Photoanisotropic properties of luminescence media for polarization holography based on new-type dyes

The size and shape distributions of particles of a dispersive medium are retrieved from measurements of the scattering matrix for aqueous suspensions of copper and zinc oxides by solving the optimization problem for the sum of the squared deviations of the experimental values of matrix elements and their values calculated using the model of spheroidal scatterers. It is shown that for dispersive media with particles of irregular shapes and with sizes corresponding to the size parameter of 0.1–2, the retrieved distribution has a distortion expressed in an increased fraction of smaller sized particles.     

Scattering properties of aqueous suspensions with absorbing dispersed phase

Scattering matrices of aqueous suspensions of copper oxide and graphite the particles of which are characterized by strong absorption at a wavelength of 0.63 μm have been measured in the scattering angle range of 10°–155°. The results of the measurements are compared with calculation data for axially symmetric scatterers (ellipsoids of revolution and cylinders). It is shown that, if the size parameter equals 4–6, even under conditions of strong radiation absorption by particles of the dispersive medium, deviation of their shape from axial symmetry has an effect on the scattering properties of the medium.     

Application limitedness of the model of spheroidal scatterers for describing scattering properties of titanium dioxide

The results of measurements of the scattering matrix of an aqueous suspension of titanium dioxide at a wavelength of 0.63 μm in the scattering angle range of 10°–150° are presented. The results of the measurements are compared with calculation data for scatterers having the shape of prolate ellipsoids. It is shown that, even when the size parameter equals 4, the experimental and calculated values of the matrix elements f ₂₂ and f ₁₂ significantly differ, which is caused by a complex form of TiO₂ particles, and that the determination of the parameters of the distribution of TiO₂ suspension particles in the interpretation of the measurement data in the context of the considered model is possible with an error of 27% in the effective size and 16% in the distribution width.     

Effect of the uncertainty of the shape of a distribution on its parameters retrieval using the scattering matrix of quartz suspension

Scattering matrices of an aqueous suspension of quartz were measured at a wavelength of 0.63 μm in the scattering angle range of 10°–150°. The angular dependences of matrix elements were measured with a laser polarimeter the optical scheme of which contained two electro-optical modulators. The results of measurements were compared with the data of calculation for scatterers having the shape of prolate ellipsoids. It was shown that, under conditions of wide distribution of particles by size and at a dimensional parameter value of 2.1, the uncertainty of the shape of the distribution leads to an increase in the error of the retrieval of the parameters of the suspension particle distribution.     

The correctness of restoring the parameters of the particle distribution of a zinc oxide suspension using the model of spherically symmetric scatterers

We present the results of measuring the scattering matrix of a water suspension of zinc oxide at a wavelength of 0.63 μm in the range of scattering angles of 15–150°. The angle dependences of matrix elements were measured using a laser polarimeter, the optical scheme of which contained two electro-optical modulators. We compare the measurement results with calculation data for spherically symmetric scatterers. We demonstrate that at a dimensional parameter value of 1.8, in interpreting the data using the model of spherically symmetric scatterers, it is possible to determine the parameters of particle distribution of a zinc oxide suspension with an error of 30%.     

T-matrix method for electromagnetic scattering from scatterers with complex structure

We describe a T-matrix program for light scattering calculations from particles with complex structure. The code treats the cases of homogeneous, layered and composite scatterers. These results are combined with basic results concerning the scattering by inhomogeneous scatterers and aggregates to apply to more general types of scatterers. Some numerical simulations are presented.     

On scattering of light by small axially symmetric particles

Light scattering by small dielectric particles of an arbitrary axially symmetric shape is analyzed. A simple approximate expression that governs the polarizability of the particle is found under the assumption of field homogeneity inside of these particles. The expression includes four relatively simple one-dimensional integrals that can be calculated analytically for some types of particles (except for spheroids). A comparison with the numerical data obtained for various Chebyshev particles and finite cylinders showed that the obtained approximation yields acceptable results, even when the shape of scatterers is significantly different from spheroidal. For spheroids, our approximation coincides with the Rayleigh one.     

Attenuation and scattering of light by a system of chaotically oriented axially symmetric particles: Analytical averaging in the modified <Emphasis Type="Italic">T</Emphasis>-matrix method

A procedure for analytical averaging of the attenuation and scattering cross sections for systems of chaotically oriented axially symmetric particles was developed for the first time within the framework of the modified T-matrix method and the method of separation of variables for spheroids. These approaches essentially complement each other: one is applicable to axially symmetric scatterers of different shape but is inefficient if the ratio of the maximum to the minimum size of the particles exceeds 3–5; the other is applicable only to spheroids, but the ratio of the major semiaxis to the minor one can be considerable, for example, 100 and larger.     

