Publications de l’axe théorie des ondes et physique mésoscopique

Résumé: We theoretically study the propagation of light in one-dimensional space- and time-dependent disorder. The disorder is described by a fluctuating permittivity ε(x, t) exhibiting short-range correlations in space and time, without cross correlation between them. Depending on the illumination conditions, we show that the intensity of the average field decays exponentially in space or in time, with characteristic length or time defining the scattering mean-free path ℓs and the scattering mean-free time τs. In the weak scattering regime, we provide explicit expressions for ℓs and τs, that are checked against rigorous numerical simulations.

Résumé: Upon impact, the free surface of a solid metal may eject a cloud of fast and fine particles. Photon Doppler Velocimetry (PDV) is one of the optical diagnostics used to characterize these ejecta. Although the technique provides a direct way to estimate the particle velocities in the single scattering regime, it has been shown that multiple scattering cannot be neglected in real ejecta. Here, we derive a model for PDV measurements starting from the first principles of wave scattering. We establish rigorously the relationship between the specific intensity and the measured signal, as well as the Radiative Transport Equation (RTE) that describes the evolution of the specific intensity upon scattering and absorption in dynamic ejecta, including the effects of inelastic scattering and inhomogeneities in the optical properties. We also establish rigorously the connection between the Monte Carlo scheme used for numerical simulations and the solution to the RTE. Using numerical simulations, we demonstrate the crucial contribution of multiple scattering to PDV spectrograms as well as the effect of statistical inhomogeneities in particle size distribution. These results could substantially impact the analysis of ejecta by PDV.

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: 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: We revisit the modelling of labyrinthine metasurfaces with space coiling design. To do so, we use homogenization theory which allows us to replace the actual structure by a slab filled with an effective, homogeneous and anisotropic, medium. The effective medium is highly anisotropic as the propagation is allowed in one direction only and its effective refractive index is obtained unambiguously thanks to the resolution of a static cell-problem. The result is compared to a classical, two-step, model which follows the intuitive idea that a coiled labyrinth and a slot being its uncoiled version behave the same. Beyond the approximation of such statement (the evanescent fields triggered at the turning regions of the labyrinth are neglected), we stress the difficulty in defining unambiguously the length of the uncoiled labyrinth.

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 present study aims to model the optical response of plasmonic metasurfaces made of a periodic arrangement of metallic particles with arbitrary shape and subwavelength dimensions. By combining homogenization with quasistatic plasmonic eigenmode expansion, the metasurface is replaced by a zero-thickness interface associated with frequency-dependent effective susceptibilities. The resulting discontinuities of the fields are responsible for strong interaction with the incoming light at the resonances when the complex permittivity of the metal passes close to the real permittivity of an eigenmode. Our modeling provides a physical picture of resonances in plasmonic metasurfaces, and it allows for a huge decrease in the numerical cost of their computations. In addition, comparisons with direct numerics in two dimensions evidence its predictive force at any incidence, particle shape, and arrangement.

Résumé: Correlations between entangled photons are a key ingredient for testing fundamental aspects of quantum mechanics and an invaluable resource for quantum technologies. However, scattering from a dynamic medium typically scrambles and averages out such correlations. Here we show that multiply scattered entangled photons reflected from a dynamic complex medium remain partially correlated. In experiments and full-wave simulations we observe enhanced correlations, within an angular range determined by the transport mean free path, which prevail over disorder averaging. Theoretical analysis reveals that this enhancement arises from the interference between scattering trajectories, in which the photons leave the sample and are then virtually reinjected back into it. These paths are the quantum counterpart of the paths that lead to the coherent backscattering of classical light. This work points to opportunities for entanglement transport despite dynamic multiple scattering in complex systems.

Résumé: Quasi-static ultrasound elastography (QSUE) is an imaging technique that mainly provides axial strain maps of tissues when the latter are subjected to compression. In this article, a method for reconstructing the relative shear modulus distribution within a linear elastic and isotropic medium, in QSUE, is introduced. More specifically, the plane stress inverse problem is considered. The proposed method is based on the variational formulation of the equilibrium equations and on the choice of adapted discretization spaces, and only requires displacement fields in the analyzed media to be determined. Results from plane stress and 3-D numerical simulations, as well as from phantom experiments, showed that the method is able to reconstruct the different regions within a medium, with shear modulus contrasts that unambiguously reveal whether inclusions are stiffer or softer than the surrounding material. More specifically, for the plane stress simulations, inclusion-to-background modulus ratios were found to be very accurately estimated, with an error lower than 3%. For the 3-D simulations, for which the plane stress conditions are no longer satisfied, these ratios were, as expected, less accurate, with an error that remained lower than 10% for two of the three cases analyzed but was around 34% for the last case. Concerning the phantom experiments, a comparison with a shear wave elastography technique from a clinical ultrasound scanner was also made. Overall, the inclusion-to-background shear modulus ratios obtained with our approach were found to be closer to those given by the phantom manufacturer than the ratios provided by the clinical system.

Résumé: We analyze the band structure of a single-phase metamaterial involving low-frequency flexural resonances by combining asymptotic homogenization and Bloch–Floquet analysis. We provide the closed-form expression of the dispersion relation in the whole Brillouin zone. The dispersion relation involves two effective, frequency-dependent, mass densities associated with symmetric and antisymmetric flexural resonances of the beams at the microscopic scale. We demonstrate that our simple locally-resonant structure produces at low-frequency band-gaps and, in the hyperbolic regions of the dispersion diagram, negative refraction. Our findings are validated by direct numerical calculations.

Résumé: Among the remarkable scattering properties of correlated disordered materials, the origin of pseudogaps and the formation of localized states are some of the most puzzling features. Fundamental differences between scalar and vector waves in both these aspects make their comprehension even more problematic. Here we present an in-depth and comprehensive analysis of the order-to-disorder transition in 2D resonant systems. We show with exact ab initio numerical simulations in finite-size hyperuniform media that localization of 2D vector waves can occur in the presence of correlated disorder, in a regime of moderate density of scatterers. On the contrary, no signature of localization is found for white noise disorder. This is in striking contrast with scalar waves, which localize at high density whatever the amount of correlation. For correlated materials, localization is associated with the formation of pseudogap in the density of states. We develop two complementary models to explain these observations. The first one uses an effective photonic crystal-type framework and the second relies on a diagrammatic treatment of the multiple scattering sequences. We provide explicit theoretical evaluations of the density of states and localization length in good agreement with numerical simulations. In this way, we identify the microscopic processes at the origin of pseudogap formation and clarify the role of the density of states for wave localization in resonant correlated media. The generality of our framework makes possible to apply our predictions for a large variety of scattering systems including dielectric structures with high quality factor, cold atoms, artificial atoms, as well as microwave resonators.

Résumé: We present a theoretical and numerical analysis of the diffraction of acoustic waves by space-time modulated gratings with rigid-type modulations. This is done by deriving the form of the modes which are exact, uncoupled, solutions of the problem in the unbounded regions, inside and outside the grating. The dispersion of the modes is studied as a function of the ratio of the modulation speed to the speed of sound which shows that each spatial diffraction order is associated with a single temporal diffraction order. For a grating of finite extend, the solution is obtained as a superposition of these modes, which couple at the grating interfaces. This provides a numerical, multimodal, method when considering a truncated version of the solution. We provide analysis of the solutions in the harmonic and in the transient regimes.

