Light attenuation by disperse layers with a high concentration of oriented anisotropic spherical particles

An analysis is made of the applicability of Beer’s law to the calculation of coefficients of directed (coherent) transmittance of light-scattering media formed by oriented anisotropic spherical liquid-crystal droplets. It is shown on the basis of comparison with experimental data that the application of Beer’s law to a layer with a high concentration of anisotropic particles leads to large errors in the calculation of transmittance. The interference approximation, taking into account the interference of waves scattered by separate particles, leads to better agreement with the experiment than Beer’s law, which assumes a linear relation between the attenuation factor of a disperse medium and the particle concentration.     

Light scattering in a layer of correlatively arranged optically soft particles

The light scattering by an ensemble of monodisperse spatially correlated optically soft spherical particles is studied in the interference approximation. A model of the interaction of particles is proposed in which the spatial correlation between particles is determined by a radius R _c exceeding the particle radius R _p. The radial distribution function is calculated in the Percus-Yevick approximation for hard spheres of the radius R _c. To simulate the radiation scattering from an individual particle of the radius R _p, the Mie equations are used. It is shown that, in a medium of correlated small nonabsorbing particles of the radius R _c > R _p, an abnormal wavelength dependence of the refractive index is possible at a low volume concentration of particles. The results obtained explain some experimentally observed features of the scattering in sodium borosilicate glasses with a small concentration of scattering centers.     

Scattering by a plane-parallel layer with high concentration of optically soft particles

A method describing light propagation in a plane-parallel light-scattering layer with large concentration of homogeneous particles is developed. It is based on the radiative transfer equation and the doubling method. The interference approximation is used to take into account collective scattering effects. Spectral dependence of transmitted light for a layer of nonabsorbing optically soft particles with subwavelength-sized particles is investigated. At small volume concentration of the particles the weak spectral dependences of wave exponents for coherently transmitted and diffuse light are observed. It is shown that in a layer with large volume concentration of the subwavelength-sized particles the wave exponent can exceed considerably the value of four, which takes place for the Rayleigh particles. The dependence of wave exponents for coherently transmitted and diffuse light on the refractive index and concentration of particles is investigated in detail. Multiple scattering of light results in the reduction of the exponent. The quantitative results are presented and discussed. It is shown that there is a range of wavelengths where the negative values of the wave exponent at the regime of multiple scattering are implemented.     

Integral light-scattering indicatrix of optically soft spherical particles

The dependences of the angular distribution of the scattered energy on the particle size and refractive index and on the phase shift (Δ) were studied. It was shown, in particular, that in the hypsometric plane for Δ≥3, the light-scattering indicatrix F calculated by the Mie theory is determined by two factors: the Fraunhofer diffraction and geometrical optics. The possibility of measuring the refractive index from the experimental values of the aperture angle of a photodetector at fixed values of F was also considered.     

Light scattering on random dielectric layers

Scattering of light by a random stack of dielectric layers represents a one-dimensional scattering problem, where the scattered field is a three-dimensional vector field. We investigate the dependence of the scattering properties (band gaps and Anderson localization) on the wavelength, strength of randomness and relative angle of the incident wave. There is a characteristic angular dependence of Anderson localization for wavelengths close to the thickness of the layers. In particular, the localization length varies non-monotonously with the angle. In contrast to Anderson localization, absorptive layers do not have this characteristic angular dependence.     

Light scattering by dielectric particles with axial symmetry

A new method is suggested for solving the problem of scattering of a plane electromagnetic wave by dielectric particles with the axial symmetry. The method is based on the separation of fields into two parts: the axially symmetric part, which is independent of the angle of rotation, and the part that is not axially symmetric, which vanishes upon averaging over this angle. The scattering problem is solved separately for each of the parts. In the first case, scalar potentials related to the azimuthal components of electromagnetic fields are used, and in the second case, superpositions of the Debye potentials and vertical components of the Hertz vectors are used. The surface integral equations for these potentials are obtained. They are represented as expansions in the spherical wave functions. The infinite systems of linear algebraic equations are obtained for unknown expansion coefficients. Our calculations demonstrated the high efficiency of the new method.     

Light absorption and scattering by a photolayer with closely packed particles

Light absorption and scattering by weakly absorbing layers of close-packed fine-grained silver halide particles was studied. Absorption characteristics of an elementary volume and a photolayer were found to have a nonlinear and nonmonotonic dependence on the concentration. Qualitative specific features of this dependence in the range of medium values of volume concentrations from 0.4 to 0.8 were expressed by an empirical formula. The average cosine of the depth brightness diagram and the probability of photon survival Λ in a concentrated photolayer were calculated. The analysis of changes in Λ in a close-packed medium in a more general case, irrespective of the size and the degree of absorption of particles, was carried out. A conclusion was made concerning the character of changes in the scattering indicatrix of a photolayer caused by an increase of its density.     

Light scattering in photopolymerizing layers under laser irradiation

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 52, No. 2, pp. 215–221, February, 1990.     

