Coherent Wave Propagation Research Articles

Elastic coupled phase theory based on the Cosserat equations: Propagation of coherent waves

We develop a new coupled phase theory (CPT) in order to model the propagation of elastic coherent waves in homogeneous solid media containing randomly distributed spherical elastic inclusions. To this end, the Buyevich’s theory previously developed for fluid media (Y. Buyevich et I. Shchelchkova, Progress in Aerospace Sciences 18, 1978.) has been adapted and applied to the Cosserat equations. A key point is to introduce the Independent Scattering Approximation (ISA). We show that the coherent wavenumbers depend explicitly on the external force applied to spheres, the torque characterizing their rotation and the stresslet which is the result of the resistance of the particles to the straining motion. Numerical results are in good agreement with experimental data.

Multi-mode multiple wave scattering in suspensions of solid particles in viscous liquids: part 1 asymptotic results

The propagation of coherent longitudinal waves in a viscous liquid containing a random distribution of spherical elastic particles is analysed using a model based on multiple scattering theory. This model, initially developed to describe the propagation of coupled longitudinal and transverse elastic waves in isotropic solid materials, takes into account wave conversions at the particle surface as well as positional correlations between particles via the pair correlation function. By modelling a Newtonian viscous liquid through complex frequency-dependent elastic moduli (i.e. using an imaginary shear modulus), the model is adapted to the case of viscous fluids and we show that conversions of longitudinal waves into transverse waves are important to take into account. We present asymptotic results from the model for case of long wavelength for the longitudinal waves, without assumptions on the shear wavelength. For high concentrations, these wave conversions are reinforced by the contribution of position correlations between the particles. In a subsequent paper, we present numerical validation of the asymptotic approximations and compare them with experimental results for solid particles in water.

Propagation of elastic waves in correlated dispersions of resonant scatterers.

The propagation of coherent longitudinal and transverse waves in random distributions of spherical scatterers embedded in an elastic matrix is studied. The investigated frequency range is the vicinity of the resonance frequencies of the translational and rotational motion of the spheres forced by the waves, where strong dispersion and attenuation are predicted. A technique for making samples made of layers of carbide tungsten beads embedded in epoxy resin is presented, which allows control of the scatterers distribution, induce short-range positional correlations, and minimize the anisotropy of samples. Comparison between phase velocity and attenuation measurements and a model based on multiple scattering theory (MST) shows that bulk effective properties accurately described by MST are obtained from three beads layers. Besides, short-range correlations amplify the effect of mechanical resonances on the propagation of longitudinal and transverse coherent waves. As a practical consequence, the use of short-range positional correlations may be used to enhance the attenuation of elastic waves by disordered, locally resonant, elastic metamaterials, and MST globally correctly predicts the effect of short-range positional order on their effective properties.

2D Analytical Modelling for Ultrasonic Inspection of Concrete Structures: Effects of Scatterers Position Correlation

Ultrasonic Non-Destructive Testing (NDT) simulation plays an important role in designing inspections of concrete structures. The concrete structural complexity (presence of different heterogeneities: aggregates, porosities, microcracks …) leads to dispersion and attenuation of the ultrasonic waves, which requires an accurate modelling of the waves scattered from heterogeneities. For that purpose, studying the mean coherent wave characterized by its attenuation and phase velocity is of great interest. Two major approaches (numerical or analytical) exist for modelling the coherent wave. Numerical methods are more efficient but still limited in the 3D case by their computation time. Therefore, semi-analytical homogenization methods are considered a practical solution for a fast 3D simulation. Nevertheless, they may encounter several limitations in estimating the attenuation in dense heterogeneous materials such as concrete. Our goal is to explain and handle these prediction errors. Since the scattered ultrasonic field depends strongly on the obstacles’ positions in concrete, a particular focus is put on the pair correlation function describing the radial distribution of scatterers’ positions around a fixed scatterer (mean concentration at a distance r from this scatterer). Existing homogenization models are employed for simulating coherent wave propagation in concrete use by simplification of a uniform distribution. In order to improve the analytical models, the effects of scatterers’ positions correlation are investigated. In the present work, we propose to evaluate precisely the existing homogenization model that is the most suitable for high scatterers concentration. A comparison between this model and a 2D finite element code under development in the CIVA NDT simulation software is presented.

