Light scattering by aggregates of varying porosity and the opposition phenomena observed in the low-albedo particulate media

The rule that the opposition phenomena in brightness and linear polarization observed in many regolith surfaces usually accompany each other is violated in the cases of very dark asteroids and particulate samples: practically no nonlinear surge of brightness to opposition is observed while the branch of negative polarization at small phase angles exists. To explain this fact, we model the light scattering by particulate media with ensembles of spherical particles (with size comparable to the wavelength) of varying packing density and refractive index. The superposition T-matrix method is used. The increase in the absorption and/or packing density diminishes the amplitude of the brightness opposition peak, and its profile becomes wider. The influence on the branch of negative polarization is more complex and depends on the relation between the size parameters of the constituents, the refractive index, and the porosity. However, the feature common to all considered cases is that the negative branch changes its shape and the polarization minimum moves to the inversion point. This behavior radically differs from that observed in nonabsorbing ensembles of particles and reflects the fact that the efficiency of the coherent backscattering, which mainly determines these characteristics in nonabsorbing ensembles (to the packing density of about 30%), decreases. Moreover, since the angular profiles are not simply damped, but the polarization minimum changes its angular position, we may conclude that the near-field interaction of the constituents becomes important: the shielding of particles by each other eliminates many constituents from the scattering and the near-field effects promote the negative polarization and smooth the backscattering brightness surge. Due to this, when the packing density exceeds 10-20%, the opposition phenomena in absorbing ensembles are caused not only by the coherent backscattering, and situations, when the opposition brightness surge is practically suppressed, but the negative branch of polarization still survives, are possible. This may explain the fact that the dark regolith surfaces show no brightness opposition effect, but produce the branch of negative polarization with the minimum shifted from opposition.     

Interference effects in backscattering of light by a layer of a discrete random medium

Multiple backscattering of light by a layer of a discrete random medium is considered. A brief derivation of equations for describing the coherent and incoherent components of scattered light is presented. These equations are solved numerically in the approximation of doubled scattering of light by a semi-infinite medium of spherical scatterers having a size comparable with the wavelength in order to study the effect of the properties of particles on the angular dependence of interference effects. Calculations show that the half-width of the interference peak decreases upon an increase in lateral scattering by particles and that the degree of polarization has a complex angular dependence on the properties of the particles. For an optically thin layer of the medium, the relations defining the interference peak half-width and the scattering angle upon extreme linear polarization as functions of the effective refractive index are given.     

Local fields close to the surface of nanoparticles and aggregates of nanoparticles

A refined discussion of the near-field scattering of spherical nanoparticles and the electromagnetic fields close to the particle surface is given. New results for the dependence on the distance from the surface and the angular distribution of the scattered light in the near-field are given. It will be shown that the radial component of the electric field leads to striking differences in the phase functions in the near-field and the far-field. Exemplary computations are presented for Ag and Au particles with different size. In a second part the discussion is extended to assemblies of spherical Ag and Au nanoparticles. It will be shown that large near-fields at wavelengths commonly used in SERS experiments are obtained for aggregates. In the near-field scattering intensity “hot spots” mark regions between particles in the aggregate where the near-field is particularly high. Received: 4 May 2001 / Revised version: 20 July 2001 / Published online: 19 September 2001     

Light-scattering properties of fractal aggregates: numerical calculations by a superposition technique and the discrete-dipole approximation

Dust particles in space often grow by mutual collisions and appear to be an agglomeration of individual grains, the morphology of which can be described by the concept of fractals. In this paper, we study light scattering by fractal aggregates of identical spheres (monomers) using the superposition technique incorporated into the T-matrix method where the orientationally averaged scattering matrix is analytically obtained. We also apply the discrete-dipole approximation, in which the dipole polarizability of spherical monomers is determined by the first term of the scattering coefficients in the Mie theory. Two cases of the ballistic aggregation process (particle–cluster and cluster–cluster aggregations) are considered to model fractal aggregates consisting of silicate or carbon material. The dependences of light-scattering properties on the monomer sizes, aggregate structures and material compositions are intensively investigated. The light-scattering properties of the fractal aggregates strongly depend on the size parameters of the monomers. The difference in the scattering function between the particle–cluster and cluster–cluster aggregates can be seen in the case of monomers much smaller than the wavelength of incident radiation. When the size parameter of monomers exceeds unity, the material composition of the monomers influences the light-scattering properties of the aggregates, but different morphologies result in similar scattering and polarization patterns. We show that silicate aggregates consisting of submicron-sized monomers, irrespective of the aggregate size and morphology, produce a backscattering enhancement and a negative polarization observed for dust in the solar system.     