Résumé: We report a theoretical and experimental investigation of the propagation of nonlinear waves passing over a submerged rectangular step. A multimodal method allows calculating the first-and second-order reflected and transmitted waves. In particular, at the second order, the propagation of free and bound waves is theoretically presented. A detailed analysis of the convergence of the second-order problem shows that a finite truncation of the series of evanescent bound waves is necessary to obtain a smooth and convergent solution. The computed coefficients of the first and second harmonics are experimentally validated via a complete space-time-resolved measurements of the wave propagation, which permits us to verify the relative amplitude, phase and spatial interference (beating) of the free and bound waves at the second order. This result can be useful in future multimodal models since it not only keeps the accuracy of the model with the inclusion of the first part of the evanescent bound terms (being also the dominants) but also ensures the convergence of the multimodal computation with an error that decreases as a function of the number of modes.

Résumé: We study acoustic wave propagation in a waveguide loaded with two resonant side-branch channels. In the low-frequency regime, one-dimensional models are derived in which the effect of the channels are reduced to jump conditions across the junction. When the separation distance is on the scale of the wavelength, which is the case that is usually considered, the jump conditions involve a single channel and acoustically induced transparency occurs due to out-of-phase interferences between the two junctions. In contrast, when the separation distance is subwavelength, a single junction has to be considered and the jump conditions account for the evanescent field coupling the two channels. Such channel pairs can scatter as a dipole, resulting in perfect transmission due to Autler-Townes splitting. We show that combining the two mechanisms offers additional degrees of freedom to control the transmission spectra.

Résumé: We study the possible expansion of the electromagnetic field scattered by a strictly convex metallic nanoparticle with dispersive material parameters placed in a homogeneous medium in a low-frequency regime as a sum of modes oscillating at complex frequencies (diverging at infinity), known in the physics literature as the quasi-normal modes expansion. We show that such an expansion is valid in the static regime and that we can approximate the electric field with a finite number of modes. We then use perturbative spectral theory to show the existence, in a certain regime, of plasmonic resonances as poles of the resolvent for Maxwell's equations with non-zero frequency. We show that, in the time domain, the electric field can be written as a sum of modes oscillating at complex frequencies. We introduce renormalised quantities that do not diverge exponentially at infinity.

Résumé: Multi-plane light conversion (MPLC) allows to perform arbitrary transformations on a finite set of spatial modes with no theoretical restriction to the quality of the transformation. Even though the number of shaped modes is in general small, the number of modes transmitted by an MPLC system is extremely large. In this paper, we aim to characterize the transmission properties of a multi-plane light converter inside and outside the design-modes subspace. We report the construction of the full transmission matrix of such systems. By performing singular value decompositions, we individuate ways to evaluate their efficiency in performing the design transformation. Moreover, we develop an analytical random matrix model that suggests that in the regime of a large number of shaped modes an MPLC system behaves like a random scattering medium with limited number of controlled channels.

Résumé: In sufficiently strong scattering media, light transport is suppressed and modes are exponentially localized. Andersonlike localized states have long been recognized as potential candidates for high-Q optical modes for low-threshold, cost-effective random lasers. Operating in this regime remains, however, a challenge since Anderson localization is difficult to achieve in optics, and nonlinear mode interaction compromises its observation. Here, we exhibit individually each lasing mode of a low-dimension solid-state random laser by applying a non-uniform optical gain. By undoing gain competition and cross-saturation, we demonstrate that all lasing modes are spatially localized.We find that selective excitation significantly reduces the lasing threshold, while lasing efficiency is greatly improved. We show further how their spatial locations are critical to boost laser power efficiency. By efficiently suppressing the spatial hole burning effect, we can turn on the optimally outcoupled random lasing modes. Our demonstration opens the road to the exploration of linear and nonlinear mode interactions in the presence of gain, as well as disorder-engineering for laser applications.

Résumé: We present a theoretical and experimental study of a resonator of the Helmholtz type for the control of the swell. An experimental demonstration of the shielding effect by a belt made of evenly distributed resonators is given. We then provide in-depth analysis of the Fano resonance resulting from the interference between the dock scattering (the background) and the resonant cavity scattering. This is done thanks to space-time resolved experiments which provides the complexvalued scattering coefficients and amplitude within the resonator. We provide a one-dimensional model derived in the shallow water regime owing to asymptotic analysis. The model contains the two ingredients of the Fano resonance and allows us to exhibit the damping due to leakage. When adding heuristically the damping due to losses, it reproduces the main features of the resonance observed experimentally.

Résumé: © 2021 The Author(s). We study some effective transmission conditions able to reproduce the effect of a periodic array of Dirichlet wires on wave propagation, in particular when the array delimits an acoustic Faraday cage able to resonate. In the study of Hewett & Hewitt (2016 Proc. R. Soc. A 472, 20160062 (doi:10.1098/rspa.2016.0062)) different transmission conditions emerge from the asymptotic analysis whose validity depends on the frequency, specifically the distance to a resonance frequency of the cage. In practice, dealing with such conditions is difficult, especially if the problem is set in the time domain. In the present study, we demonstrate the validity of a simpler unified model derived in Marigo & Maurel (2016 Proc. R. Soc. A 472, 20160068 (doi:10.1098/rspa.2016.0068)), where unified means valid whatever the distance to the resonance frequencies. The effectiveness of the model is discussed in the harmonic regime owing to explicit solutions. It is also exemplified in the time domain, where a formulation guaranteeing the stability of the numerical scheme has been implemented.

Résumé: © 2021 American Physical Society. Accurate measurements of the thermal resistance between micro-objects made of insulating materials are complex because of their small size, low conductivity, and the presence of various ill-defined gaps. We address this issue using a modified scanning thermal microscope operating in vacuum and in air. The sphere-plate geometry is considered. Under controlled heating power, we measure the temperature on top of a glass microsphere glued to the probe as it approaches a glass plate at room temperature with nanometer accuracy. In vacuum, a jump is observed at contact. From this jump in temperature and the modeling of the thermal resistance of a sphere, the sphere-plate contact resistance RK=(1.4±0.18)×107KW-1 and effective radius r=36±4 nm are obtained. In air, the temperature on top of the sphere shows a decrease starting from a sphere-plate distance of 200μm. A jump is also observed at contact, with a reduced amplitude. The sphere-plate coupling out of contact can be described by the resistance shape factor of a sphere in front of a plate in air, placed in a circuit involving a series and a parallel resistance that are determined by fitting the approach curve. The contact resistance in air RK - =(1.2±0.46)×107KW-1 is then estimated from the temperature jump. The method is quantitative without requiring any tedious multiple-scale numerical simulation, and is versatile to describe the coupling between micro-objects from large distances to contact in various environments.

Résumé: © 2020 American Physical Society. We experimentally investigate the valley-Hall effect for interfacial edge states, highlighting the importance of the modal patterns between geometrically distinct regions within a structured elastic plate. These experiments, for vibration, are at a scale where detailed measurements are taken throughout the system and not just at the input/output ports; this exposes the coupling between geometrically distinct modes that underlie the differences between wave transport around gentle and sharp bends.

Résumé: © 2020, Springer Nature B.V. The time-domain propagation of scalar waves across a periodic row of inclusions is considered in 2D. As the typical wavelength within the background medium is assumed to be much larger than the spacing between inclusions and the row width, the physical configuration considered is in the low-frequency homogenization regime. Furthermore, a high contrast between one of the constitutive moduli of the inclusions and of the background medium is also assumed. So the wavelength within the inclusions is of the order of their typical size, which can further induce local resonances within the microstructure. In Pham et al. (J. Mech. Phys. Solids 106:80–94, 2017), two-scale homogenization techniques and matched-asymptotic expansions have been employed to derive, in the harmonic regime, effective jump conditions on an equivalent interface. This homogenized model is frequency-dependent due to the resonant behavior of the inclusions. In this context, the present article aims at investigating, directly in the time-domain, the scattering of waves by such a periodic row of resonant scatterers. Its effective behavior is first derived in the time-domain and some energy properties of the resulting homogenized model are analyzed. Time-domain numerical simulations are then performed to illustrate the main features of the effective interface model obtained and to assess its relevance in comparison with full-field simulations.