Time evolution of coherent wave propagation and spin relaxation in spin-orbit-coupled systems

Time evolution of coherent wave propagation and spin relaxation in spin-orbit-coupled systems

Experimental study on laser propagation characteristics in local air turbulence disturbed by coherent acoustic waves

The existence of atmospheric turbulence seriously restricts the application of laser technology. However, the acoustic wave will affect the air density during the propagation process, change the original structure of the air turbulence, and then affect the propagation of the laser in the air turbulence. To study the effect of disturbance of atmospheric turbulence by acoustic waves on laser propagation, the propagation characteristics of lasers in local atmospheric turbulence under coherent acoustic wave perturbation are investigated experimentally. First, a coherent acoustic wave generator and a closed local air turbulence simulation device are designed. The propagation experiments of laser in a closed local air turbulence environment disturbed by coherent acoustic waves are carried out. It is found that the coherent acoustic wave will interfere with the wave reflected from the inner wall of the closed local air turbulence simulation device, and the sound pressure forms a regular standing wave intensity distribution pattern. Moreover, the variations of laser beam drift fluctuation variance, scintillation index, and beam diameter with coherent acoustic wave frequency, power, and sound source array position are studied. The results show that the original structure of air turbulence will be changed in the process of coherent acoustic wave propagation, which will affect the beam drift fluctuation variance, scintillation index, and beam diameter changes of laser propagation in air turbulence. The beam drift fluctuation variance, scintillation index, and beam diameter change regularly with the change of the frequency and power of the sound source. Changes of the fluctuations with frequency are relatively gentle, whereas changes with power are severe. This paper explores the influence of coherent acoustic waves disturbing air turbulence on laser propagation characteristics, and the research results provide a basis for improving or disturbing laser propagation performance in atmospheric turbulent environments.

Longitudinal and transverse coherent waves in media containing randomly distributed spheres

Multiple scattering effects due to a random distribution of identical spheres are investigated in the general case of elastic or poroelastic host media, where both longitudinal and transverse waves may co-exist. Propagation of plane coherent waves is assumed, and their dispersion equation looked for, as well as analytic approximations of those particular solutions that are close to the wavenumbers in the free host, when the product of the concentration with the scattering cross section of the spheres is low. Under this last condition, pair-correlation effects are seen to be of second order. Numerical studies are performed under the hole correction assumption, and compared to experimental data for tungsten carbide spheres in an epoxy matrix, which is a rather illustrative situation of how longitudinal and transverse waves participate to coherent propagation.

The Propagation of Coherent Waves Across Multiple Solar Magnetic Pores

Solar pores are efficient magnetic conduits for propagating magnetohydrodynamic wave energy into the outer regions of the solar atmosphere. Pore observations often contain isolated and/or unconnected structures, preventing the statistical examination of wave activity as a function of the atmospheric height. Here, using high-resolution observations acquired by the Dunn Solar Telescope, we examine photospheric and chromospheric wave signatures from a unique collection of magnetic pores originating from the same decaying sunspot. Wavelet analysis of high-cadence photospheric imaging reveals the ubiquitous presence of slow sausage-mode oscillations, coherent across all photospheric pores through comparisons of intensity and area fluctuations, producing statistically significant in-phase relationships. The universal nature of these waves allowed an investigation of whether the wave activity remained coherent as they propagate. Utilizing bisector Doppler velocity analysis of the Ca ii 8542 Å line, alongside comparisons of the modeled spectral response function, we find fine-scale 5 mHz power amplification as the waves propagate into the chromosphere. Phase angles approaching zero degrees between co-spatial line depths spanning different line depths indicate standing sausage modes following reflection against the transition region boundary. Fourier analysis of chromospheric velocities between neighboring pores reveals the annihilation of the wave coherency observed in the photosphere, with examination of the intensity and velocity signals from individual pores indicating they behave as fractured waveguides, rather than monolithic structures. Importantly, this work highlights that wave morphology with atmospheric height is highly complex, with vast differences observed at chromospheric layers, despite equivalent wave modes being introduced into similar pores in the photosphere.

