed by the electric optical field only, leaving aside the magnetic component of light. However, the magnetic part plays a determining role in many optical processes, from light and chiral-matter interactions and photon-avalanching to forbidden photochemistry, making the manipulation of magnetic processes extremely relevant. Here, by creating a standing wave using a metallic nanomirror, we manipulate the spatial distributions of electric and magnetic fields and their associated local densities of states, allowing selective control of the excitation and emission of electric and magnetic dipolar transitions. This control allows us to image, in 3D, the electric and magnetic nodes and anti-nodes of the fields' interference patterns. It also enables us to enhance specifically photoluminescence from quantum emitters excited only by the magnetic field, and to manipulate their spontaneous emission by acting on the excitation fields solely, demonstrating full control of magnetic and electric light-matter interactions.

Résumé: In the past few years, data privacy legislation has hampered the ability of WiFi network operators to count and map client activity for commercial and security purposes. Indeed, since client device MAC devices are now randomized at each transmission, aggregating client activity using management frames such as Probe Requests, as has been common practice in the past, becomes problematic. Recently, researchers have demonstrated that, statistically, client counts are roughly proportional to raw Probe Request counts, thus somewhat alleviating the client counting problem, even if, in most cases, ground truth measurements from alternate sensors such as cameras are necessary to establish this proportionality. Nevertheless, localizing randomized MAC clients at a network site is currently an unsolved problem. In this work, we propose a set of nine tools for extending the proportionality between client counts and Probe Requests to the mapping of client densities in real-world outdoor WiFi networks without the need for ground truth measurements. The purpose of the proposed toolkit is to transform raw, randomized MAC Probe Request counts into a density map calibrated to an estimated number of clients at each position.

Résumé: We report on the observation and correction of an imaging artifact attributed to the Talbot effect in the context of acousto-optic imaging using structured acoustic waves. When ultrasound waves are emitted with a periodic structure, the Talbot effect produces π-phase shifts of that periodic structure at every half of the Talbot distance in propagation. This unwanted artifact is detrimental to the image reconstruction, which assumes near-field diffraction is negligible. Here, we demonstrate both theoretically and experimentally how imposing an additional phase modulation on the acoustic periodic structure induces a symmetry constraint leading to the annihilation of the Talbot effect. This will significantly improve the acousto-optic image reconstruction quality and allows for an improvement of the reachable spatial resolution of the image.

Résumé: Localization of electronic wave functions in modern two-dimensional (2D) materials such as graphene can impact drastically their transport and magnetic properties. The recent localization landscape (LL) theory has brought many tools and theoretical results to understand such localization phenomena in the continuous setting, but with very few extensions so far to the discrete realm or to tight-binding Hamiltonians. In this paper, we show how this approach can be extended to almost all known 2D lattices and propose a systematic way of designing LL even for higher dimensions. We demonstrate in detail how this LL theory works and predicts accurately not only the locations, but also the energies of localized eigenfunctions in the low- and high-energy regimes for the honeycomb and hexagonal lattices, making it a highly promising tool for investigating the role of disorder in these materials.

Résumé: The dynamic movement of cell organelles is an important and poorly understood component of cellular organization and metabolism. In this work we present a non-invasive non-destructive method (Dynamic Cell Imaging, DCI) based on light scattering and interferometry to monitor dynamic events within photosynthetic cells using the diatom Phaeodactylum tricornutum as a model system. For this monitoring we acquire for a few seconds movies of the signals that are related to the motion of dynamic structures within the cell (denoted scatterers), followed by a statistical analysis of each pixel time series. Illuminating P. tricornutum with LEDs of different wavelengths associated with short pulsed or continuous-wave modes of illumination revealed that dynamic movements depend on chloroplast activity, in agreement with the reduction in the number of pixels with dynamic behaviour after addition of photosystem II inhibitors. We studied P. tricornutum under two environmentally relevant stresses, iron and phosphate deficiency. The major dynamic sites were located within lipid droplets and chloroplast envelope membranes. By comparing standard deviation and cumulative sum analyses of the time series, we showed that within the droplets two types of scatterer movement could be observed: random motion (Brownian type) but also anomalous movements corresponding to a drift which may relate to molecular fluxes within a cell. The method appears to be valuable for studying the effects of various environments on microalgae in the laboratory as well as in natural aquatic environments. HIGHLIGHTS: Light scattering is an alternative to fluorescence to rapidly evidence dynamic processes. Lipid droplets are the major metabolic active sites under stress. A non-destructive visualization method suitable for laboratory microalgae and aquatic samples.

