Spectrally dependent linear depolarization and lidar ratios for nonspherical smoke aerosols.

We use the numerically exact -matrix method to model light scattering and absorption by aged smoke aerosols at lidar wavelengths ranging from 355 to 1064 nm assuming the aerosols to be smooth spheroids or Chebyshev particles. We show that the unique spectral dependence of the linear depolarization ratio (LDR) and extinction-to-backscatter ratio (or lidar ratio, LR) measured recently for stratospheric Canadian wildfire smoke can be reproduced by a range of model morphologies, a range of spectrally dependent particle refractive indices, and a range of particle sizes. For these particles, the imaginary part of the refractive index is always less than (or close to) 0.

Electromagnetic scattering by discrete random media. IV: Coherent backscattering.

The problem of backscattering of light by a discrete random medium illuminated by an obliquely incident plane electromagnetic wave is considered. The analysis is performed in a linear-polarization basis and includes (i) a complete derivation of the cross reflection matrix for a layer with densely and sparsely distributed particles, (ii) the design of an approximate method for computing the ladder and cross reflection matrices in the case of a semi-infinite medium with a sparse distribution of particles, (iii) the derivation of the relations between the elements of the ladder and cross reflection matrices in the exact backscattering direction for dense and sparse media, and (iv) the development of practical algorithms for solving the underlying integral equations by the method of Picard iterations and the discrete ordinate method. Simulation results for particles with large size parameters are also presented.

Identify the limits of geometric optics ray tracing by numerically solving the vector Kirchhoff integral.

The properties of a pencil of light as defined approximately in the geometric optics ray tracing method are investigated. The vector Kirchhoff integral is utilized to accurately compute the electromagnetic near field in and around the pencil of light with various beam base sizes, shapes, propagation directions and medium refractive indices. If a pencil of light has geometric mean cross section size of the order p times the wavelength, it can propagate independently to a distance p times the wavelength, where most of the beam energy diffuses out of the beam region.

Modeling study of scattering and absorption properties of tar-ball aggregates.

Atmospheric tar balls (TBs) form an important class of atmospheric brown carbon (BrC) particulates. The morphology of the individual TBs is typically described as amorphous and nearly spherical. However, several studies reported observations of TBs aggregated with other aerosols or agglomerations consisting of up to tens of individual TBs.

Multiple scattering of polarized light by particles in an absorbing medium.

We study multiple scattering of light by particles embedded in an absorbing host medium using a recently developed single-scattering and vector radiative-transfer methodology directly based on the Maxwell equations. The first-principles results are compared with those rendered by the conventional heuristic approach according to which the single-scattering properties of particles can be computed by assuming that the host medium is nonabsorbing. Our analysis shows that the conventional approach yields very accurate results in the case of aerosol and cloud particles suspended in an absorbing gaseous atmosphere.

Scattering of a damped inhomogeneous plane wave by a particle in a weakly absorbing medium.

We use the volume integral equation formulation to consider frequency-domain electromagnetic scattering of a damped inhomogeneous plane wave by a particle immersed in an absorbing medium. We show that if absorption in the host medium is sufficiently weak and the particle size parameter is sufficiently small, then (i) the resulting formalism (including the far-field and radiative-transfer regimes) is largely the same as in the case of a nonabsorbing host medium, and (ii) one can bypass explicit use of sophisticated general solvers of the Maxwell equations applicable to inhomogeneous-wave illumination. These results offer dramatic simplifications for solving the scattering problem in a wide range of practical applications involving absorbing host media.

Electromagnetic scattering by discrete random media. II: The coherent field.

The computation of the coherent field in the case of a plane electromagnetic wave obliquely incident on a discrete random layer with non-scattering boundaries is addressed. For dense media, the analysis is based on a special-form solution for the conditional configuration-averaged exciting field coefficients, and is restricted to the computation of the so-called zeroth-order fields without a special treatment of the boundary regions. In this setting, we calculate the coherent fields reflected and transmitted by the layer, and the coherent field inside the layer.

Retrieval of volcanic and man-made stratospheric aerosols from orbital polarimetric measurements.

Stratospheric aerosols that are caused by a major volcanic eruption can serve as a valuable test of global climate models, as well as severely complicate tropospheric-aerosol monitoring from space. In either case, it is highly desirable to have accurate global information on the optical thickness, size, and composition of volcanic aerosols. We report sensitivity study results, which reveal the implications of making precise multi-angle photopolarimetric measurements in a 1.

An overview of methods for deriving the radiative transfer theory from the Maxwell equations. II: Approach based on the Dyson and Bethe-Salpeter equations.