Résumé: © 2020 We consider the effect of an array of plates or beams over a semi-infinite elastic ground on the propagation of elastic waves hitting the interface. The plates/beams are slender bodies with flexural resonances at low frequencies able to perturb significantly the propagation of waves in the ground. An effective model is obtained using asymptotic analysis and homogenization techniques, which can be expressed in terms of the ground alone with effective dynamic (frequency-dependent) boundary conditions of the Robin's type. For an incident plane wave at oblique incidence, the displacement fields and the reflection coefficients are obtained in closed forms and their validity is inspected by comparison with direct numerics in a two-dimensional setting.

Résumé: © 2020 American Physical Society. We study light scattering by systems combining randomly rough surface and volume dielectric fluctuations. We introduce a general model including correlations between surface and volume disorders, and we study the scattering properties within a single-scattering approach. We identify different regimes of surface and volume dominated scattering depending on length scales characterizing the surface and volume disorders. For uncorrelated disorders, we discuss the polarization response of each source of disorder, and show how polarimetric measurements can be used to separate the surface and volume contributions in the total measured diffusely scattered intensity. For correlated systems, we identify two configurations of volume disorder which, respectively, couple weakly or strongly to surface scattering via surface-volume cross correlations. We illustrate these effects on different configurations exhibiting interference patterns in the diffusely scattered intensity, which may be of interest for the characterization of complex systems or for the design of optical components by engineering the degree of surface-volume correlations.

Résumé: © 2020 by the authors. This study follows from Maurel et al., Phys. Rev. B 98, 134311 (2018), where we reported on direct numerical observations of out-of-plane shear surface waves propagating along an array of plates atop a guiding layer, as a model for a forest of trees. We derived closed form dispersion relations using the homogenization procedure and investigated the effect of heterogeneities at the top of the plates (the foliage of trees). Here, we extend the study to the derivation of a homogenized model accounting for heterogeneities at both endings of the plates. The derivation is presented in the time domain, which allows for an energetic analysis of the effective problem. The effect of these heterogeneous endings on the properties of the surface waves is inspected for hard heterogeneities. It is shown that top heterogeneities affect the resonances of the plates, hence modifying the cut-off frequencies of a wave mathematically similar to the so-called Spoof Plasmon Polariton (SPP) wave, while the bottom heterogeneities affect the behavior of the layer, hence modifying the dispersion relation of the Love waves. The complete system simply mixes these two ingredients, resulting in hybrid surface waves accurately described by our model.

Résumé: © 2019 Acoustical Society of America. An accurate and numerically inexpensive method is presented to calculate the reflection of in-plane waves at the free surface of an elastic substrate supporting a periodic array of plates. The method is based on the expansions of the elastic fields on the pseudo-periodic modes in the substrate and on the Lamb modes in the plates. These expansions involve unknown amplitudes which are determined by simple matrix inversion when accounting for the boundary conditions at the surface of the substrate and at the free edges of the plates. Exemplifying results are reported in a wide range of frequency covering two resonances of the plates which are analyzed: a flexural resonance of slender bodies and the quasi-resonance of the so-called edge mode. The convergence of the method is inspected quantitatively; it is shown that it is good in view of the fact that the stress is singular at the corners of the plates in contact with the substrate. In particular, the scattering coefficients converge as 1/N s 3/2 with N s the truncation of the expansions.

Résumé: © 2019 We address the perfect transmission of a plane acoustic wave at oblique incidence on a perforated, sound penetrable or rigid, film in two-dimensions. It is shown that the Brewster incidence θ∗ realizing so-called extraordinary transmission due to matched impedances varies significantly when the thickness e of the film decreases. For thick films, i.e. ke≫1 with k the incident wavenumber, the classical effective medium model provides an accurate prediction of the Brewster angle independent of e (this Brewster angle is denoted θB). However, for thinner films with ke<1, θ∗ becomes dependent of e and it deviates from θB. To properly describe this shift, an interface model is used (Marigo et al., 2017) which accurately reproduces the spectra of ultrathin to relatively thick perforated films. Depending on the contrasts in the material properties of the film and of the surrounding matrix, decreasing the film thickness can produce an increase or a decrease of θ∗; it can also produce the disappearance of a perfect transmission or to the contrary its appearance.

Résumé: © 2019 Cambridge University Press. We study the propagation of water waves over a ridge structured at the subwavelength scale using homogenization techniques able to account for its finite extent. The calculations are conducted in the time domain considering the full three-dimensional problem to capture the effects of the evanescent field in the water channel over the structured ridge and at its boundaries. This provides an effective two-dimensional wave equation which is a classical result but also non-intuitive transmission conditions between the region of the ridge and the surrounding regions of constant immersion depth. Numerical results provide evidence that the scattering properties of a structured ridge can be strongly influenced by the evanescent fields, a fact which is accurately captured by the homogenized model.

Résumé: © 2019 Acoustical Society of America. The influence of the spacing on the resonance of a periodic arrangement of Helmholtz resonators is inspected. An effective problem is used which accurately captures the properties of the resonant array within a large range of frequencies, and whose simplified version leaves an impedance condition. It is shown that the strength of the resonance is enhanced when the array becomes sparser. This degree of freedom on the radiative damping is of particular interest since it does not affect the resonance frequency nor the damping due to losses within each resonator; in addition, it does not affect the total thickness of the array. It is shown that it can be used for the design of a perfect absorbing wall.

Résumé: © 2019 Optical Society of America We study the propagation of waves in a set of absorbing subwavelength scatterers positioned on a stealth hyperuniform point pattern. We show that spatial correlations in the disorder substantially enhance absorption compared to a fully disordered structure with the same density of scatterers. The non-resonant nature of the mechanism provides broad angular and spectral robustness. These results demonstrate the possibility to design low-density materials with blackbody-like absorption.

Résumé: © 2019 Optical Society of America. We provide a simple semi-classical formalism to describe the coupling between one or several quantum emitters and a structured environment. Describing the emitter by an electric polarizability, and the surrounding medium by a Green function, we show that an intuitive scattering picture allows one to derive a coupling equation from which the eigenfrequencies of the coupled system can be extracted. The model covers a variety of regimes observed in light–matter interaction, including weak and strong coupling, coherent collective interactions, and incoherent energy transfer. It provides a unified description of many processes, showing that different interaction regimes are actually rooted on the same ground. It can also serve as a basis for the development of more refined models in a full quantum electrodynamics framework.

Résumé: © 2019 Author(s). 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 and robust and presents a deeply subwavelength ratio wavelength/thickness of 18.

Résumé: © 2018 American Physical Society. We inspect the unusual scattering properties reported recently for structures alternating dielectric layers of subwavelength thicknesses near the critical angle for total reflection. In TE polarization, the unusual scattering properties are captured by an effective model with an accuracy less than 1% up to kd∼0.1. It is shown that the propagation is simply dispersive with local dispersion while the boundary layer effects are captured through a nonintuitive transmission condition. The resulting model involves two parameters depending only on the characteristics of the multilayer and which are given in closed forms. Besides, we show that a discrete description of the spectrum using the layer thickness d as unit of measure misses the complexity of the continuous spectrum exhibiting strong variations within the scale d. This ultrasensitivity to variations below d is attributable to strong boundary layer effects and, for large structures, to a cooperation between the boundaries and the phase accumulation within the structure.

