First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media

Abstract

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 MaxwellLorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell-Lorentz equations, we trace the development of the firstprinciples 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.

Porous aerosol in degassing plumes of Mt. Etna and Mt. Stromboli

“…The effective medium approximation (EMA), along with the Maxwell Garnett mixing rule, has already been used in a number of works to calculate optical properties of porous particles (see, e.g., Voshchinnikov et al, 2007;Kylling et al, 2014). The question of EMA applicability is discussed in detail by Mishchenko et al (2016).…”

“…Liu et al (2014) concluded that scattering properties of the equivalent homogeneous particles agree well with those of internally mixed particles. Fundamental aspects and recent developments of the scattering of electromagnetic radiation by a discrete random medium as well as applicability of the EMAs are reported in the work by Mishchenko et al (2016).…”

Applicability of Effective Medium Approximations to Modelling of Mesocrystal Optical Properties

“…The accuracy of the effective medium approximation depends on the size of the primary particles and the homogeneity of their distribution in the medium [12][13][14][15]. In mesocrystals homogeneity is an intrinsic property provided by the high ordering of the primary particles, it should be noted that in particulate random media with high fraction of the inclusion material lack of homogeneity reduce the accuracy of the approach [15]. The appropriateness of the primary particle size can be estimated by computing the size parameter [12] …”

“…Another possibility is to simulate the response of a finite size mesocrystalline structure, like, for example, a mesocrystal of spherical shape, and compare the results with the Lorentz-Mie simulations combined with effective medium theories. This approach was applied in [12][13][14][15] to study the accuracy of the effective medium description of spherical objects composed of random particulate media. Simulations presented in this paper are closely related to one of the prospective applications of mesocrystals-the functional pigments [3], where the optical response of the pigment particles can be tuned by controlling the mesocrystal's density and shape, and the reported results can be used to optimize the properties of such systems.…”

Electromagnetic scattering by spheroidal volumes of discrete random medium

“…[1][2][3][4][5][6] and the comprehensive reference list in the recent review [7]). In particular, the effects of domain size [8], particle size [9], particle refractive index [1,9] (including the imaginary part [10]), and particle packing density [11,12] have been studied in substantial detail.…”