Phase Statistics in Random Media

P. Sebbah, O. Legrand, A. Z. Genack
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Abstract

Because the ensemble average of the field transmitted through a random medium tends to zero as the sample length increases, studies of wave propagation in random media have focused upon the field amplitude or its square, the intensity, whose statistical properties have been extensively investigated. In this paper, we show that, beyond the random phase approximation, the phase remains a rich statistical quantity which is central to the understanding of wave transport in random systems. We define the cumulative phase φ and present measurements of the frequency dependence of its average, its probability distribution and the correlation function of the phase derivative for microwave radiation transmitted through random collections of polystyrene spheres. Static field measurements are made using a network analyzer. The phase and amplitude of the wave as a function of frequency is obtained for an ensemble of samples by rotating the sample after each spectrum is taken. The probability distribution is calculated using the phase measurement at each frequency for every configuration and is found to reduce to a single gaussian in terms of the variable (φ-)/σ, where σ = (var(φ))½. We show that this is a direct result of the rapid decay of the frequency correlation function of phase derivative found at any frequency. We compare the dwell time Δτ(ν), which is the time for a gaussian pulse with carrier frequency ν to traverse the sample, with phase derivative dφ/dω(ν), where ω = 2πν. We demonstrate theoretically and experimentally that these two quantities are identical if the frequency width of the gaussian pulse is narrow enough (Fig. 1). Finally we outline some of the ways in which φ reflects wave dynamics and relate the phase derivative with the density of states.
随机介质中的相位统计
由于随样本长度的增加,在随机介质中传播的场的集合平均趋于零,因此对波在随机介质中的传播的研究主要集中在场振幅或其平方,即强度,其统计性质已经得到了广泛的研究。在本文中,我们表明,除了随机相位近似之外,相位仍然是一个丰富的统计量,这对于理解随机系统中的波输运至关重要。我们定义了通过聚苯乙烯球随机集合传播的微波辐射的累积相位φ,并给出了其平均值的频率依赖性、其概率分布和相位导数的相关函数。使用网络分析仪进行静态场测量。在每个频谱被取走后,通过旋转样本,可以得到一组样本的相位和振幅作为频率的函数。在每个配置中,使用每个频率上的相位测量来计算概率分布,并且发现可以用变量(φ-)/σ来简化为单个高斯分布,其中σ = (var(φ))½。我们表明,这是在任何频率上发现的相位导数的频率相关函数的快速衰减的直接结果。我们将停留时间Δτ(ν)与相位导数dφ/ ω(ν)(其中ω = 2πν)进行比较,停留时间Δτ(ν)是载频为ν的高斯脉冲穿过样品的时间。我们从理论上和实验上证明,如果高斯脉冲的频率宽度足够窄,这两个量是相同的(图1)。最后,我们概述了φ反映波动动力学的一些方式,并将相位导数与状态密度联系起来。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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