Résumé: © 2018 American Physical Society. We study photon echo generation in disordered media with the help of multiple scattering theory based on diagrammatic approach and numerical simulations. We show that a strong correlation exists between the driving fields at the origin of the echo and the echo beam. Opening the way to a better understanding of nonlinear wave propagation in complex materials, this work supports recent experimental results with applications to the measurement of the optical dipole lifetime T2 in powders.

Résumé: © 2018 Cambridge University Press. We consider the propagation of water waves in a waveguide with a surface-piercing circular cylinder. A plane wave interacting with the cylinder leads to a Fano resonance resulting in strong scattering with a large reflection coefficient. Using a smoothly varying bathymetry whose shape is optimized, we show both numerically and experimentally that broadband and robust backscattering reduction can be obtained below the first cutoff frequency.

Résumé: © 2018 American Physical Society. We study theoretically the mutual information between reflected and transmitted speckle patterns produced by wave scattering from disordered media. The mutual information between the two speckle images recorded on an array of N detection points (pixels) takes the form of long-range intensity correlation loops that we evaluate explicitly as a function of the disorder strength and the Thouless number g. Our analysis, supported by extensive numerical simulations, reveals a competing effect of cross-sample and surface spatial correlations. An optimal distance between pixels is proven to exist that enhances the mutual information by a factor Ng compared to the single-pixel scenario.

Résumé: © 2017 Cambridge University Press. In this paper we study both theoretically and experimentally the inverse problem of indirectly measuring the shape of a localized bottom deformation with a non-instantaneous time evolution, from either an instantaneous global state (space-based inversion) or a local time-history record (time-based inversion) of the free-surface evolution. Firstly, the mathematical inversion problem is explicitly defined and uniqueness of its solution is established. We then show that this problem is ill-posed in the sense of Hadamard, rendering its solution unstable. In order to overcome this difficulty, we introduce a regularization scheme as well as a strategy for choosing the optimal value of the associated regularization parameter. We then conduct a series of laboratory experiments in which an axisymmetric three-dimensional bottom deformation of controlled shape and time evolution is imposed on a layer of water of constant depth, initially at rest. The detailed evolution of the air-liquid interface is measured by means of a free-surface profilometry technique providing space- and time-resolved data. Based on these experimental data and employing our regularization scheme, we are able to show that it is indeed possible to reconstruct the seabed profile responsible for the linear free-surface dynamics either by space- or time-based inversions. Furthermore, we discuss the different relative advantages of each type of reconstruction, their associated errors and the limitations of the inverse determination.

Résumé: © 2017, American Association for the Advancement of Science. All rights reserved. The microstructure of a medium strongly influences how light propagates through it. The amount of disorder it contains determines whether the medium is transparent or opaque. Theory predicts that exciting such a medium homogeneously and isotropically makes some of its optical properties depend only on the medium’s outer geometry. Here, we report an optical experiment demonstrating that the mean path length of light is invariant with respect to the microstructure of the medium it scatters through. Using colloidal solutions with varying concentration and particle size, the invariance of the mean path length is observed over nearly two orders of magnitude in scattering strength. Our results can be extended to a wide range of systems—however ordered, correlated, or disordered—and apply to all wave-scattering problems.

Résumé: © 2017 American Physical Society. We study the defect-guided modes supported by a set of metallic rods structured at the subwavelength scale. Following the idea of photonic crystal waveguide, we show that spoof plasmon surface waves can be manipulated at subwavelength scale. We demonstrate that these waves can propagate without leakage along a row of rods having a different length than the surrounding medium and we provide the corresponding dispersion relation. The principle of this subwavelength colored guide is validated experimentally. This allows us to propose the design of a wavelength demultiplexer whose efficiency is illustrated in the microwave regime.

Résumé: © 2017, The Author(s).Quantum revival is described as the time-periodic reconstruction of a wave packet initially localized in space and time. This effect is expected in finite-size systems which exhibit commensurable discrete spectrum such as the infinite quantum well. Here, we report on the experimental observation of full and fractional quantum revival for classical waves in a two dimensional cavity. We consider flexural waves propagating in thin plates, as their quadratic dispersion at low frequencies mimics the dispersion relation of quantum systems governed by Schrödinger equation. Time-dependent excitation and measurement are performed at ultrasonic frequencies and reveal a periodic reconstruction of the initial elastic wave packet.

Résumé: A fundamental challenge in physics is controlling the propagation of waves in disordered media despite strong scattering from inhomogeneities. Spatial light modulators enable one to synthesize (shape) the incident wavefront, optimizing the multipath interference to achieve a specific behaviour such as focusing light to a target region. However, the extent of achievable control is not known when the target region is much larger than the wavelength and contains many speckles. Here we show that for targets containing more than g speckles, where g is the dimensionless conductance, the extent of transmission control is substantially enhanced by the long-range mesoscopic correlations among the speckles. Using a filtered random matrix ensemble appropriate for coherent diffusion in open geometries, we predict the full distributions of transmission eigenvalues as well as universal scaling laws for statistical properties, in excellent agreement with our experiment. This work provides a general framework for describing wavefront-shaping experiments in disordered systems.

Résumé: © 2017 American Physical Society.We observe time-correlated emission between a single CdSe/CdS/ZnS quantum dot exhibiting single-photon statistics and a fluorescent nanobead located micrometers apart. This is accomplished by coupling both emitters to a silver nanowire. Single plasmons are created on the latter from the quantum dot, and transfer energy to excite in turn the fluorescent nanobead. We demonstrate that the molecules inside the bead show the same blinking behavior as the quantum dot.

Résumé: © 2017 American Physical Society.Collective phenomena emerging from nonlinear interactions between multiple oscillators, such as synchronization and frequency locking, find applications in a wide variety of fields. Optomechanical resonators, which are intrinsically nonlinear, combine the scientific assets of mechanical devices with the possibility of long distance controlled interactions enabled by traveling light. Here we demonstrate light-mediated frequency locking of three distant nano-optomechanical oscillators positioned in a cascaded configuration. The oscillators, integrated on a chip along a common coupling waveguide, are optically driven with a single laser and oscillate at gigahertz frequency. Despite an initial mechanical frequency disorder of hundreds of kilohertz, the guided light locks them all with a clear transition in the optical output. The experimental results are described by Langevin equations, paving the way to scalable cascaded optomechanical configurations.

Résumé: © 2015 American Physical Society. Spatial modulation of the incident wave front has become a powerful method for controlling the diffusive transport of light in disordered media; however, such interference-based control is intrinsically sensitive to frequency detuning. Here, we show analytically and numerically that certain wave fronts can exhibit strongly enhanced total transmission or absorption across bandwidths that are orders of magnitude broader than the spectral correlation width of the speckles. Such broadband enhancement is possible due to long-range correlations in coherent diffusion, which cause the spectral degrees of freedom to scale as the square root of the bandwidth rather than the bandwidth itself.

Résumé: © 2015 Elsevier B.V. The coherent propagation of elastic waves in a solid filled with a random distribution of pinned dislocation segments is studied to all orders in perturbation theory. It is shown that, within the independent scattering approximation, the perturbation series that generates the mass operator is a geometric series that can thus be formally summed. A divergent quantity is shown to be renormalizable to zero at low frequencies. At higher frequencies said quantity can be expressed in terms of a cut-off with dimensions of length, related to the dislocation length, and physical quantities can be computed in terms of two parameters, to be determined by experiment. The approach used in this problem is compared and contrasted with the scattering of de Broglie waves by delta-function potentials as described by the Schrödinger equation.

Résumé: © 2015 American Physical Society. ©2015 American Physical Society. We study theoretically the spatial correlations between the intensities measured at the input and output planes of a disordered scattering medium. We show that at large optical thicknesses, a long-range spatial correlation persists and takes negative values. For small optical thicknesses, short-range and long-range correlations coexist, with relative weights that depend on the optical thickness. These results may have direct implications for the control of wave transmission through complex media by wave-front shaping, thus finding applications in sensing, imaging, and information transfer.