Light scattering by coated Gaussian and aggregate particles

Light scattering by nonspherical and inhomogeneous small particles is studied by varying particle shapes, sizes, and compositions. We introduce an efficient tool for deforming particle shape and composition by adding a coating on an initial particle. This concave-hull transformation is applied to wavelength-scale Gaussian and aggregate particles, and the differences in the optical properties of the coated particles are compared to those of the uncoated geometries. The light-scattering computations are performed using the discrete-dipole approximation method which allows for internal inhomogeneity and irregular particle shapes. The results are analyzed concentrating on the intensity of the scattered light, the degree of linear polarization for unpolarized incident light, and the depolarization ratio. Polarization results yield the most significant differences and, moreover, coated aggregates are observed to produce net positive polarization, whereas it is negative for the Gaussian particles, also resembling the polarization of a spherical particle. As for the depolarization ratio, an intriguing double-lobe feature is observed near the backscattering direction for both particle geometries regardless of size, shape, and composition. The double-lobe maxima and minima generally coincide with those of the intensity and 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.     

Coherent backscattering of light by a layer of discrete random medium

We consider the problem of backscattering of light by a layer of discrete random medium illuminated by an obliquely incident plane electromagnetic wave. The multiply scattered reflected radiation is assumed to consist of incoherent and coherent parts, the coherent part being caused by the interference of multiply scattered waves. Formulas describing the characteristics of the reflected radiation are derived assuming that the scattering particles are spherical. The formula for the incoherent contribution reproduces the standard vector radiative transfer equation. The interference contribution is expressed in terms of a system of Fredholm integral equations with kernels containing Bessel functions. The special case of the backscattering direction is considered in detail. It is shown that the angular width of the backscattering interference peak depends on the polar angle of the incident wave and on the azimuth angle of the reflection direction.     

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.     

Study of the angular and polarization structures of radiation scattered by monolayers of metal-containing nanostructures during their oxidation

The angular and polarization scattering characteristics of copper, nickel, and palladium monolayers composed of quasi-monodisperse nanograins 2–5 nm in size, as well as aggregates and chains of these nanograins, have been investigated during oxidation of monolayers with different packing densities of particles in a monolayer. On the basis of the experimental data, a number of integral scattering characteristics of monolayers of different metals and the angular dependences of the scattering matrix elements for laser wavelengths in the visible range have been calculated and analyzed. It is demonstrated that the polarization properties of the angular structure and the scattering matrix elements depend strongly on the degree of order of the structures and the presence of chains in monolayers of metal-containing nanostructures. Oxidation of nanostructures leads to the chaotic distribution of metal cores in a nanostructure. It is shown that scattering from nanostructures is more sensitive to oxidation in comparison with absorption. A nonlinear concentration dependence of scattering intensity was observed for copper nanostructures on a quartz substrate near the plasma resonance (at 633 nm) of all structures under study and at 440 nm for nanostructures on a silicon substrate (i.e., at the wavelength corresponding to strong absorption in silicon).     

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.     

表面分形球、柱的光散射

分形和分维是近些年才兴起的一门处理复杂事物的新方法￣［１］。本文主要研究具有表面分形的球、柱的光散射特征。我们首先利用几何光学近似研究了一种表面满足自仿射原理的分形均匀球的散射，其散射特性与分维存在一定的关系。我们还利用微扰法讨论了表面具有沟槽的分形柱的光散射的分形特征。     

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.     

