The diffraction of sound by an impedance sphere in the vicinity of a ground surface

The problem of sound diffraction by an absorbing sphere due to a monopole point source was investigated. The theoretical models were extended to consider the case of sound diffraction by an absorbing sphere with a locally reacting boundary or an extended reaction boundary placed above an outdoor ground surface of finite impedance. The separation of variables techniques and appropriate wave field expansions were used to derive the analytical solutions. By adopting an image method, the solutions could be formulated to account for the multiple scattering of sound between the sphere and its image near a flat acoustically hard or an impedance ground. The effect of ground on the reflected sound fields was incorporated in the theoretical model by employing an approximate analytical solution known as the Weyl-van der Pol formula. An approximation solution was suggested to determine the scattering coefficients from a set of linearly coupled complex equations for an absorbing sphere not too close to the ground. The approximate method substantially reduced the computational time for calculating the sound field. Preliminary measurements were conducted to characterize the acoustical properties of an absorbing sphere made of open cell polyurethane foam. Subsequent experiments were carried out to demonstrate the validity of the proposed theoretical models for various source/receiver configurations around the sphere above an acoustically hard ground and an impedance ground. Satisfactory comparative results were obtained between the theoretical predictions and experimental data. It was found that the theoretical predictions derived from the approximate solution agreed well with the results obtained by using the exact solutions.     

ICF靶腔曲面光场计算

传统的衍射计算方法都是针对衍射场为平面的计算,对于ICF靶腔衍射场为曲面时,计算困难。通过比较常用衍射计算方法的优缺点,基于层析成像的思想,提出采用快速傅里叶变换分层计算,并根据最相邻原则拟合曲面衍射场光场分布的快速计算方法。该方法可以计算出任意给定空间曲面上的光场分布,且具有计算快速、结果精确的优点。模拟分析表明,当分层数足够大时,采用该方法可有效解决ICF靶腔内壁曲面光场的计算问题。     

ICF靶腔曲面光场计算

传统的衍射计算方法都是针对衍射场为平面的计算,对于ICF靶腔衍射场为曲面时,计算困难。通过比较常用衍射计算方法的优缺点,基于层析成像的思想,提出采用快速傅里叶变换分层计算,并根据最相邻原则拟合曲面衍射场光场分布的快速计算方法。该方法可以计算出任意给定空间曲面上的光场分布,且具有计算快速、结果精确的优点。模拟分析表明,当分层数足够大时,采用该方法可有效解决ICF靶腔内壁曲面光场的计算问题。     

Scattering of a sound wave by a vibrating surface

We report an experimental study of the scattering of a sound wave of frequency f by a surface vibrating at frequency F. Both the Doppler shift at the vibrating surface and acoustic nonlinearities in the bulk of the fluid, generate the frequencies f±nF (n integer) in the spectrum of the scattered wave. We show that these two contributions can be separated because they scale differently with respect to the vibration frequency and to the distance between the vibrating scatterer and the detector. We determine the parameter ranges in which one or the other mechanism dominates and present quantitative studies of these two regimes. Received 2 December 2002 / Received in final form 27 March 2003 Published online 4 June 2003 RID="a" ID="a"e-mail: fauve@physique.ens.fr RID="b" ID="b"UMR 8550     

Velocity of sound in curved space-time

The small-perturbation method of E. M. Lifshits is used to derive expressions for the phase and group velocities of sound in matter described by the equation of state ε=3p in the curved 4-space of Fridman's cosmological model. It is inferred that the curvature of 4-space significantly influences the velocity of sound. Thus, the maximum value of the group velocity of sound in the given model exceeds the maximum value of the velocity of sound in flat 4-space for the same equation of state of matter; for matter of infinite density the velocity of sound is equal to zero at the initial instant of expansion of the universe. These results indicate that when the condition v_so ≤c is taken as the criterion for the choice of equation of state of superdense matter, as for example in relativistic astrophysics, it is necessary to take into account the influence of the curvature of 4-space on the velocity of sound.     

Influence of viscosity on the diffraction of sound by a periodic array of screens

The paper contains an analysis of the transmission of a pressure wave through a periodic grating including the influence of the air viscosity. The system of equations in this case consists of the compressible Navier-Stokes equations associated with no-slip boundary conditions on solid surfaces. The problem is reduced to two hypersingular integral equations for determining the velocity components along the slits. These equations are solved by using Galerkin's method with some special trial functions. The results can be applied in designing protective screens for miniature microphones realized in the technology of micro-electro-mechanical systems (MEMS). In this case, the physical dimensions of the device are on the order of the viscous boundary layer so that the viscosity cannot be neglected. The microfluidic model of the screen consists of a periodic array of slits in a substrate. The analysis indicates that the openings in the screen should be on the order of 10 microm in order to avoid excessive attenuation of the signal.     

