Optical properties of aggregate particles comparable in size to the wavelength

The angular dependence of brightness and linear polarization of randomly oriented aggregates has been investigated in order to find rules connecting their scattering properties with their structure, packing density, complex refractive index, and number and size of the spheres forming the aggregate. Our study is based on an interpretation in terms of successive orders of scattering, in particular on the analysis of the contribution of the interference and near-field effects. Such an approach allowed us to explain and interrelate the main peculiarities of the angular dependence of the intensity and polarization displayed by aggregates. Of special interest are the aggregates showing a so-called negative branch of linear polarization of light scattered into angles close to the backscattering direction. It has been shown that the enhancement of intensity and the negative polarization in this angular range are mainly caused by the interference of multiply scattered waves as well as by near-field effects. If the number of particles in the aggregate is large enough and its size is comparable to the wavelength, the backscattering enhancement is caused by the particles in the surface layers of the aggregate, where the radiation field is mostly homogeneous, while the negative branch is mainly generated by the deeper layers of particles, where the radiation field is inhomogeneous with chaotic changes of amplitudes and phases. This results in a rather weak dependence of the negative polarization on particle location in the deeper layers of the aggregate and on particle number but not on packing density.     

Discrete-dipole analysis of backscatter features of agglomerated debris particles comparable in size with wavelength

We study the backscattered light of agglomerated debris particles using the discrete dipole approximation (DDA) in order to isolate specific physical components that contribute to negative polarization and the brightness opposition surge. We examine a few specific particle systems that display a prominent brightness surge and significant negative polarization over a range of near backscatter angles. In all cases, removal of the far-field interaction components results in the disappearance of the brightness surge and negative polarization branch; whereas, these phenomena remained if the near-field or radial components of the interaction fields are removed. This suggests that the mechanisms for these phenomena are embedded within the far-field interaction component.     

Backscattering and negative polarization of agglomerate particles

We used the discrete dipole approximation to study the backscattering of agglomerate particles consisting of oblong monomers. We varied the aspect ratio of the monomers from approximately 1 (sphere) to 4, while we kept the total particle volume equivalent to that of an x = 10 sphere for m = 1.59 + i0 and 1.50 + i0 and considered two values of agglomerate packing density: rho = 0.25 and rho = 0.1. We found that these particles do not display a prominent brightness opposition effect but do produce significant negative polarization over a range of near-backscattering angles. Increasing the monomers' aspect ratio can make the negative polarization much more prominent. We have noted also that decreasing m and p can reduce the amplitude of the negative polarization for these particles.     

Backscatter effects of surfaces composed of dry biological particles

We present the backscattering of particulate surfaces consisting of dry biological particles using two laboratory photopolarimeters that measure intensity and degree of linear polarization in a phase-angle range 0.2-60°. We measure scattering properties from three samples composed of dry biological particles, Bacillus subtilis var. niger (BG) spores and samples of fungi Aspergillus terreus and Sporisorium cruentum spores. We find that the surfaces display a prominent brightness opposition effect and significant negative polarization near backscattering angles. The brightness and polarimetric phase curves are different for B. subtilis and the fungi.     

Similarity and diversity in photometric and polarimetric opposition effects of small Solar System bodies

The phase-angle dependences of brightness and polarization of light scattered by atmosphereless Solar System bodies (satellites, asteroids, planetary rings) as well as comets and zodiacal light are analysed on the basis of available ground-based and spacecraft observations. We study similarity and diversity in the photometric and polarimetric opposition effects. The similarity of the brightness and polarization phase functions for polydisperse dust media (cometary and interplanetary dust) and for atmosphereless bodies at small phase angles gives grounds to state that at least some physical properties of dust particles and light-scattering mechanisms should be similar for the two classes of objects. The aggregate structure of particles in different objects can be precisely the property that determines the photometric and polarimetric effects observed in the opposition region. Differences observed in opposition effects for different objects are likely caused by different physical properties (composition, sizes, structure, density) of the scattering particles and, therefore, by different relative contributions of the light-scattering mechanisms. However, the relationship between the photometric opposition effect, spike effect, negative polarization branch, and polarization opposition effect for different bodies is ambiguous.     

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.     

