Coherent Line Source Research Articles

Two-beam interferometry for characterizing subwavelength layers with a negative optical path length

In this work, we show that unequal-arm two-beam interferometers, for example, single-pass Mach–Zehnder interferometer or double-pass Michelson interferometer, illuminated with coherent point source (spherical wave front) or coherent line source (cylindrical wave front), unambiguously determine the sign of the phase shift. Theoretical consideration shows that a pattern with finite diameters of interference fringes is asymmetric with respect to the sign of the optical path difference (OPD) or phase shift (PS). In a short arm of the interferometer, the light passing through the layer of medium, characterized by positive OPD (positive PS), leads to the decrease of the diameter of interference fringe. The layer of the medium with negative OPD increases the diameter of inference fringe. When placing an object in the long arm of the interferometer, the contrary situation is observed. For variants with a coherent linear source, the above results relate to the distances between strait fringes of the same order. Experiment demonstrates that the positive optical path length of a conventional material can be compensated in air by a layer of metamaterial with a negative optical path length located at a distance significantly longer than the wavelength of light.

Comparative Analysis of Different Types of Sources on the Performance of Rigid Noise Barriers on Rigid Ground Using Analytical Formulae, a 2.5-D BEM Method and Scale Modelling Tests

With the aim of a perfect source model to simulate railway traffic noise within a shorter computational time, this paper compares coherent line, incoherent point and incoherent line sources on the performance of barriers by using an analytical solution, a 2.5-D BEM method and scale modelling tests. The comparison between the analytical solutions and the 2.5-D BEM prediction results shows that the BEM calculations for a coherent line source can be used to approximately show the barrier attenuation spectrum for a one-point source and the single-number rating for an incoherent line source when the barrier is straight on the ground. Then, validations with scale modelling tests were performed outdoors under controlled conditions. The results obtained by using several loudspeakers radiating incoherent sounds simultaneously show good agreement with the 2.5-D BEM prediction results for the one-point source and incoherent point sources, not only for a simple barrier on the ground but also for a double-straight barrier on a viaduct. Based on these agreements, the frequency and longitudinal distance dependences on the barrier attenuation for incoherent point sources are discussed to understand the barrier attenuation spectrum for the incoherent line source.

Active cancellation of sound generated by finite length coherent line sources using piston-like secondary source arrays.

The active cancellation of the sound generated by finite length coherent line sources is investigated numerically in the present study. A secondary source consists of a central circular core enclosed within an annulus is proposed. It is demonstrated that this source type can produce a much more directional secondary sound field than a single circular piston, even its size is much smaller than the latter if its two parts are vibrating out-of-phase with the right magnitude ratio. This property gives rise to more effective spanwise sound reduction. An example of a secondary source array for broadband noise control is also provided. Though the control performance becomes weaker as frequency increases, the noise reduction within the central region of the receiver plane remains significant in all the cases included in the present study.

Method to simulate waveelds from ambient-noise sources

The shear (SH)-wave transfer function and the horizontal-to-vertical (HV) spectral ratio are essential to estimate the S-wave velocity pro- le and thickness of surface layers overlying a bedrock on the basis of resonance frequencies. In practice, it is the second method the most used. In this work, we propose a full-wave numerical method, based on a pseudospectral spatial differentiation, to simulate SH and P-S waves generated by random sources distributed spatially and temporally (ambient noise). The modeling allows us to implement seis- mic attenuation, surface waves and causal source radiation patterns, based on random values of the angles of the moment tensor at each source location. We focus on the location of the resonance peaks, since this property is strictly related to the thickness of the layers. First, we analyze Lamb’s problem for which an analytical P-S solution exists. The modeling algorithm is veri ed for a Ricker time history, but the analy- sis can be performed by using spikes as sources. The experiments based on ambient noise are compared to those of a coherent line source as a reference spectrum (e.g., an earthquake event far away from the receivers). SH-wave resonance frequencies can be identi ed in the spectra only when the random sources are located below the bedrock. In the case of P-S waves, the SH-wave transfer function is a good approximation to the HV spectrum, mainly when the noise is generated in the bedrock. Finally, we have assumed a square basin and found that coherent (e.g., earthquake-type) sources may yield identi able peaks but ambient noise gives unreliable results.

An efficient quadrature for 2.5D boundary element calculations

In recent years, the boundary element method has become a widely used tool for calculating the mitigation effects of noise barriers. However, since for large structures calculations in 3D become very inefficient, most of the standard implementations are only in 2D. This means that the noise source is implicitly assumed to be given by a coherent line source, which is not realistic in most cases. By using a Fourier transform with respect to a spatial coordinate along the length of the structure it is possible to reduce the 3D problem to several 2D problems with distinct wavenumbers which allows the simulation of more realistic noise sources and which is typically referred to as 2.5D BEM. To that end, it is necessary to numerically calculate a Fourier-like integral over all the 2D solutions. In this work, an efficient way to calculate this integral is given building on existing approaches using Clenshaw–Curtis–Filon quadrature and demodulation combined with an adaptive order-selection scheme. As BEM calculations are costly, the main focus of the method introduced lies on avoiding too many of these calculations. The efficiency of the method is illustrated using two different examples: a reflecting cylinder and an L-shaped noise barrier.