Résumé: © 2015 IEEE. Multiple scattering of light in a disordered medium with gain may provide for the necessary feedback to achieve lasing action without an optical cavity. In addition to the fundamental interest raised by this regime of light-matter interaction in open cavity, the relatively simple design of these so-called "random lasers" and the possibility to control their emission open perspective of new applications in domains not yet covered by conventional lasers.

Résumé: © 2015 AIP Publishing LLC. In this paper, the influence of disorder on 1D periodic lattice of resonant scatterers is inspected. These latter have multiple resonance frequencies which produce band gaps in the transmission spectrum. One peculiarity of the presented system is that it is chosen with a nearly perfect overlap between the Bragg and the second hybridization band gaps. In the case of a perfectly ordered lattice, and around this overlap, this produces a narrow transparency band within a large second bandgap. As expected, the effect of the disorder is generally to increase the width of the band gaps. Nevertheless, the transparency band appears to be robust with respect to an increase in the disorder. In this paper, we study this effect by means of experimental investigations and numerical simulations.

Résumé: © 2015. We describe recent developments in the characterization of three-dimensional speckle fields produced by scattering of electromagnetic waves. In many practical situations the description of such fields requires approaches going beyond the Gaussian statistics approximation. Quantitative measures of spatial coherence and polarization can be defined from the field-field correlation matrix, known as the cross-spectral density matrix in coherence theory. The complex degree of mutual polarization provides a measure of the similarity between polarization states at two different points. The degree of spatial coherence describes spatial coherence and averages out the polarization properties. We discuss their behavior in speckle fields produced by multiple scattering in disordered materials. A number of non-universal properties arise, that are related to the internal microscopic structure of the scattering medium. Non-universality affects observables quantities, such as spatial correlations in speckle patterns measured in the near field of the medium surface, statistics of the local density of states or the depolarization of the exciting electromagnetic field due to scattering. Specific microscopic scales are necessary to describe the non-universal behaviors, that characterize the scale-dependent morphology of the scattering medium.

Résumé: © 2014 Elsevier B.V. We address the problem of acoustic propagation in waveguides with wall impedance, or Robin, boundary condition. Two improved multimodal methods are developed to remedy the problem of the low convergence of the series in the standard modal approach. In the first improved method, the series is enriched with an additional mode, which is thought to be able to restore the right boundary condition. The second improved method consists in a reformulation of the expansions able to restore the right boundary conditions for any truncation, similar to polynomial subtraction technique. Surprisingly, the first improved method is found to be the most efficient. Notably, the convergence of the scattering properties is increased from N-1 in the standard modal method to N-3 in the reformulation and N-5 in the formulation with a supplementary mode. The improved methods are shown to be of particular interest when surface waves are generated near the impedance wall.

Résumé: © 2014 American Physical Society. We investigate the possibility of using the independence of the transmitted speckle pattern on the illumination condition as a signature of Anderson localization in a single configuration of a two-dimensional and open disordered medium. The analysis is based on exact numerical simulations of multiple light scattering. We introduce a similarity function that we propose as a reliable observable to probe Anderson localization without requiring any statistical averaging over an ensemble.

Résumé: A fundamental insight in the theory of diffusive random walks is that the mean length of trajectories traversing a finite open system is independent of the details of the diffusion process. Instead, the mean trajectory length depends only on the system's boundary geometry and is thus unaffected by the value of the mean free path. Here we show that this result is rooted on a much deeper level than that of a random walk, which allows us to extend the reach of this universal invariance property beyond the diffusion approximation. Specifically, we demonstrate that an equivalent invariance relation also holds for the scattering of waves in resonant structures as well as in ballistic, chaotic or in Anderson localized systems. Our work unifies a number of specific observations made in quite diverse fields of science ranging from the movement of ants to nuclear scattering theory. Potential experimental realizations using light fields in disordered media are discussed.

Résumé: © 2015 American Physical Society. The flat-lens concept based on negative refraction proposed by Veselago in 1968 has been mostly investigated in the monochromatic regime. It was recently recognized that time development of the superlensing effect discovered in 2000 by Pendry is yet to be assessed and may spring surprises: Time-dependent illumination could improve the spatial resolution of the focusing. We investigate dynamics of flexural wave focusing by a 45°-tilted square lattice of circular holes drilled in a duralumin plate. Time-resolved experiments reveal that the focused image shrinks with time below the diffraction limit, with a lateral resolution increasing from 0.8λ to 0.35λ, whereas focusing under harmonic excitation remains diffraction limited. Modal analysis reveals the role in pulse reconstruction of radiating lens resonances, which repeatedly self-synchronize at the focal spot to shape a superoscillating field.

Résumé: Periodic arrays of nanorods can present a resonant response at specific geometric conditions. We use a multiple scattering approach to analyze the optical response of subwavelength nanowire gratings made of arbitrary anisotropic materials. When the rods are made of magneto-optical dielectrics we show that there is a complex interplay between the geometric resonances of the grating and the magneto-optical Kerr effects (MOKE) response. As we will show, for a given polarization of the incident light, a resonant magneto-optical response can be obtained by tuning the incidence angle and grating parameters to operate near the resonance condition for the opposite polarization. Our results could be important to understand and optimize MOKE structures and devices based on resonant subwavelength gratings and could open new perspectives in sensing applications.

Résumé: Spatial field correlation functions represent a key quantity for the description of mesoscopic phenomena in disordered media and the optical characterization of complex materials. Yet many aspects related to the vector nature of light waves have not been investigated so far. We study theoretically the polarization and coherence properties of electromagnetic waves produced by a dipole source in a three-dimensional uncorrelated disordered medium. The spatial field correlation matrix is calculated analytically using a multiple-scattering theory for polarized light. This allows us to provide a formal description of the light depolarization process in terms of “polarization eigenchannels” and to derive analytical formulas for the spatial coherence of multiply scattered light.

Résumé: The ability of left-handed materials to overcome the diffraction limit was first considered as one of the most exciting and challenging outcomes of the negative refraction concept. Flat lens focusing of elastic waves is, however, a challenge. We demonstrate broadband focusing of elastic waves at 10 kHz carrier frequency, below the first stop band, in a 45°-tilted square array of circular air holes perforated in a Duraluminium thin plate. By adjusting the relative thickness of the outer plate we achieve large-angle negative refraction with diffraction-limited lateral resolution. We find good agreement with a simple beam-lattice model and finite-difference time-domain simulations. © 2013 AIP Publishing LLC.

Résumé: We use a scattering formalism to derive a condition of strong coupling between a resonant scatterer and an Anderson localized mode for electromagnetic waves in two dimensions. The strong coupling regime is demonstrated based on exact numerical simulations, in perfect agreement with theory. The strong coupling threshold can be expressed in terms of the Thouless conductance and the Purcell factor. This connects key concepts in transport theory and cavity quantum electrodynamics, and provides a practical tool for the design or analysis of experiments. © 2013 American Physical Society.

Résumé: 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 ∈-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). © 2013 Optical Society of America.

Résumé: We study theoretically light focusing at subwavelength scale inside a disordered strongly scattering open medium. We show that broadband time reversal at a single point antenna, in conjunction with near-field interactions and multiple scattering, produces spatial focusing with a quality comparable to that obtained in an ideal closed cavity. This provides different perspectives for super-resolved optical imaging and coherent control of single nanosources or absorbers in complex media. © 2013 American Physical Society.