Coherent backscattering effects for discrete random media: Numerical and theoretical results

Manifestation of the backscattering enhancement phenomenon in the reflection matrix elements of the coherent component of scattered radiation is considered. The dependence of the coherent backscattering effects on the microphysical properties of the medium scatterers are investigated. It is shown that random media of fractal-like clusters exhibit brightness and polarization opposition effects, which are like those observed for some atmosphereless Solar system bodies. Conditions for a bimodal angle dependence in the degree of linear polarization are discussed and the manifestation of the enhanced backscattering phenomenon in the intensity of scattered radiation is studied.     

Collective effects by agglomerated debris particles in the backscatter

We present an analysis of backscattered light by agglomerated debris particles whose size is comparable with the wavelength. We consider agglomerates that consist of one or two large central particles and a few relatively small fragments surrounding the particles. We find that for the particles we studied, the attachment of small fragments onto the particles leads to a decrease of the negative polarization branch (NPB) at small phase angles in comparison with the branch produced by the isolated particles. For relatively large agglomerates (with size parameters x about 25) the internal scatter in the agglomerates may produce a secondary minimum of the NPB. In this case the second order of scatter between constituents of aggregates plays the dominant role.     

Scattering of electromagnetic waves by ensembles of particles and discrete random media

Current problems of the theory of multiple scattering of electromagnetic waves by discrete random media are reviewed, with an emphasis on densely packed media. All equations presented are based on the rigorous theory of electromagnetic scattering by an arbitrary system of non-spherical particles. The main relations are derived in the circular-polarization basis. By applying methods of statistical electromagnetics to a discrete random medium in the form of a plane-parallel layer, we transform these relations into equations describing the average (coherent) field and equations for the sums of ladder and cyclical diagrams in the framework of the quasi-crystalline approximation. The equation for the average field yields analytical expressions for the generalized Lorentz-Lorenz law and the generalized Ewald-Oseen extinction theorem, which are traditionally used for the calculation of the effective refractive index. By assuming that the particles are in the far-field zones of each other, we transform all equations asymptotically into the well-known equations for sparse media. Specifically, the equation for the sum of the ladder diagrams is reduced to the classical vector radiative transfer equation. We present a simple approximate solution of the equation describing the weak localization (WL) effect (i.e., the sum of cyclical diagrams) and validate it by using experimental and numerically exact theoretical data. Examples of the characteristics of WL as functions of the physical properties of a particulate medium are given. The applicability of the interference concept of WL to densely packed media is discussed using results of numerically exact computer solutions of the macroscopic Maxwell equations for large ensembles of spherical particles. These results show that theoretical predictions for spare media composed of non-absorbing or weakly absorbing particles are reasonably accurate if the particle packing density is less than ∼30%. However, a further increase of the packing density and/or absorption may cause optical effects not predicted by the low-density theory and caused by near-field effects. The origin of the near-filed effects is discussed in detail.     

Numerically exact computer simulations of light scattering by densely packed, random particulate media

Direct computer simulations of electromagnetic scattering by discrete random media have become an active area of research. In this progress review, we summarize and analyze our main results obtained by means of numerically exact computer solutions of the macroscopic Maxwell equations. We consider finite scattering volumes with size parameters in the range [20] and [59], composed of varying numbers of randomly distributed particles with different refractive indices. The main objective of our analysis is to examine whether all backscattering effects predicted by the low-density theory of coherent backscattering (CB) also take place in the case of densely packed media. Based on our extensive numerical data we arrive at the following conclusions: (i) all backscattering effects predicted by the asymptotic theory of CB can also take place in the case of densely packed media; (ii) in the case of very large particle packing density, scattering characteristics of discrete random media can exhibit behavior not predicted by the low-density theories of CB and radiative transfer; (iii) increasing the absorptivity of the constituent particles can either enhance or suppress typical manifestations of CB depending on the particle packing density and the real part of the refractive index. Our numerical data strongly suggest that spectacular backscattering effects identified in laboratory experiments and observed for a class of high-albedo Solar System objects are caused by CB.     

Coherent opposition effects for semi-infinite discrete random medium in the double-scattering approximation

The rigorous equations of the theory of multiple scattering of light by a layer of disordered medium have been used in the double-scattering approximation for semi-infinite medium to determine the influence of the particle properties on the coherent opposition effects. The effects were found to be strongly dependent on the concentration of scatterers in the medium. The polarization opposition effect is more sensitive to the properties of the scatterers than the photometric opposition effect. The interference of waves could result in the negative polarization at the backscattering direction as well as in the positive polarization.     

