Janna M. Dlugach

DIRECT SOLUTIONS OF THE MAXWELL EQUATIONS EXPLAIN OPPOSITION PHENOMENA OBSERVED FOR HIGH-ALBEDO SOLAR SYSTEM OBJECTS

Several spectacular backscattering effects observed for particulate planetary surfaces have been interpreted in terms of the effect of weak localization (WL) of electromagnetic waves. However, the interference concept of WL explicitly relies on the notion of phase of an electromagnetic wave and is strictly applicable only when particles forming the surface are widely separated. Therefore, one needs a definitive quantitative proof of the WL nature of specific optical effects observed for densely packed particulate media. We use numerically exact computer solutions of the Maxwell equations to simulate electromagnetic scattering by realistic models consisting of large numbers of randomly positioned, densely packed particles. By increasing the particle packing density from zero to ~40%, we track the onset and evolution of the full suite of backscattering optical effects predicted by the low-density theory of WL, including the brightness and polarization opposition effects (BOE and POE). We find that all manifestations of WL, except the circular polarization ratio and POE, are remarkably immune to packing-density effects. Even POE can survive packing densities typical of planetary regolith surfaces. Our numerical data coupled with the results of unique observations at near-backscattering geometries demonstrate that the BOE and POE detected simultaneously for high-albedo solar system objects are caused by the effect of WL.

COHERENT BACKSCATTERING VERIFIED NUMERICALLY FOR A FINITE VOLUME OF SPHERICAL PARTICLES

We consider electromagnetic scattering by a spherical volume sparsely and randomly populated by spherical particles of equal size and optical properties. The far-field scattering matrix of the entire volume is computed using an exact method and an approximate method. The former is a direct computer solver of the Maxwell equations called the superposition T-matrix method (STMM). The latter is a solver based on numerical Monte Carlo integration of the ladder and cyclical diagrams appearing in the microphysical theory of radiative transfer and coherent backscattering (RT-CB). The quantitative agreement between the STMM and RT-CB computations provides verification of the RT-CB theory. Prominent backscattering features exhibited by the STMM data cannot be reproduced by keeping only the ladder diagrams of RT. Our results strongly support the CB explanation of opposition brightness and polarization phenomena observed for a class of atmosphereless solar-system objects. Further research is necessary to determine the range of quantitative applicability of the RT-CB theory to densely packed particulate media.

First-Principles Modeling Of Electromagnetic Scattering By Discrete and Discretely Heterogeneous Random Media

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 Maxwells 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.

Light scattering by wavelength-sized particles “dusted” with subwavelength-sized grains

The numerically exact superposition T-matrix method is used to compute the scattering cross sections and the Stokes scattering matrix for polydisperse spherical particles covered with a large number of much smaller grains. We show that the optical effect of the presence of microscopic dust on the surfaces of wavelength-sized, weakly absorbing particles is much less significant than that of a major overall asphericity of the particle shape.

Adhesion of mineral and soot aerosols can strongly affect their scattering and absorption properties

We use the numerically exact superposition T-matrix method to compute the optical cross sections and the Stokes scattering matrix for polydisperse mineral aerosols (modeled as homogeneous spheres) covered with a large number of much smaller soot particles. These results are compared with the Lorenz-Mie results for a uniform external mixture of mineral and soot aerosols. We show that the effect of soot particles adhering to large mineral particles can be to change the extinction and scattering cross sections and the asymmetry parameter quite substantially. The effect on the phase function and degree of linear polarization can be equally significant.

Weak localization of electromagnetic waves and radar polarimetry of Saturn's rings

We use a state-of-the-art physics-based model of electromagnetic scattering to analyse average circular polarization ratios measured for the A and B rings of Saturn at a wavelength of 12.6 cm. This model is directly based on the Maxwell equations and accounts for the effects of polarization, multiple scattering, weak localization of electromagnetic waves and ring particle non-sphericity. Our analysis is based on the assumption that the observed polarization ratios are accurate, mutually consistent and show a quasi-linear dependence on the opening angle. Also, we assume that the ring system is not strongly stratified in the vertical direction. Our numerical simulations rule out the model of spherical ring particles, favour the model of ring bodies in the form of nearly spherical particles with small-scale surface roughness and rule out non-spherical particles with aspect ratios significantly exceeding 1.2. They also favour particles with effective radii in the range 4–10 cm and definitely rule out effective radii significantly smaller than 4 cm. Furthermore, they seem to rule out effective radii significantly >10 cm. The retrieved ring optical thickness values are in the range 2–3 or even larger. If the rings do have a wake-like horizontal structure, as has been recently suggested, then these optical thickness values should be attributed to an average wake rather than to the optical thickness averaged over the entire horizontal extent of the rings.