随机取向双层椭球粒子偏振散射特性研究

基于T矩阵方法,给出了随机取向、轴对称、含核椭球粒子的散射计算方法.散射体的核和外壳均可为非球形粒子,整个粒子具有轴对称性.以含核椭球粒子为模型,计算了含有吸收性内核(黑炭,black carbon)的水凝物气溶胶的散射特性,分析了核的大小、形状对消光系数、散射系数、吸收系数、不对称因子、单次散射反照率以及Muller矩阵等的影响. 关键词： 光散射 T矩阵 Muller矩阵 椭球粒子     

Multiple scattering of light by a layer of discrete random medium: backscattering

The problem of multiple scattering of light by a layer of discrete random medium is considered. The medium is supposed to be rarefied with scatterers randomly positioned in the layer. Backscattering of light incident normal to the plane of the layer is considered. The scattering matrix is presented as a sum of three matrices, one of them corresponding to incoherent scattering of light and difference of the other two matrices describing coherent scattering. Equations for the calculation of these matrices are given.     

On optical properties of nonspherical inhomogeneous particles

To solve the problem of light scattering by multilayer scatterers of an arbitrary axisymmetric shape, a separation of variables method that involves special scalar potentials and their expansions in spherical functions is developed. The approach is shown to yield highly exact results even for particles that have 100 layers or more. A graphic library that illustrates the optical properties of layered and homogeneous (with an effective refractive index) spheroids, spheres, and Chebyshev particles of various shapes and sizes (about 650 figures) is created and is put on the Internet. It is noted that the linear polarization of radiation transmitted forward through a polydisperse medium containing partially oriented nonspherical porous particles strongly depends on the structure of scatterers. It is shown that the difference between the degrees of polarization of layered and corresponding homogeneous scatterers can exceed 200–300%.     

A review of the light scattering properties of cirrus

In this review paper the light scattering properties of naturally occurring ice crystals that are found in cirrus are discussed. Cirrus, also referred to as ice crystal clouds, due to their cold temperatures, consist of a variety of non-spherical ice particles which may take on a variety of geometrical forms. These geometrical forms can range from symmetric pristine hexagonal ice columns and plates, single bullets and bullet-rosettes to non-symmetric aggregates of these shapes. These aggregates may also consist of highly complex three-dimensional structures, which may themselves consist of symmetric components. Not only does cirrus consist of a wide variety of shapes but also sizes too, and these sizes can range between <10 μm to over 1 cm. With such a variety of shapes and sizes predicting the light scattering properties from such an ensemble of ice crystals is the current challenge. This challenge is important to overcome since with cirrus being so high in the Earth's atmosphere it has an important influence on the Earth-atmosphere radiation balance and consequently adds to the uncertainty of predicting climate change. This is why it is important to represent as accurately as possible the single-scattering properties of cirrus ice crystals within general circulation models so that uncertainties in climate change predictions can be reduced.In this review paper the current measurements and observations of ice crystal size and shape are discussed and how these observations relate to current ice crystal models is reviewed. The light scattering properties of the current ice crystal models are also discussed and it is shown how space-based instruments may be used to test these models. The need for particular microphysical and space-based measurements is stressed in order to further constrain ice crystal light scattering models.     

Polarimetric weak-localization effect in scattering of natural light in the region of small phase angles

Results of laboratory measurements and interpretations of the polarimetric effect of weak localization (negative polarization) appearing under scattering of natural light by a dark ultradisperse surface (soot with albedo of 2.5%) are presented. The measurements were carried out in red light in a range of phase angles of 0.2°–4.2°. It was revealed that the soot, despite the low albedo, shows the polarimetric weak-localization effect inherent in bright surfaces such as the surface formed by smoked MgO. The results of measurements are interpreted using numerical simulation of multiple light scattering in a medium consisting of particles whose characteristics are close to those observed for soot. As the result of simulation, it was found that the scattering with the multiplicity exceeding two can give rise to a negative polarization branch, which becomes narrower with increasing scattering order. For the case of soot, four orders of scattering is sufficient to describe the observed polarimetric effect of weak localization with a necessary accuracy.     

The shape influence on the overall single scattering properties of a sample in random orientation

In order to identify the type of scattering profile that corresponds to some specific shapes, we have performed calculations of some scattering properties for those shapes with a fixed size distribution. Aggregates of different numbers of spheres have been used to fit the laboratory measurements of fly ashes. The results for other shapes, such as rectangular prisms with different axial proportions, particles made of joined cubes, and particles with different fluffiness, are also shown. From all these calculations, it is concluded that the size-averaged scattering matrix elements resembles Rayleigh features, for the size distribution stopping at , when either the number of spheres or cubes of the aggregates is increased, the shape becomes flatter or the particles become fluffier. We also show the effect of the refractive index on the Q_sca vs. X curve in the case of strongly absorbing particles. A tendency to reach the geometric optic regime is observed instead of the Rayleigh regime using the same size distribution.     