Interrelating scattering characteristics to internal electric fields for Gaussian-random-sphere particles

We investigate the single-scattering interference mechanism related to the negative polarization branch (NPB) and intensity enhancement branch (IEB) near the backscattering direction for wavelength-scale Gaussian-random-sphere particles. Previously, we showed that for wavelength-scale spherical particles there is a two-part mechanism related to the longitudinal and the transverse components of the internal electric fields that are responsible for producing both the NPB and IEB near the backscattering direction. For comparison with the previous study, we have chosen the ensemble-averaged parameters of the Gaussian-random-sphere particles to be equivalent to those for spherical particles. We conclude that the same mechanism also can explain the NPB and IEB for non-spherical particles and that the mechanism seems to be stronger inside spherical particles, mainly because of stronger interference, and becomes weaker as the particle becomes more non-spherical.     

Modeling variations in near-infrared spectra caused by the coherent backscattering effect

We study a new optical effect, a spectral manifestation of coherent backscattering, which reveals itself as systematic variations in the depth of absorption bands with changing phase angle. We used Cassini VIMS near-infrared spectra of Saturn's icy satellite Rhea in order to identify and characterize the spectral change with phase angle, focusing on the change in the depth of water-ice absorption bands. To model realistic characteristics of the surfaces of icy satellites, which are most likely covered by micron-sized densely packed particles, we perform simulations using a theoretical approach based on direct computer solutions of the macroscopic Maxwell equations. Our results show that this approach can reproduce the observed phase-angle variations in the depth of the absorption bands. The modeled changes in the absorption bands are strongly affected by physical properties of the regolith, especially by the size and packing density of the ice particles. Thus, the phase-angle spectral variations demonstrate a promising remote-sensing capability for studying properties of the surfaces of icy bodies and other objects that exhibit a strong coherent backscattering effect.     

Model of light scattering by dust particles in the solar system: Applications to cometary comae and planetary regoliths

We analyze both the intensity and linear polarization of cosmic dust particles by using the physically exact superposition T-matrix method in a fixed orientation for various aggregates of spheres and DDA for the aggregates of Gaussian random spheres. We study both the spherical geometry (in cometary comae) and cylindrical slabs (for regoliths) up to 2000 monomers with size parameters less than ∼3. It is straightforward to produce the observed linear polarization in both geometries while the typically convex and strong opposition spike seems to require wide regolith geometries. The dependence of various parameters on light scattering has also been studied in a rather detailed form. In applications to the cometary polarization we can fit the data in six colors from UV to the J band at a very good accuracy. We, however, emphasize that we do not claim our model to be unique. The most important parameters here are the refractive index and the size distribution of submicron particles. Rest of the parameters has only a minor role. We also found that it is critically important to use several realizations from any assumed particle geometry model because corresponding scattering characteristics can vary quite a lot.     

强壮前沟藻的后向散射特性研究

基于2012年7月藻类培养实验期间的实测生物-光学数据,分析了强壮前沟藻的后向散射特性及其影响因素。结果表明,强壮前沟藻的后向散射系数值具有光谱变化性,并随叶绿素浓度的升高而增大,两者之间呈很好的幂函数关系,相关系数R2最小值可达0.96;此外,由于色素的吸收作用,使得其光谱形状会随叶绿素的变化而变化;同时获得的后向散射比率620 nm处的变化范围在0.006 4～0.011 6之间;总体上,各波段颗粒物后向散射比率也呈现随叶绿素浓度增加而增大的趋势,但在高叶绿素浓度下,这种变化规律并不明显,并且就其光谱形状而言,无论叶绿素浓度高低,其光谱形状始终保持一致;颗粒密度是影响后向散射比率的主要因素之一,两者之间呈幂函数关系,相关系数r在620 nm处高达0.98。     

Coherence effects in scattering systems of two interacting dipoles at resonance

Coherence effects in the backward-scattering direction, such as enhanced backscattering (EBS) and the appearance of a negative polarization branch (NPB), are investigated for a simple scattering system composed of two dipolelike particles separated by a fixed distance. The influence on these effects of coupling resonances between the particles is analyzed. The appearance of these coherent phenomena (EBS and NPB) and their relationship as a function of the optical properties of the particles (polarizability) and particle separation are also studied.     