Résumé: In this paper, we study the possibility of using lifetime data to estimate the position and orientation of a fluorescent dipole source within a disordered medium. The vector Foldy-Lax equations are employed to calculate the interaction between the fluorescent source and the scatterers that are modeled as point-scatterers. The numerical experiments demonstrate that if good prior knowledge about the positions of the scatterers is available, the position and orientation of the dipole source can be retrieved from its lifetime data with precision. If there is uncertainty about the positions of the scatterers, the dipole source position can be estimated within the same level of uncertainty. © 2013 Optical Society of America.

Résumé: Random lasing is reported in a dye-circulated structured polymeric microfluidic channel. The role of disorder, which results from limited accuracy of photolithographic process, is demonstrated by the variation of the emission spectrum with local-pump position and by the extreme sensitivity to a local perturbation of the structure. Thresholds comparable to those of conventional microfluidic lasers are achieved, without the hurdle of state-of-the-art cavity fabrication. Potential applications of optofluidic random lasers for on-chip sensors are discussed. Introduction of random lasers in the field of optofluidics is a promising alternative to on-chip laser integration with light and fluidic functionalities. © 2012 American Institute of Physics.

Résumé: 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. © 2012 American Physical Society.

Résumé: Active control of the spatial pump profile is proposed to exercise control over random laser emission. We demonstrate numerically the selection of any desired lasing mode from the emission spectrum. An iterative optimization method is employed, first in the regime of strong scattering where modes are spatially localized and can be easily selected using local pumping. Remarkably, this method works efficiently even in the weakly scattering regime, where strong spatial overlap of the modes precludes spatial selectivity. A complex optimized pump profile is found, which selects the desired lasing mode at the expense of others, thus demonstrating the potential of pump shaping for robust and controllable single mode operation of a random laser. © 2012 American Physical Society.

Résumé: We develop a perturbative formalism for the interaction of a magneto-optical nanoparticle with a flat surface made of a dielectric or metallic material. The formalism leads to a simple interpretation of the interplay between the purely dielectric and the magneto-optical responses, in terms of excitation of (and radiation by) two orthogonal electric dipoles. We analyze two different routes for the enhancement of the magneto-optical response with respect to the purely dielectric contribution, both based on the nanoparticle-surface interaction. The enhancement is discussed in terms of relevant magneto-optical signals, such as changes in reflectivity, polarization (Kerr) rotation, and ellipticity. © 2012 American Physical Society.

Résumé: We present a study of the attenuation length in a one-dimensional array of alternating left- and right-handed materials in which both the permittivities and the permeabilities are disordered. This type of structure has been shown to present an anomaly in the attenuation length when only permeabilities are disordered. We derive a simple analytical expression of the attenuation length, when the disorder in the refraction index is due to perturbations in both the permeability and the permittivity. Our expression is able to explain the transition to the anomalous behavior when perturbation only in the permeability or only in the permittivity is considered. Besides, we show that the anomaly is dramatically affected when considering perturbations in permeability and permittivity. The coupling effects are able to restore the ordinary localization length. © 2012 American Physical Society.

Résumé: The scattering of a scalar wave propagating in a waveguide containing weak penetrable scatterers is inspected in the Born approximation. The scatterers are of arbitrary shape and present a contrast both in density and in wavespeed (or bulk modulus), a situation that can be translated in the context of SH waves, water waves, or transverse electric/transverse magnetic polarized electromagnetic waves. For small size inclusions compared to the waveguide height, analytical expressions of the transmission and reflection coefficients are derived, and compared to results of direct numerical simulations. The cases of periodically and randomly distributed inclusions are considered in more detail, and compared with unbounded propagation through inclusions. Comparisons with previous results valid in the low frequency regime are proposed. © 2012 Acoustical Society of America.

Résumé: Radiation by elementary sources is a basic problem in wave physics. We show that the time-domain energy flux radiated from electromagnetic and acoustic subwalength sources exhibits remarkable features. In particular, a subtle trade-off between source emission and absorption underlies the mechanism of radiation. This behavior should be observed for any kind of classical waves, thus having broad potential implications. We discuss the implication for subwavelength focusing by time reversal with active sources. Copyright © EPLA, 2012.

Résumé: Recent numerical and theoretical studies have demonstrated that the modes at threshold of a random laser are in direct correspondence with the resonances of the same system without gain, a feature which is well known in conventional lasers but not known until recently for random lasers. This paper presents numerical results of the multimode regime that takes place when the pumping rate is progressively increased above threshold. Behavior that is already known in standard lasers, such as mode competition and nonlinear wave mixing, are shown to also take place in random lasers thus reinforcing their recent modal description. However, due to the complexity of the laser modes and to the openness of such lasers, which require large external pumping to compensate for strong loss, one observes that these effects are systematic and can be more pronounced than in a conventional laser. © 2011 Optical Society of America.

Résumé: 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. © 2011 American Physical Society.

Résumé: In this Letter, we study the Purcell effect in a 3D disordered dielectric medium through fluorescence decay rates of nanosized light sources. We report distributions of Purcell factor with non-Gaussian long-tailed statistics and an enhancement of up to 8 times the average value. We attribute this large enhancement to strong fluctuations of the local density of states induced by near-field scattering sustained by more than one particle. Our findings go beyond standard diagrammatic and single-scattering models and can be explained only by taking into account the full near-field interaction. © 2011 American Physical Society.

Résumé: We present an experimental study on the trapped modes occurring around a vertical surface-piercing circular cylinder of radius a placed symmetrically between the parallel walls of a long but finite water waveguide of width 2d. A wavemaker placed near the entrance of the waveguide is used to force an asymmetric perturbation into the guide, and the free-surface deformation field is measured using a global single-shot optical profilometric technique. In this configuration, several values of the aspect ratio a/d were explored for a range of driving frequencies below the waveguide's cutoff. Decomposition of the obtained fields in harmonics of the driving frequency allowed for the isolation of the linear contribution, which was subsequently separated according to the symmetries of the problem. For each of the aspect ratios considered, the spatial structure of the trapped mode was obtained and compared to the theoretical predictions given by a multipole expansion method. The waveguide'obstacle system was further characterized in terms of reflection and transmission coefficients, which led to the construction of resonance curves showing the presence of one or two trapped modes (depending on the value of a/d), a result that is consistent with the theoretical predictions available in the literature. The frequency dependency of the trapped modes with the geometrical parameter a/d was determined from these curves and successfully compared to the theoretical predictions available within the frame of linear wave theory. © 2011 Cambridge University Press.

Résumé: Acoustic scattering by an ensemble of scatterers whose positions are close to the positions of a periodic arrangement (with small and random perturbations in the position of each scatterer) is considered in one dimension. Three methods are compared to obtain the effective wavenumber of the coherent field. The first two methods, the quasi-crystalline approximation (QCA) and the coherent potential approximation (CPA), give the exact Floquet solution in the periodic case. However, in a perturbed almost periodic configuration, they give different dispersion relations. These methods are compared to a perturbation approach and confronted with the results obtained from direct numerical calculations. It is shown that CPA is able to get the first correction to the Floquet dispersion relation due to the introduced perturbation, in agreement with the perturbation approach and with direct numerical results, while QCA is unable to get this correction. © 2010 Taylor & Francis.

Résumé: We measure the statistical distribution of the local density of optical states (LDOS) on disordered semicontinuous metal films. We show that LDOS fluctuations exhibit a maximum in a regime where fractal clusters dominate the film surface. These large fluctuations are a signature of surface-plasmon localization on the nanometer scale. © 2010 The American Physical Society.