In this paper, the vector radiative transfer equation is derived by means of the vector integral Foldy equations describing the electromagnetic scattering by a group of particles. By Assuming that in a discrete random medium the positions of the particles are statistically independent and by applying the Twersky approximation to the order-of-scattering expansion of the total field, we derive the Dyson equation for the coherent field and the ladder approximated Bethe-Salpeter equation for the dyadic correlation function. Then, under the far-field assumption for sparsely distributed particles, the Dyson equation is reduced to the Foldy integral equation for the coherent field, while the iterated solution of the Bethe-Salpeter equation ultimately yields the vector radiative transfer equation.

Additivity of integral optical cross sections for a fixed tenuous multi-particle group.

We use the volume integral equation formulation of frequency-domain electromagnetic scattering to settle the issue of additivity of the extinction, scattering, and absorption cross sections of a fixed tenuous group of particles. We show that all the integral optical cross sections of the group can be obtained by summing up the corresponding individual-particle cross sections, provided that the single-scattering approximation applies.

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.

Addendum to “Impressed sources and fields in the volume-integral-equation formulation of electromagnetic scattering by a finite object: A tutorial” [J. Quant. Spectrosc. Radiat. Transfer 214 (2018) 158–167].

Our recent tutorial referred to in the title has summarized a general theoretical formalism of electromagnetic scattering by an arbitrary finite object in the presence of arbitrarily distributed impressed currents. This addendum builds on the tutorial to provide a streamlined discussion of specific far-field limits and the corresponding reciprocity relations by introducing appropriate far-field operators and linear maps and deriving the reciprocity relations through the pseudo adjoint of these maps. We thereby extend the compact operator calculus used previously to consider the fields and sources near or inside the scattering object.

Radiative transfer in a discrete random medium adjacent to a half-space with a rough interface.

For a macroscopically plane-parallel discrete random medium, the boundary conditions for the specific coherency dyadic at a rough interface are derived. The derivation is based on a modification of the Twersky approximation for a scattering system consisting of a group of particles and the rough surface, and reduces to the solution of the scattering problem for a rough surface illuminated by a plane electromagnetic wave propagating in a discrete random medium with non-scattering boundaries. In a matrix-form setting, the boundary conditions for the specific coherency dyadic imply the boundary conditions for specific intensity column vectors which in turn, yield the expressions for the reflection and transmission matrices.

Far-field Lorenz-Mie scattering in an absorbing host medium. II: Improved stability of the numerical algorithm.

A recently developed FORTRAN program computing far-field optical observables for spherical particles in an absorbing medium has exhibited numerical instability arising when the product of the particle vacuum size parameter and the imaginary part of the refractive index of the host becomes sufficiently large. We offer a simple analytical explanation of this instability and propose a compact numerical algorithm for the stable computation of Lorenz-Mie coefficients based on an upward recursion formula for spherical Hankel functions of a complex argument. Extensive tests confirm an excellent accuracy of this algorithm approaching machine precision.

Radiative-transfer modeling of spectra of planetary regoliths using cluster-based dense packing modifications.

In remote sensing of planetary bodies, the development of analysis techniques that lead to quantitative interpretations of datasets has relatively been deficient compared to the wealth of acquired data, especially in the case of regoliths with particle sizes on the order of the probing wavelength. Radiative transfer theory has often been applied to the study of densely packed particulate media like planetary regoliths, but with difficulty; here we continue to improve theoretical modeling of spectra of densely packed particulate media. We use the superposition T-matrix method to compute the scattering properties of an elementary volume entering the radiative transfer equation by modeling it as a cluster of particles and thereby capture the near-field effects important for dense packing.

Impressed sources and fields in the volume-integral-equation formulation of electromagnetic scattering by a finite object: a tutorial.

Although free space cannot generate electromagnetic waves, the majority of existing accounts of frequency-domain electromagnetic scattering by particles and particle groups are based on the postulate of existence of an impressed incident field, usually in the form of a plane wave. In this tutorial we discuss how to account for the actual existence of impressed source currents rather than impressed incident fields. Specifically, we outline a self-consistent theoretical formalism describing electromagnetic scattering by an arbitrary finite object in the presence of arbitrarily distributed impressed currents, some of which can be far removed from the object and some can reside in its vicinity, including inside the object.

Electromagnetic scattering and emission by a fixed multi-particle object in local thermal equilibrium: General formalism.

The majority of previous studies of the interaction of individual particles and multi-particle groups with electromagnetic field have focused on either elastic scattering in the presence of an external field or self-emission of electromagnetic radiation. In this paper we apply semi-classical fluctuational electrodynamics to address the ubiquitous scenario wherein a fixed particle or a fixed multi-particle group is exposed to an external quasi-polychromatic electromagnetic field as well as thermally emits its own electromagnetic radiation. We summarize the main relevant axioms of fluctuational electrodynamics, formulate in maximally rigorous mathematical terms the general scattering-emission problem for a fixed object, and derive such fundamental corollaries as the scattering-emission volume integral equation, the Lippmann-Schwinger equation for the dyadic transition operator, the multi-particle scattering-emission equations, and the far-field limit.

