Multiple Scattering of Waves

Lax, M.

doi:10.1103/revmodphys.23.287

Cited by 1,145 publications

(469 citation statements)

References 66 publications

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“…The saturation effect of the 1D density of states due to disorder is well known, 35 and can be calculated for instance by using the effective-medium model and the coherent-potential approximation ͑CPA͒. 36 However this calculation does not take into account the dissipation such as intrinsic out-of-plane losses. We develop here a simple 1D transfer quasiperiodic matrix model involving the effective indices of the modes of the 2D system to estimate quantitatively the amount of disorder as well as of dissipation.…”

Section: One-dimensional Modeling Of the Disorder And Of The Dissmentioning

confidence: 99%

Influence of residual disorder on the anticrossing of Bloch modes probed inkspace

et al. 2008

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We retrieve the dispersion properties of photonic crystal waveguides near the band edge with high experimental accuracy. The dispersion diagram of the waveguide modes in the complex-valued plane is directly measured in the far field by using a Fourier space imaging technique. We show that the investigation of the modes in k space provides a clear signature of the transition between propagating, evanescent, and localized modes. It allows us to determine the impact of the structural disorder and of the dissipation on the group velocity of the propagating wave in the slow light regime.

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Section: One-dimensional Modeling Of the Disorder And Of The Dissmentioning

confidence: 99%

Influence of residual disorder on the anticrossing of Bloch modes probed inkspace

et al. 2008

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“…. When positional and orientational degrees of freedom are statistically independent, the result of averaging over positional disorder is known to be a sum of two terms describing the coherent and the incoherent scattering [10,29,35]. So, we have…”

Section: Scattering Mean Free Pathmentioning

confidence: 99%

Ordering of droplets and light scattering in polymer dispersed liquid crystal films

Kiselev

Yaroshchuk

Dolgov

2004

J. Phys.: Condens. Matter

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We study the effects of droplet ordering in initial optical transmittance through polymer dispersed liquid crystal (PDLC) films prepared in the presence of an electrical field. The experimental data are interpreted by using a theoretical approach to light scattering in PDLC films that explicitly relates optical transmittance and the order parameters characterizing both the orientational structures inside bipolar droplets and orientational distribution of the droplets. The theory relies on the Rayleigh-Gans approximation and uses the Percus-Yevick approximation to take into account the effects due to droplet positional correlations.

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Section: At T E N Uat I O N O F T H E a M B I E N T S E I S M I C F Imentioning

confidence: 99%

“…At the same time, a wave traveling through an assemblage of isotropic point scatterers can be described by an effective wavenumber whose phase velocity and rate of attenuation depend on (i) the wavenumber of the background medium, (ii) the scatterer density and (iii) the average strength of the scatterers. We note that isotropic point scattering is not essential for the description of a heterogeneous medium by an effective wavenumber (Lax 1951;Waterman & Truell 1961).The total wavefield at a location r can be described as the sum of the background wavefield 0 and the wavefield due to the scatterers s , that is,Since the medium in which the scatterers are embedded is assumed lossless and homogeneous, propagation in this background medium is described by a real wavenumber k 0 . Similarly, the velocity of the background medium is denoted by c 0 and its wavelength by λ 0 .…”

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confidence: 99%

On the estimation of attenuation from the ambient seismic field: inferences from distributions of isotropic point scatterers

Weemstra¹,

Snieder

Boschi

2015

Geophys. J. Int.

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S U M M A R YCross-correlation of ambient seismic noise recorded by two seismic stations may result in an estimate of the Green's function between those two receivers. Several authors have recently attempted to measure attenuation based on these interferometric, receiver-receiver surface waves. By now, however, it is well established that the loss of coherence of the crosscorrelation as a function of space depends strongly on the excitation of the medium. In fact, in a homogeneous dissipative medium, uniform excitation is required to correctly recover attenuation. Applied to fundamental-mode ambient seismic surface waves, this implies that the cross-correlation will decay at the local attenuation rate only if noise sources are distributed uniformly on the Earth's surface. In this study we show that this constraint can be relaxed in case the observed loss of coherence is due to multiple scattering instead of dissipation of energy. We describe the scattering medium as an effective medium whose phase velocity and rate of attenuation are a function of the scatterer density and the average strength of the scatterers. We find that the decay of the cross-correlation in the effective medium coincides with the local attenuation of the effective medium in case the scattering medium is illuminated uniformly from all angles. Consequently, uniform excitation is not a necessary condition for the correct retrieval of scattering attenuation. We exemplify the implications of this finding for studies using the spectrally whitened cross-correlation to infer subsurface attenuation.Key words: Surface waves and free oscillations; Seismic attenuation; Theoretical seismology; Wave scattering and diffraction. I N T RO D U C T I O NIt is now generally accepted that the cross-correlation of recordings made by two receivers is related to (and can in practice be treated as an approximation of) the Green's function at one of these receivers position if there were an impulsive source at the other. The first successful application to the solid Earth is due to Campillo & Paul (2003) who used earthquake coda to obtain empirical Green's functions. Shapiro & Campillo (2004) showed that broad-band Rayleigh waves emerge by simple cross-correlation of continuous recordings of ambient seismic noise. The latter finding holds in media other than the Earth: for example, helioseismology (Duvall et al. 1993), underwater acoustics (Roux & Fink 2003), ultrasonics (Weaver & Lobkis 2001, 2002, engineering (Snieder & Şafak 2006;Kohler et al. 2007) and infrasound (Haney 2009 the Earth's ambient seismic field use ambient seismic surface wave energy: ocean gravity waves, the main source of ambient seismic noise on Earth, excite surface waves much more effectively than other seismic phases. The process of generating new responses by cross-correlation of ambient seismic signal is often referred to as 'passive seismic interferometry'.Recently, several researchers have focused on estimating attenuation based on interferometric measurements of surface waves (Prieto e...

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Multiple Scattering of Waves

Cited by 1,145 publications

References 66 publications

Influence of residual disorder on the anticrossing of Bloch modes probed inkspace

Influence of residual disorder on the anticrossing of Bloch modes probed inkspace

Ordering of droplets and light scattering in polymer dispersed liquid crystal films

On the estimation of attenuation from the ambient seismic field: inferences from distributions of isotropic point scatterers

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