Résumé: The problem of how a wave propagates in an infinite medium filled with scatterers has revealed the notion of an effective medium: the mean wave propagates as in an homogeneous medium with complex index. Is this notion of an effective medium still valid when the scatterers are bounded in space? The problem is treated here for isotropic point scatterers. It is shown that (i) the waves propagate inside the slab with an effective wavenumber K being the same as that in an infinite medium, (ii) the reflection and transmission coefficients of the slab mainly behave as R≃(1-eiKL)(k-K)2k and T≃eiKL at leading order, (iii) the reflection and transmission coefficients of a single interface are related to R and T with the usual law of optics and (iv) the boundary conditions to be applied at the interface are the continuity of the field and its first derivative for isotropic scatterers. Finally, numerical experiments in one dimension show satisfactory agreement with the presented theory. © 2009 Elsevier B.V.

Résumé: We study the number of propagating Bloch modes NB of an infinite periodic billiard chain. The asymptotic semiclassical behavior of this quantity depends on the phase-space dynamics of the unit cell, growing linearly with the wave number k in systems with a non-null measure of ballistic trajectories and going like ∼√k in diffusive systems. We have calculated numerically NB for a waveguide with cosine-shaped walls exhibiting strongly diffusive dynamics. The semiclassical prediction for diffusive systems is verified to good accuracy and a connection between this result and the universality of the parametric variation of energy levels is presented. © 2010 The American Physical Society.

Résumé: We study the statistics of the fluorescence decay rate of a dipole emitter embedded in a strongly scattering medium. In the multiple-scattering regime, the probability of observing a decrease in the decay rate is substantial, as predicted by exact numerical simulations. The decrease originates from a reduction of the local density of optical states and is due to collective interactions and interferences. In the strong-scattering regime, signatures of recurrent scattering are visible in the behavior of the average decay rate. © 2010 The American Physical Society.

Résumé: We introduce a method to experimentally measure the monochromatic transmission matrix of a complex medium in optics. This method is based on a spatial phase modulator together with a full-field interferometric measurement on a camera. We determine the transmission matrix of a thick random scattering sample. We show that this matrix exhibits statistical properties in good agreement with random matrix theory and allows light focusing and imaging through the random medium. This method might give important insight into the mesoscopic properties of a complex medium. © 2010 The American Physical Society.

Résumé: Radiative corrections to the polarizability tensor of isotropic particles are fundamental to understand the energy balance between absorption and scattering processes. Equivalent radiative corrections for anisotropic particles are not well known. Assuming that the polarization within the particle is uniform, we derived a closed-form expression for the polarizability tensor which includes radiative corrections. In the absence of absorption, this expression of the polarizability tensor is consistent with the optical theorem. An analogous result for infinitely long cylinders was also derived. Magneto optical Kerr effects in non-absorbing nanoparticles with magneto-optical activity arise as a consequence of radiative corrections to the electrostatic polarizability tensor. © 2010 Optical Society of America.

Résumé: We study the spontaneous decay rate of a dipóle emitter close to a metallic nanoparticle in the extreme nearfield regime. The metal is modeled using a nonlocal dielectric function that accounts for the microscopic length scales of the free electron gas. We describe quantitatively the crossover between the macroscopic and microscopic regimes and the enhanced nonradiative decay due to microscopic interactions. Our theory is in agreement with results previously established in the asymptotic near- and far-field regimes. © 2010 Optical Society of America.

Résumé: We study theoretically the detection of the fluorescence intensity emitted by a single emitter coupled to a nanoparticle through a metallic thin film. The coupling results from the overlap of the surface plasmon modes propagating on each interface of the film. We show that the distance between the nanoparticle and the film can be used to tune the apparent quantum yield and the radiation pattern with nanometer-scale sensitivity. Such a system is appealing from the experimental point of view since it involves simple structures that can be controlled using current scanning near-field optical techniques. It could be used to improve the detection sensitivity of molecules embedded in substrates, or to design sensitive biological or chemical plasmonic sensors. © 2009 IOP Publishing Ltd.

Résumé: A subsurface moving dislocation in an elastic half space generates vertical displacements at the free surface. We compare this displacement for two different values of the dislocation viscous drag coefficient. The different resulting surface patterns suggest the free surface plays a decisive dynamical effect. We thus compare this displacement, using the dynamic Green function for an elastic half space, with the result of the calculation using the static Green function for an infinite space, as in the work of Zolotoyabko and Shilo [preceding paper, Phys. Rev. B 80, 136101 (2009), and Shilo and Zolotoyabko, Phys. Rev. Lett. 91, 115506 (2003)] when the dislocation dynamics is the same. Considering the static Green function of an infinite space instead of the correct dynamic Green function of the half space leads to an underestimation of the resulting displacement at the free surface by a factor up to 50 for dislocation depths smaller than one Rayleigh wavelength λR. We also discuss the constraints that recent ultrasound attenuation and resonant ultrasound spectroscopy experiments place on dislocation parameters, such as density and viscous drag coefficient. © 2009 The American Physical Society.

Résumé: The properties of prismatic dislocation loops, generated by radiation in metals, have remained elusive for decades, and recent advances in computational capabilities as well as transmission electron microscopy have renewed interest in their study. Acoustic and elastic waves could become an interesting, nonintrusive, probe to this end, as they have for other dislocation configurations. What then are the characteristics of elastic wave scattering that would be sensitive to a prismatic loop signature? In this paper, we report the scattering cross section for an elastic wave by a prismatic dislocation loop. It differs in significant ways from the analog quantity in the case of pinned dislocation segments, the most significant being the polarization of the scattered wave. The properties of a coherent wave traveling through an elastic medium filled with randomly placed and randomly oriented such loops are also reported. At long wavelengths, the effective wave velocity and attenuation coefficients resemble those for a similar case with pinned dislocation segments. © 2009 American Institute of Physics.

Résumé: In this paper, we present an optical profilometric technique that allows for single-shot global measurement of free-surface deformations. This system consists of a high-resolution system composed of a videoprojector and a digital camera. A fringe pattern of known characteristics is projected onto the free surface and its image is registered by the camera. The deformed fringe pattern arising from the surface deformations is later compared to the undeformed (reference) one, leading to a phase map from which the free surface can be reconstructed. Particularly, we are able to project wavelength-controlled sinusoidal fringe patterns, which considerably increase the overall performance of the technique and the quality of the reconstruction compared to that obtained with a Ronchi grating. In comparison to other profilometric techniques, it allows for single-shot non-intrusive measurement of surface deformations over large areas. In particular, our measurement system and analysis technique is able to measure free surface deformations with sharp slopes up to 10 with a 0.2 mm vertical resolution over an interrogation window of size 450 × 300 mm2 sampled on approximately 6.1 × 106 measurement points. Some illustrative examples of the application of this measuring system to fluid dynamics problems are presented. © 2009 Springer-Verlag.

Résumé: We establish a fundamental relationship between the averaged local density of states and the extinction mean free path of waves propagating in random media. From the principle of causality and the Kramers-Kronig relations, we show that both quantities are connected by dispersion relations and are constrained by a frequency sum rule. The results should be helpful in the analysis of wave transport through complex media and in the design of materials with specific transport properties. © 2009 The American Physical Society.

Résumé: We introduce a methodology to determine quantitatively the depth resolution limit in luminescence diffuse optical imaging. The approach is based on a Cramer-Rao statistical analysis, a noise model, and calculations of photon transport in tissues. We illustrate the method in the case of luminescence imaging in a brain-skull model, showing its potential applications in molecular imaging on small animals. © 2008 Optical Society of America.

Résumé: Acoustic scattering by random collections of identical circular cylinders is considered. Each cylinder is penetrable, with a sound-speed that is close to that in the exterior: the scattering is said to be "weak". Two classes of methods are used. The first is usually associated with the names of Foldy and Lax. Such methods require a "closure assumption", in addition to the governing equations. The second class is based on iterative approximations to integral equations of Lippmann-Schwinger type. Such methods do not use a closure approximation. Our main result is that both approaches lead to exactly the same formulas for the effective wavenumber, correct to second-order in scattering strength and second-order in filling fraction. Approximations for the average wavefield are also derived and compared. © 2008 Elsevier B.V. All rights reserved.