Propagation of coherent longitudinal and shear waves in two-dimensional elastic media with randomly distributed resonant cavities

Propagation of coherent elastic waves in solids containing randomly distributed resonant cylindrical cavities is studied numerically and experimentally. This work focuses especially on the case of water-filled cavities in aluminum alloys, which exhibit numerous Mie resonances in the frequency range investigated. Coherent wave measurements are performed in transmission at normal incidence for longitudinal waves and at oblique incidence beyond the critical angle for shear waves. Experimental observations are completed by numerical simulations made with an in-house code called MuScat adapted to the solid matrix case with wave conversions at the surface of each scatterer. The effective wave numbers obtained experimentally and numerically are compared with those predicted by statistical models based on the multiple scattering theory. Remarkable agreements between theoretical, numerical, and experimental results are obtained up to a concentration of 9.9% of cylinders.

Propagation of scalar waves in dense disordered media exhibiting short- and long-range correlations.

Correlated disorder is at the heart of numerous challenging problematics in physics. In this work we focus on the propagation of acoustic coherent waves in two-dimensional dense disordered media exhibiting long- and short-range structural correlations. The media are obtained by inserting elastic cylinders randomly in a stealth hyperuniform medium itself made up of cylinders. The properties of the coherent wave is studied using an original numerical software. In order to understand and discuss the complex physical phenomena occurring in the different media, we also make use of effective media models derived from the quasicrystalline approximation and the theory of Fikioris and Waterman that provides an explicit expression of the effective wave numbers. Our study shows a very good agreement between numerical and homogenization models up to very high concentrations of scatterers. This study shows that media with both short- and long-range correlations are of strong interest to design materials with original properties.

Photonic extreme learning machine by free-space optical propagation

Photonic brain-inspired platforms are emerging as novel analog computing devices, enabling fast and energy-efficient operations for machine learning. These artificial neural networks generally require tailored optical elements, such as integrated photonic circuits, engineered diffractive layers, nanophotonic materials, or time-delay schemes, which are challenging to train or stabilize. Here, we present a neuromorphic photonic scheme, i.e., the photonic extreme learning machine, which can be implemented simply by using an optical encoder and coherent wave propagation in free space. We realize the concept through spatial light modulation of a laser beam, with the far field acting as a feature mapping space. We experimentally demonstrate learning from data on various classification and regression tasks, achieving accuracies comparable with digital kernel machines and deep photonic networks. Our findings point out an optical machine learning device that is easy to train, energetically efficient, scalable, and fabrication-constraint free. The scheme can be generalized to a plethora of photonic systems, opening the route to real-time neuromorphic processing of optical data.

Propagation of coherent shear waves in scattering elastic media.

We measure the reflection and transmission of shear waves by slabs of random dispersions of hard, dense spheres in a viscoelastic matrix. By modeling the slab as a Fabry-Pérot interferometer, we determine the effective wave number of coherent shear waves in this scattering medium and its effective mass density. We evidence the effect of the resonant rigid-body translation and rotation of the spheres on the propagation. We validate a vectorial model of multiple scattering for volume fractions of spheres up to 10%, revealing the signature of two modes of propagation.

Binary Amplitude Reflection Gratings for X-ray Shearing and Hartmann Wavefront Sensors.

New, high-coherent-flux X-ray beamlines at synchrotron and free-electron laser light sources rely on wavefront sensors to achieve and maintain optimal alignment under dynamic operating conditions. This includes feedback to adaptive X-ray optics. We describe the design and modeling of a new class of binary-amplitude reflective gratings for shearing interferometry and Hartmann wavefront sensing. Compact arrays of deeply etched gratings illuminated at glancing incidence can withstand higher power densities than transmission membranes and can be designed to operate across a broad range of photon energies with a fixed grating-to-detector distance. Coherent wave-propagation is used to study the energy bandwidth of individual elements in an array and to set the design parameters. We observe that shearing operates well over a ±10% bandwidth, while Hartmann can be extended to ±30% or more, in our configuration. We apply this methodology to the design of a wavefront sensor for a soft X-ray beamline operating from 230 eV to 1400 eV and model shearing and Hartmann tests in the presence of varying wavefront aberration types and magnitudes.

Observation of the dispersion relations for quantized coherent spin waves excited by a microwave antenna

The propagation of coherent spin waves in permalloy microstrips was investigated using a heterodyne-magneto-optical Kerr effect technique. The two-dimensional imaging reveals the mode interference with a high-order spin-wave mode along the microstrip width. The spin-wave dispersion relations across the microstrip width were deduced from fast Fourier transformations on the complex spin-wave amplitude of the one-dimensional scan, and multiple spin-wave modes were observed at the edges of the microstrips. These experimental results provide direct evidence for the quantization of spin-wave dispersion due to the finite width of the microstrips and enables us to evaluate the attenuation length for each quantized spin-wave mode.

