A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell's equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell-Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell-Lorentz equations, we trace the development of the first-principles formalism enabling accurate calculations of monochromatic and quasi-monochromatic scattering by static and randomly varying multiparticle groups. We illustrate how this general framework can be coupled with state-of-the-art computer solvers of the Maxwell equations and applied to direct modeling of electromagnetic scattering by representative random multi-particle groups with arbitrary packing densities. This first-principles modeling yields general physical insights unavailable with phenomenological approaches. We discuss how the first-order-scattering approximation, the radiative transfer theory, and the theory of weak localization of electromagnetic waves can be derived as immediate corollaries of the Maxwell equations for very specific and well-defined kinds of particulate medium. These recent developments confirm the mesoscopic origin of the radiative transfer, weak localization, and effective-medium regimes and help evaluate the numerical accuracy of widely used approximate modeling methodologies.

中文翻译：

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离散和离散异质随机介质电磁散射的第一性原理建模


离散随机介质是一种有限体积的真空或均质材料介质形式的物体，其中充满了准随机和准均匀分布的离散宏观杂质（称为小颗粒）。此类物体在自然和人造环境中无处不在。它们的特点通常是对光和其他电磁辐射散射的实验室、现场或遥感测量结果进行理论分析。粒子的电磁散射和吸收也会影响离散随机介质的能量预算，从而影响各种周围的物理和化学过程。在任何一种情况下，电磁散射都必须根据适当​​的光学可观测量进行建模，即量化相关光学仪器的读数或电磁能量预算的场中的二次或双线性形式。人们普遍认为，时谐麦克斯韦方程可以准确地描述宏观颗粒介质的弹性电磁散射，这些介质随时间的变化比入射电磁场慢得多。然而，直到最近，离散随机介质的这些方程的直接解还是不切实际的。这导致了各种现象学方法在其适用性受到质疑的情况下被广泛使用。然而，最近出现了物理光学的一个新分支，其中通过使用麦克斯韦方程的解析或数值精确计算机解来直接对离散和离散异质随机介质的电磁散射进行建模。 因此，本报告的主要目标是制定植根于麦克斯韦-洛伦兹电磁学的离散随机介质电磁散射的一般理论框架，并讨论其直接的分析和数值结果。从微观的麦克斯韦-洛伦兹方程开始，我们追溯了第一原理形式主义的发展，使得能够通过静态和随机变化的多粒子群精确计算单色和准单色散射。我们说明了如何将这个通用框架与最先进的麦克斯韦方程组计算机求解器结合起来，并通过具有任意堆积密度的代表性随机多粒子组应用于电磁散射的直接建模。这种第一原理建模产生了现象学方法无法获得的一般物理见解。我们讨论如何将一阶散射近似、辐射传输理论和电磁波弱局域化理论导出为麦克斯韦方程组的直接推论，适用于非常具体和明确的颗粒介质类型。这些最新进展证实了辐射传输的介观起源、弱局域化和有效介质状态，并有助于评估广泛使用的近似建模方法的数值精度。