Application of the Model of Spheroidal Scatterers for Determination of Particles Sizes of Aqueous Suspensions by the Laser-Polarimetry and Dynamic-Light-Scattering Methods

Results of measurements of particle sizes of a dispersed medium by the methods of laser polarimetry and dynamic light scattering are presented for water suspensions of ZnO, CuO, TiO₂, and BaTiO₃ with particles of irregular shape. When using the laser-polarimetry method, the particle-size distributions within the framework of the spheroidal-scatterer model are reconstructed. The same model was used to correct data obtained by the method of dynamic light scattering. The data obtained are compared with results obtained by electron microscopy. It is shown that, at values of the size parameter of 2–5, correction of the results of measurements obtained by the dynamic-light-scattering method makes it possible to reduce the error in determining the average particle size by this method to no more than 11%.     

On the low-frequency sound scattering in a moving microinhomogeneous medium

The Rayleigh law that governs low-frequency sound attenuation due to the scattering by inhomogeneities in a microinhomogeneous medium is generalized to the case of particles moving in a flow or falling under gravity. Corrections to the scattering’s cross section that adjust the Rayleigh law to the case of a potential flow around inhomogeneities are calculated. It is shown that, when microinhomogeneities are moving in a viscous medium, the characteristics of discrete scatterers may considerably deviate from the Rayleigh law. Based on the data on the velocity and size distribution of falling drops of water in air, refinements are proposed for the laws of low-frequency sound scattering by rain.     

Using simple particle shapes to model the Stokes scattering matrix of ensembles of wavelength-sized particles with complex shapes: possibilities and limitations

We investigate to what extent the full Stokes scattering matrix of an ensemble of wavelength-sized particles with complex shapes can be modeled by employing an ensemble of simple model shapes, such as spheres, spheroids, and circular cylinders. We also examine to what extent such a simple-shape particle model can be used to retrieve meaningful shape information about the complex-shaped particle ensemble. More specifically, we compute the Stokes scattering matrix for ensembles of randomly oriented particles having several polyhedral prism geometries of different sizes and shape parameters. These ensembles serve as proxies for size-shape mixtures of particles containing several different shapes of higher geometrical complexity than the simple-shaped model particles we employ. We find that the phase function of the complex-shaped particle ensemble can be accurately modeled with a size distribution of volume-equivalent spheres. The diagonal elements of the scattering matrix are accurately reproduced with a size-shape mixture of spheroids. A model based on circular cylinders accurately fits the full scattering matrix including the off-diagonal elements. However, the modeling results provide us with only a rough estimate of the effective shape parameter of the complex-shaped particle ensemble to be modeled. They do not allow us to infer detailed information about the shape distribution of the complex-shaped particle ensemble.     

Zur Quantentheorie der Transportprozesse im Magnetfeld. II

Applying Kubo's formulae and damping theoretical arguments the electric, thermoelectric and thermal transport coefficients for a system of free and independent electrons and fixed scatterers in the presence of an external magnetic field are calculated. Assumingδ-type scatterers it is shown that in the quantum regionkT?ω?ζ the Wiedemann-Franz law holds for the oscillating symmetric conductivities, whereas in the case of the antisymmetric ones quantum mechanical deviations from this law occur. For strong magnetic fields and arbitrary scattering potential the symmetric transversal transport coefficients can be expressed by Titeica type formulae.     

Light scattering by dielectric particles with axial symmetry: II

A new method is developed for calculating optical characteristics of axially symmetric particles. Electromagnetic fields are separated into two (axisymmetric and non-axisymmetric) parts. The light scattering problem is formed in the integral form and solved independently for each of the parts by using specially chosen scalar potentials. The potentials are expanded into series in spherical wave functions, and the expansion coefficients are calculated from solving the infinite systems of linear algebraic equations. The applicability of the proposed method for solving the problem of light scattering by Chebyshev particles, spheroids, and finite circular cylinders is briefly discussed, and some results of calculations performed for these particles are presented.     

Light scattering by multilayer axially symmetric particles

An exact solution to the problem of light scattering by multilayer axially symmetric particles is derived and some aspects of its computer-aided implementation are discussed. The main specific features of the solution are (i) separation of the incident, scattered, and internal fields into two parts and special selection of the scalar potentials for each of them; (ii) expansion of the potentials in terms of spherical wave functions; (iii) formulation of the problem in the form of surface integral equations; and (iv) solution of the reduced systems of the linear algebraic equations for the coefficients of the potential expansions. Mathematical justification of the solution is discussed, which is formulated in the recursive and nonrecursive form (for the T-matrix). The developed computer program has shown that the proposed approach makes it possible to consider axially symmetric particles with essentially different internal structures (i.e., with a spherical core, oblate spheroidal shell, or prolate spheroidal intermediate layer). The results of calculations of the optical properties of the multilayer nonspherical particles are presented and discussed.