Influence of the microstructure of two-dimensional random heterogeneous media on propagation of acoustic coherent waves.

Multiple scattering of waves arises in all fields of physics in either periodic or random media. For random media the organization of the microstructure (uniform or nonuniform statistical distribution of scatterers) has effects on the propagation of coherent waves. Using a recent exact resolution method and different homogenization theories, the effects of the microstructure on the effective wave number are investigated over a large frequency range (ka between 0.1 and 13.4) and high concentrations. For uniform random media, increasing the configurational constraint makes the media more transparent for low frequencies and less for high frequencies. As a side but important result, we show that two of the homogenization models considered here appear to be very efficient at high frequency up to a concentration of 60% in the case of uniform media. For nonuniform media, for which clustered and periodic aggregates appear, the main effect is to reduce the magnitude of resonances and to make network effects appear. In this case, homogenization theories are not relevant to make a detailed analysis.

From power law to Anderson localization in nonlinear Schrödinger equation with nonlinear randomness.

We study the propagation of coherent waves in a nonlinearly induced random potential and find regimes of self-organized criticality and other regimes where the nonlinear equivalent of Anderson localization prevails. The regime of self-organized criticality leads to power-law decay of transport [Y. Sharabi et al., Phys. Rev. Lett. 121, 233901 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.233901], whereas the second regime exhibits exponential decay.

Phonon engineering with superlattices: Generalized nanomechanical potentials

Earlier implementations to simulate coherent wave propagation in one-dimensional potentials using acoustic phonons with gigahertz-terahertz frequencies were based on coupled nanoacoustic resonators. Here, we generalize the concept of adiabatic tuning of periodic superlattices for the implementation of effective one-dimensional potentials giving access to cases that cannot be realized by previously reported phonon engineering approaches, in particular the acoustic simulation of electrons and holes in a quantum well or a double well potential. In addition, the resulting structures are much more compact and hence experimentally feasible. We demonstrate that potential landscapes can be tailored with great versatility in these multilayered devices, apply this general method to the cases of parabolic, Morse and double-well potentials and study the resulting stationary phonon modes. The phonon cavities and potentials presented in this work could be probed by all-optical techniques like pump-probe coherent phonon generation and Brillouin scattering.

Multiscale Coherent Excitations in Microscopic Acoustic Wave Turbulence of Cold Dusty Plasma Liquids.

We experimentally demonstrate the observation of thermally excited microscopic acoustic wave turbulence at the discrete level in quasi-two-dimensional cold dusty plasma liquids. Through multidimensional empirical mode decomposition of individual dust particle motions over a large area, the turbulence is decomposed into multiscale traveling wave modes, sharing self-similar dynamics. All modes exhibit intermittent excitation, propagation, scattering, and annihilation of coherent waves, in the form of clusters in the xyt space, with cluster sizes exhibiting self-similar power law distribution. The poor particle interlocking in the region with poor structural order is the key origin of the easier excitations of the large amplitude slow modes. The sudden phase synchronization of slow wave modes switches particle motion from cage rattling to cooperative hopping.

Coherent Wave Propagation in Multimode Systems with Correlated Noise.

Imperfections in multimode systems lead to mode mixing and interferences between propagating modes. Such disorder is typically characterized by a finite correlation time (in quantum evolution) or correlation length (in paraxial evolution). We show that the long-scale dynamics of an initial excitation that spread in mode space can be tailored by the coherent dynamics on a short scale. In particular we unveil a universal crossover from exponential to power-law ballisticlike decay of the initial mode. Our results have applications to various wave physics frameworks, ranging from multimode fiber optics to quantum dots and quantum biology.

Time-domain Brillouin Scattering as a Local Temperature Probe in Liquids

ABSTRACTWe present results of time-domain Brillouin scattering (TDBS) to determine the local temperature of liquids. TDBS is based on an ultrafast pump-probe technique to determine the light scattering frequency shift caused by the propagation of coherent acoustic waves in a sample. Since the temperature influences the Brillouin scattering frequency shift, the TDBS signal probes the local temperature of the liquid. Results for the extracted Brillouin scattering frequencies recorded at different liquid temperatures and at different laser powers are shown to demonstrate the usefulness of TDBS as a temperature probe.