Numerical Investigation of the Effect of Crosswind on Sound Propagation Outdoors

The effect of wind on sound propagation in the atmosphere has been studied extensively before with an emphasize on downwind sound propagation, typically representing worst-case scenarios. However, the influence of oblique and crosswind on propagation from various types of sources raises some questions in acoustic literature. In this work, the effect of a logarithmic wind speed profile at different wind directions has been studied for sound emitted by a point source, a coherent line source and an incoherent line source. For this purpose, a full three-dimensional wave-based method was used. For the incoherent line source simulation, the Harmonoise engineering approach based on a summation of source segments was considered as well and shows to be in satisfying agreement with the latter. While for a point source and coherent line source crosswind shows to have an insignificant effect, it is important in case of an incoherent line source. Also, the stretch of the incoherent line source contributing to the noise level at a receiver close to this line differs strongly depending on the wind direction.

Noise source identification in high speed jets based on virtual microphone arrays

Phased arrays have become a popular experimental technique for noise source identification. These techniques are generally limited in resolution due to the number of available microphones. In addition, noise source models are relatively simple, involving either uncorrelated point sources or simple coherent line sources. The former limitation is not present in numerical simulations, where the number and location of virtual microphones is effectively unlimited. The present paper describes numerical simulations of high speed jet noise using a Detached Eddy Simulation turbulence model. The nozzle, which is included in the simulations, is typical of the geometries found in high performance military aircraft. An Immersed Boundary Method is used simulate the effect of chevrons at the nozzle exit. The far field noise is predicted using solutions of the Ffowcs Williams – Hawkings equation. Phased array results are presented for both a baseline and chevron nozzle and the differences are discussed. In addition, near field virtual arrays are sampled and analyzed to include both radiating and non-radiating components. The implications of the results from the far and near field arrays in terms of noise source characteristics are presented. The results are compared with available experimental observations.

Coherent field emission image of graphene predicted with a microscopic theory

Electrons in the mono-layer atomic sheet of graphene have a long coherence length of the order of micrometers. We will show that this coherence is transmitted into the vacuum via electric field assisted electron emission from the graphene edge. The emission current density is given analytically. The parity of the carbon pi-electrons leads to an image whose center is dark as a result of interference. A dragonfly pattern with a dark body perpendicular to the edge is predicted for the armchair edge whose emission current density is vanishing with the mixing angle of the pseudo-spin. The interference pattern may be observed up to temperatures of thousand Kelvin as evidence of coherent field emission. Moreover, this phenomenon leads to a novel coherent electron line source that can produce interference patterns of extended objects with linear sizes comparable to the length of the graphene edge.

The 2.5-dimensional equivalent sources method for directly exposed and shielded urban canyons

When a domain in outdoor acoustics is invariant in one direction, an inverse Fourier transform can be used to transform solutions of the two-dimensional Helmholtz equation to a solution of the three-dimensional Helmholtz equation for arbitrary source and observer positions, thereby reducing the computational costs. This previously published approach [D. Duhamel, J. Sound Vib. 197, 547-571 (1996)] is called a 2.5-dimensional method and has here been extended to the urban geometry of parallel canyons, thereby using the equivalent sources method to generate the two-dimensional solutions. No atmospheric effects are considered. To keep the error arising from the transform small, two-dimensional solutions with a very fine frequency resolution are necessary due to the multiple reflections in the canyons. Using the transform, the solution for an incoherent line source can be obtained much more efficiently than by using the three-dimensional solution. It is shown that the use of a coherent line source for shielded urban canyon observer positions leads mostly to an overprediction of levels and can yield erroneous results for noise abatement schemes. Moreover, the importance of multiple facade reflections in shielded urban areas is emphasized by vehicle pass-by calculations, where cases with absorptive and diffusive surfaces have been modeled.

On the efficiency of screens near roadside cuttings

The prediction of acoustic propagation from a monofrequency coherent line source in a cutting with impedance boundary conditions over a noise-screen onto surrounding flat grassland is presented. It is well known that over flat ground the spectra for single-noise screens have significant marked differences for propagation over absorbing ground where the screen obstructs surface wave attenuation over the absorbing ground cover. The aim here is to extend the study of this phenomenon for screens adjacent to cuttings or dips surrounded by absorbing ground. The study is based on a numerical model using boundary element techniques that enables the excess attenuation and insertion loss for various noise barriers and cuttings of complex profile and surface cover to be calculated. The model is applied to single-foundation noise barriers to which additional absorbent or rigid side-panels are added to create profiles and a double-barrier configuration is also studied. Spectra of insertion loss, change in insertion loss and excess attenuation results for a broadband traffic-source are presented. It is concluded that “multiple-edged” barriers only show a minor increase in acoustic efficiency over simple vertical screens for a noise source located in perturbed flat ground conditions such as a cutting; in addition it is shown that a screen placed close to the source shows sign of partial improvement.