Wave diffraction by a concave statistically rough surface

Abstract

We consider a statistically rough impedance surface that is concave on average in contrast to a plane. Backscattering from such a surface is considered based on the small perturbation theory method. The diffraction problem is divided into two parts which are considered separately: the problem of scattering by small roughness (assumed to be local) and the propagation of incident and scattered fields over a smooth large-scale concave surface. In contrast to the ‘two-scale’ scattering model, the zero-order unperturbed wavefield is not assumed to be specularly reflected from the local tangent plane to the smooth surface, but it is a solution of a corresponding diffraction problem. Two particular cases of smooth surfaces are considered: first, the inner surface of a concave cylinder with a constant radius and finite angular pattern, and second, a compound surface that consists of a coupled half-plane and the cylindrical surface mentioned above. In a geometrical optics limit and with propagation at low grazing angles, the analytical results for a zero-order (unperturbed) field are obtained for these two cases in the form of a series over multiple specular reflected fields. It is shown that these non-local processes lead to the essential increase in the backscattering cross section in comparison with the two-scale model and tangent-plane approach.     

Collinear diffraction of restricted light beams by nonmonochromatic sound

The collinear diffraction of Gaussian light beams by a two-frequency sound beam is investigated theoretically. A set of equations relating the amplitudes of transmitted and diffracted waves is derived in the case of third-order nonlinearity. The distributions of light intensities along an acousto-optical cell are calculated at different ratios between the radii of the light and sound beams. The transmission curves for detuned light waves and combination components of the diffracted waves are constructed at different ratios between the radii of the light and sound beams. The changes in the dynamic range of an acousto-optical device are calculated for different diffraction efficiencies.     

Wave diffraction by a concave statistically rough surface

We consider a statistically rough impedance surface that is concave on average in contrast to a plane. Backscattering from such a surface is considered based on the small perturbation theory method. The diffraction problem is divided into two parts which are considered separately: the problem of scattering by small roughness (assumed to be local) and the propagation of incident and scattered fields over a smooth large-scale concave surface. In contrast to the 'two-scale' scattering model, the zero-order unperturbed wavefield is not assumed to be specularly reflected from the local tangent plane to the smooth surface, but it is a solution of a corresponding diffraction problem. Two particular cases of smooth surfaces are considered: first, the inner surface of a concave cylinder with a constant radius and finite angular pattern, and second, a compound surface that consists of a coupled half-plane and the cylindrical surface mentioned above. In a geometrical optics limit and with propagation at low grazing angles, the analytical results for a zero-order (unperturbed) field are obtained for these two cases in the form of a series over multiple specular reflected fields. It is shown that these non-local processes lead to the essential increase in the backscattering cross section in comparison with the two-scale model and tangent-plane approach.     

Influence of viscosity on the diffraction of sound by a circular aperture in a plane screen

The linearized equations of viscous fluid flow are used to analyze the diffraction of a time-harmonic acoustic plane wave by a circular aperture in a rigid plane screen. Arbitrary aperture size and arbitrary angle of incidence are considered. Sets of dual integral equations are derived for the diffracted velocity and pressure fields, and are solved by analytic reduction to sets of linear algebraic equations. In the case of normal incidence, numerical results are presented for the fluid velocity in the aperture and the power absorption due to viscous dissipation. The theoretical results for power absorption are compared to previously obtained results from high amplitude acoustic experiments in air. The conditions under which the dissipation predicted by linear theory becomes significantare quantified in terms of the fluid viscosity and sound speed, the acoustic frequency, and the aperture radius.     

Highly effective acoustooptic diffraction of light by multifrequency sound using a nonaxial deflector

The subject of investigation is multiple-beam Bragg diffraction of light, i.e., the formation of a highly effective multiple-beam field representing a superposition of equidistant monochromatic acoustic waves with determinate phases and amplitudes using a nonaxial TeO₂ deflector. It is shown theoretically and experimentally that the anisotropic character of interaction considerably changes the basic parameters of multiple-beam diffraction (compared with the isotropic case): the net diffraction efficiency grows to 100%, and the frequency band expands noticeably. A modulator splitting the initial laser radiation into five beams of equal intensity with a net efficiency approaching 100% is designed.     