Evanescent wave scattering by aggregates of clusters – application to optical near-field microscopy

Extended Mie-theory is used to investigate scattering and extinction of evanescent waves by aggregates of clusters. In an application to apertureless near-field optical microscopy involving total internal reflection at the surface substrate–air, the variation of the scattered power is calculated when a silicon particle is scanned across single clusters or aggregates of clusters in the evanescent field. Metallic, dielectric, and semiconducting particles are taken into consideration, and the dependence on sizes, materials, and the wavelength is discussed. Received: 27 August 1999 / Revised version: 8 November 1999 / Published online: 1 March 2000     

Reflection of waves from a strong scatterer buried in a random medium

Reflection of waves from a mirror covered by a random layer of isotropic, absorbing scatterers is studied and the angular distribution of the scattered intensity is calculated both analytically and numerically. It is shown that backscattering enhancement as well as an enhancement of the incoherent signal in the specular direction take place even in the singly scattered random field. The dependence of the retroreflected intensity is shown to be a non-monotonic function of the depth of the mirror, with a maximum at a depth of the order of the scattering mean free path. Possibilities for employing the results obtained to detect buried strong scatterers and to retrieve parameters of the random media are discussed. In particular, it is shown that in the case of strong absorption the reflecting plane manifests itself by the presence of a peak in the retroreflected intensity which is missing from the scattering diagram of a free-standing or an infinitely thick random layer.     

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.     

Influence of the boundary of a medium on the coherent backscattering of light

The multiple scattering of light from an inhomogeneous medium occupying a half-space is investigated on the basis of the Bethe-Salpeter equation. The latter is integrated over the spatial variables to obtain an identity having the significance of the energy balance of the incident and scattered radiations. This relation is then used to derive a length parameter that plays the role of the Milne interpolation length. The use of this parameter in the method of mirror images for describing the shape of the coherent backscattering peak in isotropic single scattering yields results in almost perfect agreement with the predictions of the Milne theory. The application of the given approach for an anisotropic single-scattering diagram yields quantitative agreement of the theory with experiments on the angular dependence of coherent backscattering. The new approach is generalized to an electromagnetic (vector) field, and backscattering polarization effects are investigated. Zh. éksp. Teor. Fiz. 116, 1912–1928 (December 1999)     

Coherent backscattering under conditions of pulsed radiation trapping

Coherent backscattering of pulsed radiation emitted by optically dense atomic ensembles is considered. The diagrammatic technique is used for deriving analytic expressions for correlation functions of scattered light, which make it possible to take into account all main factors affecting the dynamics of the process, including the hyperfine and Zeeman structure of the ground and first excited states of atoms, polarization of probe radiation, the actual shape and size of an atomic cloud, its spatial inhomogeneity, motion of atoms, and angular-momentum polarization of atoms. On the basis of these relations, the time dependence of the total intensity and the dependence of enhancement factor of backscattered light on the pulse duration, type of polarization of the polarization system of observation, optical thickness of the scattering medium, and the carrier frequency of the pulse are investigated. The calculations are performed for an ensemble of rubidium-85 atoms cooled in magnetooptical traps.     

The effect of multiple scattering in disperse media on polarization characteristics of scattered light

The effect of scattering of different multiplicity on polarization characteristics of scattered light is studied by the Monte Carlo computer simulation technique. The scattering multiplicity distribution versus the direction of scattering and dimensions of the scattering system is obtained for monodisperse systems of spherical particles of different size. The angular dependences of the elements of the light-scattering matrix (LSM) are calculated. It is shown that in a system of spherical particles, specific features of the LSM structure associated with multiple scattering have much in common with similar features of the LSM in systems of nonspherical particles under conditions of single scattering. The angular dependences of the degree of depolarization of the scattered light are studied.     

Influence of Electric and Magnetic Fields on Interference Effects upon Multiple Light Scattering in Cold Atomic Ensembles

The correlation functions of the electromagnetic radiation scattered by an ensemble of atoms cooled to sub-Doppler temperatures and placed in an external static electric or magnetic field have been calculated by the diagram technique. Based on the derived relations, we have studied in detail the effect of coherent backscattering (CBS) of light. We have calculated the enhancement factor for CBS and analyzed its polarization and spectral dependences. We show that external fields affect the nature of multiple light scattering in an atomic ensemble, in particular, the character of interference upon such scattering, by leading to its optical anisotropy and related birefringence and dichroism. This, in turn, affects all of the observed CBS characteristics.