Résumé: The aim of this paper is to test a simple damage model of a cohesive granular medium to study the relationship between the damage and velocity of elastic waves. Our numerical experiments of edometric compression show that the microscopic deformation quickly becomes very heterogeneous, while our simulations of elastic waves propagation show that a small amount of damage induces a dramatic decrease in the elastic velocity. This shows that cohesive discrete media are very sensitive to strain field heterogeneity, and that the wave velocities in these media can measure subtle transient deformation processes, such as earthquake initiation phases.

Résumé: We study the propagation of water waves in a three-dimensional device alternating open canals and resonant canals with subwavelength resonances. The dispersion of water waves in such a medium is obtained by analysing the full three-dimensional problem and combining Bloch-Floquet analysis with an asymptotic technique. We obtain the closed forms of the dispersions for resonant canals containing one or two resonators, which depend on only two functions associated with symmetric and antisymmetric modes, and on a geometric parameter analogous to the hopping parameter in topological systems. The analysis of the complete band structure reveals frequency ranges alternating between elliptical and hyperbolic dispersions; in particular, the hyperbolic regime gives rise to a negative effective water depth with a consequent negative refraction. Throughout the course of our study, our theoretical results are validated by comparison with numerical calculations of the full three-dimensional problem.

Résumé: By studying the effects of quadratic anisotropy and quartic perturbations on two-dimensional harmonic oscillators, one arrives at a simple model, termed here the Ince oscillator, whose analytic solutions are given in terms of Ince polynomials. This one model unifies diverse physical systems, including aberrated optical cavities that are shown to support Ince-Gauss beams as their modes, and the two-mode Bose-Hubbard dimer describing two coupled superfluids. The Ince oscillator model describes a topological transition which can have very different origins: in the optical case, which is fundamentally linear, it is driven by the ratio of astigmatic to spherical mirror aberrations, whereas in the superfluid case it is driven by the ratio of particle tunneling to interparticle interactions and corresponds to macroscopic quantum self-trapping.

Résumé: While the properties and the shape of the ground state of a gas of ultracold bosons are well understood in harmonic potentials, they remain for a large part unknown in the case of random potentials. Here we use localization-landscape (LL) theory to study the properties of the solutions to the Gross-Pitaevskii equation (GPE) in one-dimensional (1D) speckle potentials. In the cases of attractive interactions, we find that the LL allows one to predict the position of the localization center of the ground state (GS) of the GPE. For weakly repulsive interactions, we point out that the GS of the quasi-1D GPE can be understood as a superposition of a finite number of single-particle states, which can be computed by exploiting the LL. For intermediate repulsive interactions, we introduce a Thomas-Fermi-like approach for the GS which holds in the smoothing regime, well beyond the usual approximation involving the original potential. Moreover, we show that, in the Lifshitz glass regime, the particle density and the chemical potential can be well estimated by the LL. Our approach can be applied to any positivevalued random potential endowed with finite-range correlations and can be generalized to higher-dimensional systems.

Résumé: We report experimental results where a momentum entangled biphoton state with a Schmidt number of a few thousand is retrieved and manipulated when only one photon of the pair is transmitted through a thin scattering medium. For this purpose, the transmission matrix of the complex medium is first measured with a phase-shifting interferometry measurement method using a spatial light modulator (SLM) illuminated with a laser source. From this matrix, different phase masks are calculated and addressed on the SLM to spatially control the focusing of the laser through the complex medium. These same masks are used to manipulate the phase of the biphoton wave function transmitted by the thin diffuser in order to restore and control in the same way the momentum correlations between the far-field images of twin beams issued from strongly spatial-multi-mode spontaneous parametric down conversion.

Résumé: Ambient noise correlations allow the passive recovery of Green’s functions between two probes. Recently, the same approach has been applied to electromagnetism, but by correlating diffuse fields in mode stirred chambers. Until now, only correlation of S-parameters has been studied. However, it has very recently been shown that the result can be difficult to interpret. To overcome this limitation, a new approach is proposed in this paper to directly estimate the self and mutual impedances of two coupled antennas from impedance correlations. The theoretical developments presented are validated experimentally in a reverberation chamber excited by a single antenna where mechanical and source stirring techniques are combined to generate a sufficiently diffuse field environment. It is shown, with antennas of different properties, that this approach allows to reconstruct with a good accuracy the complex impedance matrix between two receiving antennas as well as the transmission coefficient between them. The extracted gain pattern, in good agreement with that measured in an anechoic chamber, shows the good sensitivity of the proposed passive characterization technique.