Electromagnetic scattering by spheroidal volumes of discrete random medium.

We use the superposition -matrix method to compare the far-field scattering matrices generated by spheroidal and spherical volumes of discrete random medium having the same volume and populated by identical spherical particles. Our results fully confirm the robustness of the previously identified coherent and diffuse scattering regimes and associated optical phenomena exhibited by spherical particulate volumes and support their explanation in terms of the interference phenomenon coupled with the order-of-scattering expansion of the far-field Foldy equations. We also show that increasing nonsphericity of particulate volumes causes discernible (albeit less pronounced) optical effects in forward and backscattering directions and explain them in terms of the same interference/multiple-scattering phenomenon.

On Babinet's principle and diffraction associated with an arbitrary particle.

Babinet's principle is widely used to compute the diffraction by a particle. However, the diffraction by a 3-D object is not totally the same as that simulated with Babinet's principle. This Letter uses a surface integral equation to exactly formulate the diffraction by an arbitrary particle and illustrate the condition for the applicability of Babinet's principle.

Extinction by a homogeneous spherical particle in an absorbing medium.

We use a recent computer implementation of the first-principles theory of electromagnetic scattering to compute far-field extinction by a spherical particle embedded in an absorbing unbounded host. Our results show that the suppressing effect of increasing absorption inside the host medium on the ripple structure of the extinction efficiency factor as a function of the size parameter is similar to the well-known effect of increasing absorption inside a particle embedded in a nonabsorbing host. However, the accompanying effects on the interference structure of the extinction efficiency curves are diametrically opposite.

Information content of bistatic lidar observations of aerosols from space.

We present, for the first time, a quantitative retrieval error-propagation study for a bistatic high spectral resolution lidar (HSRL) system intended for detailed quasi-global monitoring of aerosol properties from space. Our results demonstrate that supplementing a conventional monostatic HSRL with an additional receiver flown in formation at a scattering angle close to 165° dramatically increases the information content of the measurements and allows for a sufficiently accurate characterization of tropospheric aerosols. We conclude that a bistatic HSRL system would far exceed the capabilities of currently flown or planned orbital instruments in monitoring global aerosol effects on the environment and on the Earth's climate.

On the concept of random orientation in far-field electromagnetic scattering by nonspherical particles.

Although the model of randomly oriented nonspherical particles has been used in a great variety of applications of far-field electromagnetic scattering, it has never been defined in strict mathematical terms. In this Letter, we use the formalism of Euler rigid-body rotations to clarify the concept of statistically random particle orientations and derive its immediate corollaries in the form of the most general mathematical properties of the orientation-averaged extinction and scattering matrices. Our results serve to provide a rigorous mathematical foundation for numerous publications in which the notion of randomly oriented particles and its light-scattering implications have been considered intuitively obvious.

Linear depolarization of lidar returns by aged smoke particles.

We use the numerically exact (superposition) T-matrix method to analyze recent measurements of the backscattering linear depolarization ratio (LDR) for a plume of aged smoke at lidar wavelengths ranging from 355 to 1064 nm. We show that the unique spectral dependence of the measured LDRs can be modeled, but only by assuming expressly nonspherical morphologies of smoke particles containing substantial amounts of nonabsorbing (or weakly absorbing) refractory materials such as sulfates. Our results demonstrate that spectral backscattering LDR measurements can be indicative of the presence of morphologically complex smoke particles, but additional (e.

Electromagnetic scattering by fully ordered and quasi-random rigid particulate samples.

In this paper we have analyzed circumstances under which a rigid particulate sample can behave optically as a true discrete random medium consisting of particles randomly moving relative to each other during measurement. To this end, we applied the numerically exact superposition T-matrix method to model far-field scattering characteristics of fully ordered and quasi-randomly arranged rigid multiparticle groups in fixed and random orientations. We have shown that, in and of itself, averaging optical observables over movements of a rigid sample as a whole is insufficient unless it is combined with a quasi-random arrangement of the constituent particles in the sample.

First-principles definition and measurement of planetary electromagnetic-energy budget.

The imperative to quantify the Earth's electromagnetic-energy budget with an extremely high accuracy has been widely recognized but has never been formulated in the framework of fundamental physics. In this paper we give a first-principles definition of the planetary electromagnetic-energy budget using the Poynting-vector formalism and discuss how it can, in principle, be measured. Our derivation is based on an absolute minimum of theoretical assumptions, is free of outdated notions of phenomenological radiometry, and naturally leads to the conceptual formulation of an instrument called the double hemispherical cavity radiometer (DHCR).