Light scattering by composite particles comparable with wavelength and their approximation by systems of spheres

Scattering properties of an ensemble of independent, randomly-oriented systems consisting of two contacting wavelength-sized dielectric particles of spherical and random shapes are studied. The optical properties of such ensembles are shown to be determined, to a considerable degree, by the properties of individual components of the system; the role of collective effects is insignificant. For large scattering angles, systems consisting of two spheres form the negative branch of the degree of linear polarization when an individual sphere also forms it, and when systems composed of equivalent particles of random shape do not exhibit the negative branch. The conclusion is made that the modeling of the scattering properties of aspherical and aggregate particles by using systems of spheres of size of the order of the optical wavelength is inadequate.     

Polarization of near-forward-scattered light from particulate substrates illuminated at near-grazing angles

Laboratory photopolarimetric measurements of light scattered by substrates consisting of semitransparent particles with sizes significantly larger than the wavelength show a polarization shoulder at small scattering angles near θ=10-30° in addition to the Brewster maximum positioned near θ=50°. With ray-tracing simulations, we find that the shoulder appears to be related to light passing through particles in the upper layers of the substrates. We study the dependence on particle absorption and packing density of particulate substrates. The studies show that the shoulder weakens with increased absorption and packing density.     

Computer simulations for multiple scattering of light rays in systems of opaque particles

A new computer model for multiple light scattering in arbitrary systems of opaque diffusely scattering particles is considered. For ray tracing and scattering in such systems, the geometric optics approximation is used. Semi-infinite media and clusters with spherical and irregular shaped particles are investigated. The irregular particles are approximated with a discrete set of small triangular facets attached to each other. The particle surface is supposed to scatter by the Lambertian indicatrix. Scattering of the first six orders is considered, but the model can be effectively used for calculations of higher orders too. Phase-angle curves of scattering for media and clusters with different packing density are calculated. It is shown that the contributions of scattering orders rapidly diminish as the order grows even for non-absorbing particulate surfaces. Only the first scattering order shows the opposition effect and is rather sensitive to packing density. Higher orders do not show any features near zero phase angle. The contributions of high orders increase slightly, when the packing density increases. The form of particles is important mostly for the second scattering order. For clusters of particles both packing density and number of particles are important for phase function behavior. Clusters consisting of 100 particles show weak phase-angle dependences of high orders of scattering. These dependences become more prominent with increase of number of particles. Phase curves for spherical and cubic clusters are compared. It turns out that the influence of cluster shape is only a minor factor.     

Polarization of light backscattered by small particles

We study scattering of light by wavelength-scale spherical, cubic, and spheroidal particles as well as clusters of spherical particles for equal-volume-sphere size parameters 4≤x≤10 and refractive indices 1.1≤m≤2.0. Such particles exhibit three specific features in the regime of backscattering: first, the intensity shows a backscattering peak; second, the degree of linear polarization for unpolarized incident light is negative; and, third, the depolarization ratio is double-lobed. We find that the overall characteristics of the scattering-matrix elements can be explained by an internal field composed of waves propagating in opposite directions near the particle perimeter and forming standing waves, as well as a wave propagating forward with the wavelength of the internal medium. When moving from the central axis of the particle toward its perimeter, the internal field changes from a forward-propagating wave with a wavelength dictated by the particle refractive index toward a standing wave with an apparent wavelength of the surrounding medium. The mapping of the internal field to the scattered far field is like an interference dial where rotation of the dial by a quarter of a wavelength on the particle perimeter results in a change from a destructive to constructive interference feature in the angular patterns (or vice versa). The dial is a manifestation of a well-known rule of thumb: the number of maxima or minima in the scattering-matrix elements is given by the size parameter. We explain the backscattering peak as deriving from the backward-propagating internal wave near the particle perimeter. Negative polarization follows from the spatial asymmetry of the internal fields: inside the particle, the fields are amplified near the central plane perpendicular to the polarization state of incident light, resulting in more pronounced interference effects for the perpendicular polarization than for the parallel polarization. The double-lobe feature in the depolarization results from the same internal-field structure with leading cross-polarized fields located slightly different from the copolarized fields. We discuss practical implications of these findings for the retrieval of particle sizes, shapes, and refractive indices from observations and laboratory experiments.