Light scattering by axisymmetric multilayer particles

A new recursive algorithm for solving the problem of scattering a plane electromagnetic wave by axisymmetric dielectric multilayer particles is constructed. The approach that was proposed earlier and demonstrated for uniform axisymmetric particles is used. It has the following basic features: (1) the fields are represented in the form of a sum of two terms, one of which is independent of the azimuthal angle, whereas averaging of the second term over this angle gives zero; (2) the axisymmetric problem is solved by using the scalar potentials related to the azimuthal components of electromagnetic fields; and (3) the non-axisymmetric problem is solved by using the superposition of Debye potentials and vertical components of the magnetic and electric Hertz vectors. It is of principal importance for the solution proposed here that the scattering problem is formulated in the form of surface integral equations in these scalar potentials, which are represented in the form of expansions in wave spherical functions. Infinite systems of linear algebraic equations for unknown expansion coefficients are obtained, which are rather simple in structure. The reduced systems for multilayer particles have the same dimension as the systems for identical uniform particles. In the case of multilayer spherical particles, the algorithm gives an explicit solution to the problem, and the dependence on the radial spherical functions for the layers is specified in terms of the derivative of the logarithm (i.e., the ratio of the derivative to the function itself) and the ratio of the functions of neighboring layers. Numerical calculations demonstrated the high efficiency of the algorithm.     

随机取向群聚椭球粒子光散射特性研究

利用离散偶极子近似方法,考虑单元粒子之间的电磁相互作用,数值计算了随机取向的不同尺度参数、不同纵横比的群聚椭球粒子的缪勒矩阵元素,给出了各个缪勒矩阵元素的角分布曲线,探讨了随机取向的群聚椭球粒子的尺度参数、纵横比、基本粒子相对位置对其缪勒矩阵元素的影响。并将随机取向群聚椭球粒子的光散射特性与单个等效球形粒子的数值结果进行了比较。结果表明,随机取向群聚椭球粒子的光散射特性与等效球形粒子的光散射特性存在很大差别,基本粒子的形状越偏离球形,这种差别就越大; 随机取向群聚椭球粒子中椭球粒子的纵横比和相对位置对整个群聚粒子的缪勒矩阵元素存在不同程度的影响,并且此影响随着粒子尺度参数的增大而变得更加显著。     

随机取向群聚椭球粒子光散射特性研究

利用离散偶极子近似方法,考虑单元粒子之间的电磁相互作用,数值计算了随机取向的不同尺度参数、不同纵横比的群聚椭球粒子的缪勒矩阵元素,给出了各个缪勒矩阵元素的角分布曲线,探讨了随机取向的群聚椭球粒子的尺度参数、纵横比、基本粒子相对位置对其缪勒矩阵元素的影响。并将随机取向群聚椭球粒子的光散射特性与单个等效球形粒子的数值结果进行了比较。结果表明,随机取向群聚椭球粒子的光散射特性与等效球形粒子的光散射特性存在很大差别,基本粒子的形状越偏离球形,这种差别就越大; 随机取向群聚椭球粒子中椭球粒子的纵横比和相对位置对整个群聚粒子的缪勒矩阵元素存在不同程度的影响,并且此影响随着粒子尺度参数的增大而变得更加显著。     

Light scattering by an inhomogeneous spherical particle with intermediate layers

A model of a radially inhomogeneous multilayer spherical particle with a continuously varying refractive index in the intermediate layers between the shells of the particle and between the particle and the surroundings is proposed. Such a particle scatters light much like a dust particle with a rough and ragged surface of the layers, which is simulated with the help of the discrete dipole approximation method. For dust particles whose surface shape deviates from the spherical one, the refractive index profile and the behavior of the extinction Q _ext(x) and absorption Q _abs(x) efficiency factors with increasing thickness of the intermediate layers are studied. Properties of such particles in dependence on the number of layers are also studied. It is revealed that, as the number of shells increases, the order of the relative position of substances ceases to play a role, as is also the case for a multilayer spherical particle without intermediate layers. It is shown that, upon an increase in the number of shells at the same percentages of substances in the intermediate layers, the difference of the values of Q _ext(x) and Q _abs(x) from the corresponding values calculated with the model without intermediate layers decreases.     

Light scattering by groups of spherical particles

Light scattering by groups of spherical particles is considered. It is shown that the structure of the groups and their orientational distribution can be judged from the spectrum and polarization of the scattered light. Syktyvkar State University, 55, Oktyabr'skii Ave., Syktyvkar, 167001, Russia. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 2, pp. 228–231, March–April, 1997.     

Light Reflection and Transmission by layers with oriented spheroidal particles

On the basis of the numerical solution of the radiative transfer equation (RTE), the influence of non-sphericity of oriented spheroidal particles on radiation intensity formation in a layer with a multiple scattering regime is considered. For solving the RTE with characteristics depending on the propagation direction of the radiation beam, an algorithm is developed based on the method of layer doubling. Calculations are presented of angle correlations for intensities of radiation in a layer with Fresnel reflection on the boundaries, and reflection and transmission coefficients.     

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.     

Light scattering by needle-type and disk-type particles

A powerful tool to analyze light scattering by 3D arbitrary-shaped homogeneous or inhomogeneous obstacles located in free space is based on volume integral equation. In this paper we apply a weak form of volume integral equation to simulate light scattering by needle- and disk-type particles such as straight and curved cylinders, cylindrical plate and hexagonal prism with high aspect ratio and low and high values of refractive indexes. For problems where discrete sources method could be applied, we calculated differential scattering cross-section using both methods and got excellent agreement in results.