Demonstration of Numerical Equivalence of Ensemble and Spectral Averaging in Electromagnetic Scattering by Random Particulate Media

The numerically exact superposition T-matrix method is used to model far-field electromagnetic scattering by two types of particulate object. Object 1 is a fixed configuration that consists of N identical spherical particles (with N=200 or 400) quasi-randomly populating a spherical volume V having a median size parameter of 50. Object 2 is a true discrete random medium (DRM) comprising the same number N of particles randomly moving throughout V. The median particle size parameter is fixed at 4. We show that if Object 1 is illuminated by a quasi-monochromatic parallel beam then it generates a typical speckle pattern having no resemblance to the scattering pattern generated by Object 2. However, if Object 1 is illuminated by a parallel polychromatic beam with a 10% bandwidth then it generates a scattering pattern that is largely devoid of speckles and closely reproduces the quasi-monochromatic pattern generated by Object 2. This result serves to illustrate the capacity of the concept of electromagnetic scattering by a DRM to encompass fixed quasi-random particulate samples provided that they are illuminated by polychromatic light.

Coherent backscattering by polydisperse discrete random media: exact T-matrix results.

The numerically exact superposition T-matrix method is used to compute, for the first time to our knowledge, electromagnetic scattering by finite spherical volumes composed of polydisperse mixtures of spherical particles with different size parameters or different refractive indices. The backscattering patterns calculated in the far-field zone of the polydisperse multiparticle volumes reveal unequivocally the classical manifestations of the effect of weak localization of electromagnetic waves in discrete random media, thereby corroborating the universal interference nature of coherent backscattering. The polarization opposition effect is shown to be the least robust manifestation of weak localization fading away with increasing particle size parameter.

Retrieval of microphysical characteristics of particles in atmospheres of distant comets from ground-based polarimetry

We summarize unique aperture data on the degree of linear polarization observed for distant comets C/2010 S1, C/2010 R1, C/2011 KP36, C/2012 J1, C/2013 V4, and C/2014 A4 with heliocentric distances exceeding 3 AU. Observations have been carried out at the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences (Nizhnij Arkhyz, Russia) during the period from 2011 to 2016. The measured negative polarization proves to be significantly larger in absolute value than what is typically observed for comets close to the Sun. We compare the new observational data with the results of numerical modeling performed with the T-matrix and superposition T-matrix methods. In our computer simulations, we assume the cometary coma to be an optically thin cloud containing particles in the form of spheroids, fractal aggregates composed of spherical monomers, and mixtures of spheroids and aggregate particles. We obtain a good semi-quantitative agreement between all polarimetric data for the observed distant comets and the results of numerical modeling for the following models of the cometary dust: (i) a mixture of submicrometer water-ice oblate spheroids with aggregates composed of submicrometer silicate monomers; and (ii) a mixture of submicrometer water-ice oblate spheroids and aggregates consisting of both silicate and organic monomers. The michrophysical parameters of these models are presented and discussed.

Scattering and extinction by spherical particles immersed in an absorbing host medium

Abstract Many applications of electromagnetic scattering involve particles immersed in an absorbing rather than lossless medium, thereby making the conventional scattering theory potentially inapplicable. To analyze this issue quantitatively, we employ the FORTRAN program developed recently on the basis of the first-principles electromagnetic theory to study far-field scattering by spherical particles embedded in an absorbing infinite host medium. We further examine the phenomenon of negative extinction identified recently for monodisperse spheres and uncover additional evidence in favor of its interference origin. We identify the main effects of increasing the width of the size distribution on the ensemble-averaged extinction efficiency factor and show that negative extinction can be eradicated by averaging over a very narrow size distribution. We also analyze, for the first time, the effects of absorption inside the host medium and ensemble averaging on the phase function and other elements of the Stokes scattering matrix. It is shown in particular that increasing absorption significantly suppresses the interference structure and can result in a dramatic expansion of the areas of positive polarization. Furthermore, the phase functions computed for larger effective size parameters can develop a very deep minimum at side-scattering angles bracketed by a strong diffraction peak in the forward direction and a pronounced backscattering maximum.