Résumé: We study the fluctuations of the fluorescence decay rate of a single emitter in a random cluster of nanoparticles, in a regime dominated by near-field scattering. Configurational changes of the environment induce statistical changes of the decay rate. Two regimes are considered which differ in terms of transition dipole orientation. In one regime, the orientation of the transition dipole is assumed to remain constant while the configuration of the cluster changes randomly. In another regime, the orientation of the transition dipole is assumed unknown and continuously averaged over the three directions of space. Using exact numerical simulations and a simple analytical model, we show that the statistical distributions of the spontaneous decay rate are substantially different in both regimes. In both cases, the decay rate fluctuations are strongly dependent on the level of absorption at the nanoscale. We discuss the impact of this result in terms of imaging in complex media. © 2008 WILEY-VCH Verlag GmbH & Co. KGaA.

Résumé: The scattering of a surface wave by a pinned edge dislocation in a semi-infinite, homogeneous, isotropic, three-dimensional elastic solid is investigated analytically and numerically. An incident wave excites the dislocation that responds by oscillating as a string endowed with mass, line tension, and damping. The oscillations of the stringlike dislocation generate secondary ("scattered") elastic waves that are the primary object of interest in this study. The back reaction of the re-emitted waves on the dislocation dynamics is neglected, but the wavelength of the radiation is allowed to be large, comparable, or small compared to the length of the dislocation. In view of recent experimental visualizations of these phenomena, we focus particularly on the field behavior at the free surface near the dislocation, and not just on the far field. For the same reason, it is the vertical component of displacement at the free surface that is studied in detail. An efficient numerical procedure for the computation of the appropriate components of the Green's function, using a Filon quadrature for the integration of rapidly oscillating functions, is developed. The numerics is validated with known analytical expressions. The secondary radiation generated by the response of the dislocation to the incident wave is also calculated numerically, and the results are also validated by comparing them with the analytical expressions that can be obtained when the radiation wavelength is very long compared to dislocation length. The interference pattern between incident wave and secondary wave that is generated at the free surface is studied in detail and found to depend strongly not only on wavelength and dislocation geometry (length and orientation) but also on dislocation depth, with the response of the dislocation being a particularly sensitive function of such depth. Results are compared with recent experiments of Shilo and Zolotoyabko [Phys. Rev. Lett. 91, 115506 (2003)] that report visualizations of the surface-wave-dislocation interaction using stroboscopic x-ray imaging. A satisfactory agreement is found. Dislocation velocities of a few percent of the speed of sound and viscosity coefficients of about 10-5 Pa s are inferred. © 2007 The American Physical Society.

Résumé: The problem of Lamb wave propagation in waveguides with varying height is treated by a multimodal approach. The technique is based on a rearrangement of the equations of elasticity that provides a new system of coupled mode equations preserving energy conservation. These coupled mode equations avoid the usual problem at the cut-offs with zero wavenumber. Thereafter, we define an impedance matrix that is governed by a Riccati equation yielding a stable numerical computation of the solution. Incidentally, the versatility of the multimodal method is exemplified by treating analytically the case of slowly varying guide and by showing how to get easily the Green tensor in any geometry. The method is applied for a waveguide whose height is described by a Gaussian function and the energy conservation in verified numerically. We determine the Green tensor in this geometry. © 2006 The Royal Society.

Résumé: We address the problem of an elastic wave coherently propagating through a two-dimensional polycrystal. The main source of scattering is taken to be the interaction with grain boundaries that are in turn modelled as line distribution of dislocations-a good approximation for low angle grain boundaries. First, the scattering due to a single linear array is worked out in detail in a Born approximation, both for longitudinal and transverse polarization and allowing for mode conversion. Next, the polycrystal is modelled as a continuum medium filled with such lines that are in turn assumed to be randomly distributed. The properties of the coherent wave are worked out in a multiple scattering formalism, with the calculation of a mass operator, the main technical ingredient. Expansion of this operator to second-order in perturbation theory gives expressions for the index of refraction and attenuation length. This work is motivated by two sources of recent experiments: firstly, the experiments of Zhang et al. (Zhang, G., Simpson Jr, W. A., Vitek, J. M., Barnard, D. J., Tweed, L. J. & Foley J. 2004 J. Acoust. Soc. Am. 116, 109-116.) suggesting that current understanding of wave propagation in polycrystalline material fails to interpret experimental results; secondly, the experiments of Zolotoyabko & Shilo who show that dislocations are potentially strong scatterers for elastic waves. © 2006 The Royal Society.

Résumé: A quantitative theory of the elastic wave damping and velocity change due to interaction with dislocations is presented. It provides a firm theoretical basis and a generalization of the Granato and Lücke model [J. Appl. Phys. 27, 583 (1956)]. This is done considering the interaction of transverse (T) and longitudinal (L) elastic waves with an ensemble of dislocation segments randomly placed and randomly oriented in an elastic solid. In order to characterize the coherent wave propagation using multiple scattering theory, a perturbation approach is used, which is based on a wave equation that takes into account the dislocation motion when forced by an external stress. In our calculations, the effective velocities of the coherent waves appear at first order in perturbation theory while the attenuations have a part at first order due to the internal viscosity and a part at second order due to the energy that is taken away from the incident direction. This leads to a frequency dependence law for longitudinal and transverse attenuations that is a combination of quadratic and quartic terms instead of the usual quadratic term alone. Comparison with resonant ultrasound spectroscopy (RUS) and electromagnetic acoustic resonance (EMAR) experiments is proposed. The present theory explains the difference experimentally observed between longitudinal and transverse attenuations [Ledbetter, J. Mater. Res. 10, 1352 (1995)]. © 2005 The American Physical Society.

Résumé: We study the coherent propagation of an elastic wave in a two-dimensional continuous elastic medium filled with dislocation arrays randomly distributed and oriented in space. This configuration reasonably mimics grain boundaries in polycrystals. Interest is in evaluating the plastic contributions to the multiple scattering of waves in polycrystals that may superpose to other known scattering processes, like scattering due to inhomogeneities of elastic properties among grains. Calculations are performed in a multiple scattering formalism, based on the derivation of the so-called mass operator, in the approximation of weak scattering. We find that sound attenuation increases when the frequency decreases, a trend opposite to the usual behavior, suggesting that dislocations could sensibly modify the acoustic properties of materials at low frequency. © 2005 Elsevier B.V. All rights reserved.

Résumé: The vortex burst in a laminar-flow environment was shown to be responsible for the build up of the energy cascade. It was believed to be the first time that a single isolated flow structure was identified to produce the part of the turbulent energy spectrum described by Kolmogorov's k-5/3 law. In addition, this structure seems to have some common feature with the theoretical one of Lundgren.

Résumé: 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. © 2001 Acoustical Society of America.

Résumé: We present an experimental study of a vertical planar water jet impinging from below on a water/air interface. Varying the jet velocity and the cavity depth, three regimes are observed: at small velocities or high cavity depths, the jet is stable and the surface bump vertically above the jet is stationary. Increasing the velocity, the bump starts oscillating along the free surface at a well-defined frequency. This motion corresponds to the destabilization of the jet confined in the bulk of the cavity to a self-sustained oscillation regime, characteristic of the behavior of confined jets. Increasing further the velocity induces a transition to a behavior with more complex frequency spectrum. This paper presents a detailed study of the self-sustained oscillation regime. The frequency at the onset is studied as a function of the cavity depth and we show an unusual behavior of the frequency with the distance from the threshold.