Parameter study of sound propagation between city canyons with a coupled FDTD-PE model

A parameter study is performed for the case of two-dimensional sound propagation from a (source) city canyon to a nearby, identical (receiver) city canyon. Focus was on sound pressure levels, relative to the free field, in the shielded canyon. An accurate and efficient coupled FDTD-PE model was applied, exploiting symmetry of the source and receiver canyon. With the proposed calculation method, simulations were necessary in only half the sound propagation domain. The shielding in the receiver canyon in case of a coherent line source was compared to the shielding by an incoherent line source, by means of sound propagation calculations in a number of 2D cross-sections through source and receiver. It was found that the shielding is rather insensitive to the width-height ratio of the canyons. The presence of diffusely reflecting façades and balconies lead to an important increase in shielding compared to flat façades. Rigid façades yield significantly lower shielding compared to partly reflecting façades. Effects of a moving atmosphere were modeled in detail. Shielding decreases significantly in case of downwind sound propagation when comparing to sound propagation in a non-moving atmosphere. Refraction is the most important effect in the latter. In case of upwind sound propagation, turbulent scattering plays an important role and the shielding is similar to the one of a non-moving atmosphere for the parameters used in this paper. The combination of effects, as is shown by some examples, is in general not a simple addition of the separate effects.

NUMERICAL PREDICTIONS OF SOUND PROPAGATION FROM A CUTTING OVER A ROAD-SIDE NOISE BARRIER

A boundary integral equation is described for the prediction of acoustic propagation from a monofrequency coherent line source in a cutting with impedance boundary conditions onto surrounding flat impedance ground. The problem is stated as a boundary value problem for the Helmholtz equation and is subsequently reformulated as a system of boundary integral equations via Green's theorem. The numerical solution of the coupled boundary integral equations by a simple boundary element method is then described. Predictions of A-weighted insertion losses for a traffic noise spectrum are made illustrating the effects of depth of the cutting and the profile of the associated noise barrier.

Integration of the efficiency of noise barrier caps in a 3D ray tracing method. Case of a T-shaped diffracting device

Road barrier diffracting caps have shown a renewed interest for several years since they give the opportunity of increasing the barrier efficiency without changing its overall height. First investigations on the efficiency of road barrier caps calculated with a boundary element method (BEM) have shown that the efficiency obtained with coherent line sources is underestimated compared to that with incoherent line sources, more representative of road traffic noise. The present work deals with the characterisation of the real performance of a T-shaped absorbing cap with road traffic noise conditions. Two different approaches are compared: on one hand calculations with the help of a BEM program able to achieve 2D and 2D 1 2 simulations are made; on the other hand outdoor measurements on a test-wall using a maximum length sequence technique are carried out. The goal in the two approaches is to isolate the top edge diffracted sound field in order to determine an extrinsic value of octave band efficiency of the cap for many source–receiver pairs. These results integrated in a ray tracing prediction method enable the integration of air absorption along each ray path and give the real efficiency of such a device in the case of complex and realistic configurations for barriers of finite length.

NUMERICAL MODELLING OF MEDIAN ROAD TRAFFIC NOISE BARRIERS

Outdoor sound propagation from road traffic is modelled by solving a boundary integral equation formulation of the wave equation using boundary element techniques in two dimensions. In the first model, the source representing a traffic stream can be considered as a coherent line source of sound. The results can then be transformed to derive a pseudo-three dimensional solution to the problem. In the second model the line source is incoherent. For receivers near the ground, the second model predicted significantly higher values of ground attenuation than the first. The first model generally produced better agreement with ground attenuation results obtained using the U.K. traffic noise prediction model. For conditions when a noise barrier was present and the ground was absorbent, the incoherent line source model generally predicted significantly higher values of attenuation than those from the barrier and ground attenuation calculated separately. Over a range of receiver positions and barrier heights a similar, but less marked effect was observed when the coherent line source model was used. On dual carriageway roads, it is possible to incorporate barriers on the central reservation as a noise control measure. These are “median” noise barriers. The incoherent line source model is used to assess the performance of median barriers in reducing noise when installed alone and also with associated roadside barriers. A sound absorbent median noise barrier 1m in height produced consistent values of insertion loss of between 1 and 2dB over the range of receiver positions and ground conditions considered. When the median barrier was used in conjunction with a roadside barrier it produced a consistent improvement in insertion loss of between 1 and 2 dB over the range of conditions considered.

