Low-coherence light-scattering calculations for polydisperse size distributions

The calculation of angular light-scattering distributions is considered for low-coherence light incident on a polydisperse particle size distribution of scatterers. As low-coherence light is now commonly used in interferometry schemes when applied to biomedical imaging, the difference between detecting scattered intensity and interferometrically detecting the scattered field is examined. An expression is derived that allows the presence of multiple wavelengths lambda and particle sizes d to be described by a single distribution in the size parameter x = pi d/lambda, which simplifies numerical calculations. The applicability of this expression is examined numerically.     

Effects of polydispersity of chainlike aggregates on light-scattering properties and data inversion

A systematic evaluation of the effects of polydispersity of chainlike aggregates in terms of primary particle number density and size on the scattering quantities and data inversion is presented. For aggregates with refractive index in the range absolute value(m-1) = 0.8-1.2, average size parameter x < 0.40, and primary particle number Np < 20, it is shown that the effects of polydispersity of primary particle size on the light-scattering quantities are much stronger than the polydispersity of the number of primary particles per aggregate. For aggregates with polydisperse primary particle size, the assumption of monodispersity tends to underestimate the real and imaginary parts of the refractive index and the number of primary particles. Specifically, for values of the distribution width sigma greater than 0.10, the effect of polydispersity of the size of primary particles must be considered in the data inversion schemes. Furthermore, in the same range of values for the refractive index, particle size parameter, and primary particle number, the assumption of monodispersity for aggregates with polydisperse particle number tends to underestimate the value of the real part of the refractive index and overestimate the value of the imaginary part of the refractive index and primary particle size. However, for values of the distribution width sigma less than 0.60, the effects of polydispersity of primary particle number can be neglected. In addition, the suitable pairing sets of the measured scattering quantities for data inversion are presented and discussed.     

Discrete-dipole-approximation-based light-scattering calculations for particles with a real refractive index smaller than unity

To assess the efficiency and accuracy of light-scattering calculations based on the discrete dipole approximation (DDA) for particles with a real relative refractive index smaller than unity, differential scattering cross sections and scattering efficiency factors were calculated for spherical particles. We performed the calculations for oxide particles and voids embedded in glass and silicon, using the exact scattering theory (Mie scattering) and the DDA. A comparison of the results shows that the DDA is applicable in the above refractive-index regime, and the conditions under which DDA-based calculations can provide scattering data with good accuracy are discussed.     

Calculation of diffusion analogy constant for aggregates of regular packings of uniform spheres

For the diffusion model which gives a probabilistic prediction of stresses in a half-space of granular material subjected to normal surface loads, the diffusion analogy constant is calculated exactly assuming a granular material consisting of randomly-oriented zones of regularly packed uniform spheres. The most open (simple cubic) and the most dense (face-centered cubic) packings are considered and the values obtained are very close to those earlier obtained using an “approximate” cone method.     

Calculation of the near field of aggregates of arbitrary spheres

We study a numerical method of calculating the near field of ensembles of arbitrary spheres by extending Mie theory. A recursive method based on the orders of scattering is presented. This method represents a concise way to calculate the near field of aggregates of any number of arbitrary spheres, Numerical examples are given to show its validity.     

Experimental and theoretical results of light scattering by aggregates of spheres

We present laboratory microwave scattering measurements for complex amplitude scattering matrices of three aggregates of 2, 8, and 27 identical spheres and compare them with theoretical predictions. Electromagnetic multiparticle-scattering calculations involve the determination of a large number of vector translation coefficients introduced by the addition theorems for vector spherical harmonics. For one of the two classes of vector translation coefficients there is an overall-sign discrepancy between two groups of formulations that exist in the literature. We compare our experimental data with the theoretical results from scattering calculations using the two different sets of formulas for computation of the translation coefficients. This comparison of experiment with theory reveals that Cruzan's original research on the vector addition theorems [Q. Appl. Math. 20, 33-40 (1962)] is correct, although many authors believe that Cruzan's formulation contains an overall-sign error.     

Mean-field approximation of Mie scattering by fractal aggregates of identical spheres

We apply the recent exact theory of multiple electromagnetic scattering by sphere aggregates to statistically isotropic finite fractal clusters of identical spheres. In the mean-field approximation the usual Mie expansion of the scattered wave is shown to be still valid, with renormalized Mie coefficients as the multipolar terms. We give an efficient method of computing these coefficients, and we compare this mean-field approach with exact results for silica aggregates of fractal dimension 2.     

Observations and calculations of light scattering from clusters of spheres

Two-dimensional angular optical scattering (TAOS) patterns from clusters of polystyrene latex spheres are measured in the near-forward and near-backward directions. In both cases, the scattering pattern contains a rich and complicated structure that is the result of the interaction and interference of light among the primary particles. Calculations are made for aggregates that are similar to those generated experimentally and also demonstrate the rich structure in the scattering pattern. A comparison of the experimental and theoretical TAOS patterns gives good qualitative agreement.     

