Mesoscopic Phase Statistics of Diffuse Ultrasound in Dynamic Matter

Abstract

Temporal fluctuations in the phase of waves transmitted through a dynamic, strongly scattering, mesoscopic sample are investigated using ultrasonic waves, and compared with theoretical predictions based on circular Gaussian statistics. The fundamental role of phase in Diffusing Acoustic Wave Spectroscopy is revealed, and phase statistics are also shown to provide a sensitive and accurate way to probe scatterer motions at both short and long time scales.PACS numbers: 43.35.+d, 42.25.Dd, 43.60.Cg, 81.70.Cv For all waves, phase is irrefutably the most fundamental property. On macroscopic scales, however, phase is randomized by multiple scattering or obscured by decoherence. It is now generally accepted that a mesoscopic regime exists where wave phenomena persist on even hydrodynamic scales. Mesoscopic fluctuations can sometimes be long-range and non-Gaussian [1,2]. The universal conductance fluctuations are best known, originally discovered for electrons [3], and later also observed with visible light [4] and microwaves [5]. In the optics of soft condensed matter, the existence of dynamic mesoscopic fluctuations has led to a new technique called diffusing wave spectroscopy (DWS) [6]. In the acoustic counterpart, diffusing acoustic wave spectroscopy (DAWS) [7], the fluctuations of the scattered wave field are measured directly to probe the dynamics of disordered media. In seismology, the closely related technique of Coda Wave Interferometry [8] is extending the range of applications being studied.For acoustic, seismic or radio waves, the phase can be easily extracted. While many applications, including interferometric techniques such as InSAR [9], make use of phase for precise measurements, the phase of multiply scattered waves has often been neglected, since it is generally more challenging to extract useful information from phase in multiple-scattering systems. Mesoscopic studies have revealed the fundamental relation of phase to the screening of zeros of random fields [10], but most of the literature has focussed on quantities such as the probability distribution functions of intensity, transmission or conductance [1], and does not address the phase directly. Recent studies with microwaves [11], infrared light [12] and Terahertz radiation [13] have explored frequency correlations of the phase. In this Letter, we study time-dependent phase fluctuations of ultrasound in a dynamic, strongly scattering medium, and examine the statistics of both the wrapped and cumulative phase evolution. This combination of theory and experiment reveals a deeper insight into the mesoscopic physics of multiply scattered waves, and explicitly shows the relationship between the average phase evolution of a typical multiple scattering path -a crucial concept in D(A)WS modelling [6,7] -and the measured phase evolution of the transmitted waves. We also find that phase statistics can sometimes provide a more accurate method of measuring the dynamics than the field autocorrelation method that is used in D(A)WS. In our materials, the tempo...

CoGeNT interpretations

“…When forming confidence intervals in the WIMP parameter space below, we use the likelihood profile method to eliminate the nuisance parameters associated with the background [16]. This is done by first minimizing the χ 2 function (defined over the 28 bins) with respect to the background parameters, c i , at every point in the m χ − σ n space while keeping m χ and σ n fixed,…”

Phase Statistics of Seismic Coda Waves

“…From the joint Gaussian distribution of 3 and 4 fields, we can derive analytically the joint probability functions P (φ ′ , φ ′′ ), P (φ ′ , φ ′′ , φ ′′′ ) , featuring two new constants R and S [9]. From these formulas, the marginal distributions P (φ ′′ ), P (φ ′′′ ) can be evaluated numerically.…”

“…Then, the off-diagonal elements are equal to the field correlation function C ij = C(| r i − r j |). From the joint distribution of two fields, the probability distribution of the phase difference at two points located δ apart can be obtained by integrating over the amplitudes [9]:…”

A statistical approach to direct density of states measurements in disordered systems

“…Even though imaging inside multiply scattering media is still a challenge, multiply scattered waves have been demonstrated to be very sensitive to motion of the scatterers, leading to the new techniques of diffusing acoustic wave spectroscopy and diffusing reverberant acoustic wave spectroscopy for characterizing scatterer dynamics. [17][18][19] Despite the wealth of information that has been gleaned on wave transport from ultrasonic experiments, relatively little attention has been paid to another fundamental quantity-the density of states-and a reliable method of measuring this quantity remains essential to obtaining a complete picture of wave transport.…”

“…Ultrasonics has played an important role in studying these strongly scattering disordered systems. [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] Initial investigations focused on the applicability of the diffusion approximation to describe the transport of energy by multiply scattered waves in pulsed experiments, where a time-dependent "coda" is observed after the initial arrivals due to ballistic transport. 6,7 Even though the diffusion approximation neglects all phase information, it gives a remarkably accurate description of wave transport under a wide variety of experimental conditions, including transmission and reflection ͑coherent backscattering͒ experiments.…”