Efficient calculation of two-dimensional periodic and waveguide acoustic Green’s functions

New representations and efficient calculation methods are derived for the problem of propagation from an infinite regularly spaced array of coherent line sources above a homogeneous impedance plane, and for the Green's function for sound propagation in the canyon formed by two infinitely high, parallel rigid or sound soft walls and an impedance ground surface. The infinite sum of source contributions is replaced by a finite sum and the remainder is expressed as a Laplace-type integral. A pole subtraction technique is used to remove poles in the integrand which lie near the path of integration, obtaining a smooth integrand, more suitable for numerical integration, and a specific numerical integration method is proposed. Numerical experiments show highly accurate results across the frequency spectrum for a range of ground surface types. It is expected that the methods proposed will prove useful in boundary element modeling of noise propagation in canyon streets and in ducts, and for problems of scattering by periodic surfaces.

Submicrometer coherent neutron beam production using a thin-film waveguide.

We have experimentally demonstrated that planar neutron waveguides can be used as resonant beam couplers to efficiently produce a coherent neutron line source with cross sections in the submicrometer range. The Fraunhofer far-field diffraction pattern of the first three resonance modes was measured and found to be in excellent agreement with the theoretical model. Our measurements confirm that an excited exiting mode is fully coherent in the direction perpendicular to the surface of the thin-film coupler and may therefore be used for applications of interest to a broad user community in biochemical and semiconductor nanosciences such as static and time-resolved coherent speckle experiments or phase-contrast imaging.

THE IMPORTANCE OF SOURCE TYPE ON THE ASSESSMENT OF NOISE BARRIERS

A two-dimensional (2-D) boundary element method is used to compute the efficiency of noise barriers in attenuating traffic noise. Different types of source are considered. Point sources and incoherent line sources can be introduced as results of a post-treatment of the 2-D pressure field. The insertion loss of barriers is significantly reduced in the case of more realistic incoherent line sources, as compared to that of coherent line sources. However, the relative efficiency of tops added to a straight barrier is higher.

NOISE PROPAGATION FROM A CUTTING OF ARBITRARY CROSS-SECTION AND IMPEDANCE

A boundary integral equation is described for the prediction of acoustic propagation from a monofrequency coherent line source in a cutting with impedance boundary conditions onto surrounding flat impedance ground. The problem is stated as a boundary value problem for the Helmholtz equation and is subsequently reformulated as a system of boundary integral equations via Green's theorem. It is shown that the integral equation formulation has a unique solution at all wavenumbers. The numerical solution of the coupled boundary integral equations by a simple boundary element method is then described. The convergence of the numerical scheme is demonstrated experimentally. Predictions of A-weighted excess attenuation for a traffic noise spectrum are made illustrating the effects of varying the depth of the cutting and the absorbency of the surrounding ground surface.

A coherent line source in a turbulent atmosphere

The sound field of a coherent line source in a nonrefracting, turbulent atmosphere is studied. An expression for the sound pressure level in the frequency domain is developed, based on a discretization of the line source into a set of point sources. Atmospheric turbulence is taken into account by the mutual coherence function. Numerical computations for various turbulent atmospheres show that the geometrical attenuation is 3 dB per distance doubling (3 dB/dd) at a small distance (cylindrical spreading), 6 dB/dd at a large distance (spherical spreading), and 7.5 dB/dd in a transition region. The anomalous value of 7.5 dB/dd is confirmed by an analytic approximation. Next, a computational method in the time domain is developed, for arbitrary wave forms emitted by the source. Atmospheric turbulence is taken into account in this method by including random fluctuations of the acoustic travel times, based on the spectral density of the travel time correlation function. For a harmonic coherent line source, the method yields results that agree with results computed in the frequency domain.

SOUND PROPAGATION OVER NOISE BARRIERS WITH ABSORBING GROUND

The main purpose of this article is to present a numerical method for calculating the sound pressure around noise barriers of arbitrary geometry. Varying impedance boundary conditions on the barrier and constant impedance on the ground are assumed. Sound propagation over an infinite barrier with a constant cross-section for an harmonic point source is determined by solving 2D problems only, avoiding the computational complexity of the solution of a true 3D problem. This can be done by using the solutions of a set of 2D models for a coherent line source for real andimaginarywavenumbers. This extension to calculations forimaginarywavenumbers is the main feature of the proposed method. A Fourier transform of the 2D solutions allows a calculation of the 3D solution for a point source. The 2D numerical solutions are obtained by a classical use of the Boundary Element Method. Moreover, the 2D Green function forimaginarywavenumbers in the case of a half-space bounded by a surface of uniform impedance is developed. Finally, examples are given to estimate the accuracy of the method and some practical cases of calculations around barriers are presented and compared with experimental data.