Résumé: A label-free approach to improving the performances of confocal scanning imaging is proposed. We experimentally demonstrate its feasibility using acoustic waves. It relies on a way to encode spatial information using the temporal dimension. By moving an emitter, used to insonify an object, along a circular path, we create a temporally modulated wavefield. Because of the symmetries of the problem, the spatiotemporal input field can be decomposed into harmonics corresponding to different spatial vortices. Acquiring the back-reflected waves with receivers that are also rotating, multiple images of the same object with different point spread functions are obtained. Not only is the resolution improved compared to a standard confocal configuration, but the accumulation of information also allows the building of images that beat the diffraction limit.

Résumé: In this paper, we show that it is possible to overcome one of the fundamental limitations of super-resolution microscopy: the necessity to be in an optically homogeneous environment. Using recent modal approximation results from [10, 7], we show, as a proof of concept, that it is possible to recover the position of a single point-like emitter in a known resonant environment from far-field measurements, with a precision two orders of magnitude below the classical Rayleigh limit. The procedure does not involve solving any partial differential equation, is computationally light (optimisation in Rd with d of the order of 10) and is therefore suited for the recovery of a very large number of single emitters.

Résumé: Band gap tunability of lead mixed halide perovskites makes them promising candidates for various applications in optoelectronics. Here we use the localization landscape theory to reveal that the static disorder due to iodide:bromide compositional alloying contributes at most 3 meV to the Urbach energy. Our modeling reveals that the reason for this small contribution is due to the small effective masses in perovskites, resulting in a natural length scale of around 20 nm for the “effective confining potential” for electrons and holes, with short-range potential fluctuations smoothed out. The increase in Urbach energy across the compositional range agrees well with our optical absorption measurements. We model systems of sizes up to 80 nm in three dimensions, allowing us to accurately reproduce the experimentally observed absorption spectra of perovskites with halide segregation. Our results suggest that we should look beyond static contribution and focus on the dynamic temperature dependent contribution to the Urbach energy.

Résumé: Numerical experiments of seismic wave propagation in a laterally homogeneous layered medium explore subsurface imaging at subwavelength distances for dense seismic arrays. We choose a time-reversal approach to simulate fundamental mode Rayleigh surface wavefields that are equivalent to the cross-correlation results of three-component ambient seismic field records. We demonstrate that the synthesized 2-D spatial autocorrelation fields in the time domain support local or so-called focal spot imaging. Systematic tests involving clean isotropic surface wavefields but also interfering body wave components and anisotropic incidence assess the accuracy of the phase velocity and dispersion estimates obtained from focal spot properties. The results suggest that data collected within half a wavelength around the origin is usually sufficient to constrain the used Bessel functions models. Generally, the cleaner the surface wavefield the smaller the fitting distances that can be used to accurately estimate the local Rayleigh wave speed. Using models based on isotropic surface wave propagation we find that phase velocity estimates from vertical-radial component data are less biased by P-wave energy compared to estimates obtained from vertical-vertical component data, that even strong anisotropic surface wave incidence yields phase velocity estimates with an accuracy of 1 per cent or better, and that dispersion can be studied in the presence of noise. Estimates using a model to resolve potential medium anisotropy are significantly biased by anisotropic surface wave incidence. The overall accurate results obtained from near-field measurements using isotropic medium assumptions imply that dense array seismic Rayleigh wave focal spot imaging can increase the depth sensitivity compared to ambient noise surface wave tomography. The analogy to elastography focal spot medical imaging implies that a high station density and clean surface wavefields support subwavelength resolution of lateral medium variations.

Résumé: We study the diffraction of acoustic waves by thin grating with varying slit width. Using quasi-periodic homogenization, we derive an effective model in which the grating is replaced by effective jump conditions with effective parameters varying along the equivalent interface. The numerical implementations of the actual problem and of its homogenized counterpart are achieved using multimodal methods for a periodic grating with a macro-period containing many slits with varying widths. The ability of the effective grating to reproduce the scattering properties of the actual one is inspected and discussed.