Derivation of a one-way radiative transfer equation in random media.
Derivation of a one-way radiative transfer equation in random media.
复制标题
随机介质中单向辐射传输方程的推导。
DOI：
10.1103/physreve.93.022115
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
J. Garnier
中科院分区：
文献类型：
--
作者：
L. Borcea;J. Garnier
我们从第一原理推导出随机介质中沿方向解析的波强度（波场的维格纳变换）的单向辐射传递方程。这是一个初始值问题，涉及来自沿首选向前方向发射波的源的激励。该方程是在波速随机波动较小但相对于波长的传播距离较长的情况下导出的，因此累积散射很重要。介质的相关长度和源的支撑尺度均略大于波长，并且波在张角小于180°的宽锥体中传播，使得后向波和倏逝波可以忽略不计。散射区是辐射传输区（波在各个方向上传播）和近轴区（波在窄角锥中传播）之间的桥梁。我们将单向辐射传递方程与这些状态下波场的维格纳变换所满足的方程联系起来。
We derive from first principles a one-way radiative transfer equation for the wave intensity resolved over directions (Wigner transform of the wave field) in random media. It is an initial value problem with excitation from a source which emits waves in a preferred, forward direction. The equation is derived in a regime with small random fluctuations of the wave speed but long distances of propagation with respect to the wavelength, so that cumulative scattering is significant. The correlation length of the medium and the scale of the support of the source are slightly larger than the wavelength, and the waves propagate in a wide cone with an opening angle less than 180°, so that the backward and evanescent waves are negligible. The scattering regime is a bridge between that of radiative transfer, where the waves propagate in all directions, and the paraxial regime, where the waves propagate in a narrow angular cone. We connect the one-way radiative transfer equation with the equations satisfied by the Wigner transform of the wave field in these regimes.