A study of sound transmission in curved duct bends by the Galerkin method

A computational procedure based on the Galerkin method is developed to study the sound transmission and reflection characteristics of circularly curved bends of rectangular ducts. This procedure is adaptable to routine computer calculation. An important component of the computer program consists of a QR iterative algorithm which solves the matrix eigenvalue problem generated by the Galerkin method. The present procedure produced very satisfactory convergent results when applied even to cases where the incident wave has high frequency and high wave mode numbers. Some properties of the Galerkin solution are investigated. Its relationship to the classical solution by the method of separation of variables is discussed.     

The diffraction of electromagnetic waves by sound in conducting crystals

The diffraction of electromagnetic waves by sound in conducting crystals is investigated. It is shown that in such crystals a significant contribution to the scattering of electromagnetic waves can be made by electron waves which are generated by a sound wave and accompany it. An estimate shows that in the ‘hydrodynamic’ case ql 1 (where q is the wave number of the sound and l is the electron mean free path) the contribution from an electron density wave to the scattering of electromagnetic waves in the infrared and millimeter ranges in substances with a low electron effective mass (of the type of InSb) can be comparable to the contribution from the lattice deformation waves, or may even exceed it. The results of a concrete calculation of the first and second order intensities of Raman-Nath diffraction in a semiconductor are presented.     

Optical wavelength filtering by diffraction from a surface relief

We present an analytical solution to the problem of finding a diffractive surface relief that generates a specific optical amplitude and phase spectral reflection in a particular direction. We show that any discrete finite impulse response filter can be generated to within a multiplicative constant at nonzero frequencies. We propose an implementation of such a filter that works in the visible and the near infrared, based on a two-dimensional array of dual-state tiltable mirrors. A 1024 x 1024 array results in a 1024-tap filter with 10-bit quantization of the impulse response. The applications of such a device include spectroscopy and wavelength-division multiplex switching.     

Bragg diffraction of microcavity polaritons by a surface acoustic wave

Bragg scattering of polaritons by a coherent acoustic wave is mediated and strongly enhanced by the exciton states resonant with the acoustic and optic fields in the intraband and interband transitions, respectively. In this case, in contrast with conventional acousto-optics, the resonantly enhanced Bragg spectra reveal the multiple orders of diffracted light. For polaritons in GaAs microcavities driven by a surface acoustic wave of nu(SAW)=1 GHz and I(ac)< or approximately 100 W/cm(2) the main acoustically induced band gap can be as large as Delta(MC)(ac) approximately equal to 0.6 meV and the Bragg replicas up to n=3 can be observed.     

On the diffraction of He by a Ni(110) surface

The diffraction of low-energy He atoms by a Ni(110) surface is studied using hard and soft wall models for the elastic scattering. The effects of thermal vibrations and inelastic processes on the He intensities are estimated. It is shown that the experimental spectra imply a corrugation height along the [001] direction that is maximally 0.12 au. A value of 0.30 au, calculated recently within a scheme that assumes the repulsive interaction to be proportional to the electron density of unperturbed Ni(110), leads to “double rainbow” diffraction patterns qualitatively different from those observed.     

On the neutron diffraction in crystals in the field of a sound wave

Diffraction of neutrons in crystals under influence of a sound wave is considered. The probability of scattering of neutrons at the elastic interaction with the crystal is calculated. On the contrary, scattering of neutrons by an acoustical phonon has inelastic character. The possibility to control the Debye-Waller factor is shown.     

干涉、衍射实验中衍射物位置的估算

从光源的空间相干性和实际光源的边缘衍射特性两个方面分析给出了干涉、衍射实验中衍射物到光源的距离的估算公式,分析了双缝干涉和泊松亮斑两个实验实例.     

Experimental studies of sound diffraction by moving inhomogeneities under shallow-water conditions

The experimental data on the sound propagation and diffraction by moving test inhomogeneities under lake conditions are presented. It is shown that the diffracted signals under multimode propagation are adequately described by simplified theoretical models proposed earlier. The detection of the diffracted signals against the background of a fluctuating direct signal is demonstrated for the reception by a horizontal or vertical array. It is also shown that the direct and diffracted signals observed in the lake are similar in their characteristics to the signals in a shallow sea, which allows one to use the lake experiment for testing various underwater acoustic techniques intended for shallow-sea conditions.