Integral light-scattering and absorption characteristics of large, nonspherical particles

We obtain and analyze simple analytical formulas for asymmetry parameters and absorption cross sections of large, nonspherical particles. The formulas are based on the asymptotic properties of these characteristics at strong and weak absorption of radiation inside particles. The absorption cross section depends on parameter phi, which determines the value of the light-absorption cross section for weakly absorbing particles. It is larger for nonspherical scatterers. The asymmetry parameter depends on two parameters. The first is the asymmetry parameter g(0) of a nonspherical, transparent particle with the same shape as an absorbing one. The second parameter, beta, determines the strength of the influence of light absorption on the value of the asymmetry parameter. Parameter beta is larger for nonspherical particles. One can find these three parameters (phi, g(0), and beta) using a ray-tracing code (RTC) for nonabsorbing and weakly absorbing particles. The RTC can then be used to check the accuracy of the equations at any absorption for hexagonal cylinders and spheroids. It is found that the error of computing the absorption cross section and 1 - g (g is the asymmetry parameter) is less than 20% at the refractive index of particles n = 1.333. Values for asymmetry parameters of large, nonabsorbing, spheroidal particles with different aspect ratios are tabulated for the first time to our knowledge. They do not depend on the size of particles and can serve as an independent check of the accuracy of T-matrix codes for large parameters.     

Self-consistent finite-difference electronic structure calculations for large systems

An efficient and flexible self-consistent method of solving the Schrödinger equation for large systems is presented. This uses a finite-difference method, with the atomic cores replaced by an embedding potential. The resulting Hamiltonian matrix is sparse and can be diagonalised using the Lanczos algorithm, with computer time proportional to the system size. This all-electron method uses a small muffin tin radius and allows for the full potential outside the muffin tin. Within the self-consistent local density functional framework, Poisson's equation is solved using the multigrid method. Results for fcc copper are shown.     

Geometrical-optics code for computing the optical properties of large dielectric spheres

Absorption of electromagnetic radiation by absorptive dielectric spheres such as snow grains in the near-infrared part of the solar spectrum cannot be neglected when radiative properties of snow are computed. Thus a new, to our knowledge, geometrical-optics code is developed to compute scattering and absorption cross sections of large dielectric particles of arbitrary complex refractive index. The number of internal reflections and transmissions are truncated on the basis of the ratio of the irradiance incident at the nth interface to the irradiance incident at the first interface for a specific optical ray. Thus the truncation number is a function of the angle of incidence. Phase functions for both near- and far-field absorption and scattering of electromagnetic radiation are calculated directly at any desired scattering angle by using a hybrid algorithm based on the bisection and Newton-Raphson methods. With these methods a large sphere's absorption and scattering properties of light can be calculated for any wavelength from the ultraviolet to the microwave regions. Assuming that large snow meltclusters (1-cm order), observed ubiquitously in the snow cover during summer, can be characterized as spheres, one may compute absorption and scattering efficiencies and the scattering phase function on the basis of this geometrical-optics method. A geometrical-optics method for sphere (GOMsphere) code is developed and tested against Wiscombe's Mie scattering code (MIE0) and a Monte Carlo code for a range of size parameters. GOMsphere can be combined with MIE0 to calculate the single-scattering properties of dielectric spheres of any size.     

Simple preparation of monodisperse,large gold spheres

In this letter, I demonstrate a simple preparative route to monodispersed, large gold spheres (∼450 nm in diameter) by directly mixing a HAuCl₄ aqueous solution and an ortho-phenylenediamine (OPD) tetrahydrofuran (THF) solution at room temperature.     

Experiments on light scattering and extinction by small, micrometer-sized aggregates of spheres

We performed experiments to study the extinction, scattering, and polarization of light by ensembles of fractal dust aggregates that consist of spherical monomers large compared with the wavelength. Extinction was measured on a homogeneous dust cloud. Scattering and polarization were measured on a collimated dust beam. We found that polarization and extinction are determined only by a small size scale that is defined by a monomer and its closest neighbors in an aggregate. The scattering function might also depend on the overall size of the aggregate or the total number of monomers in an aggregate.     

Using spectral low rank preconditioners for large electromagnetic calculations

For solving large dense complex linear systems that arise in electromagnetic calculations, we perform experiments using a general purpose spectral low rank update preconditioner in the context of the GMRES method preconditioned by an approximate inverse preconditioner. The goal of the spectral preconditioner is to improve the convergence properties by shifting by one the smallest eigenvalues of the original preconditioned system. Numerical experiments on parallel distributed memory computers are presented to illustrate the efficiency of this technique on large and challenging real‐life industrial problems. Copyright © 2004 John Wiley & Sons, Ltd.     

Efficient rapid microwave-assisted route to synthesize InP micrometer hollow spheres

The efficiencies of two methods of synthesizing InP micro-scale hollow spheres are compared via the analogous solution-liquid-solid (ASLS) growth mechanism, either through a traditional solvothermal procedure, or via a microwave-assisted method. Scanning electronic microscopy (SEM) images show that most of the as-grown samples are micrometer hollow spheres, which indicates the efficiency of both methods. For traditional solvothermal route, long time (10 h) is necessary to obtain the desired samples, however, for the microwave-assisted route, 30 min is enough for hollow spherical products. An optimal choice of microwave irradiating time allows reducing the reaction time from hours to minutes. The proposed ASLS growth mechanism has also been discussed in detail.     

Efficient force calculations based on continuum sensitivity analysis

Using continuum design sensitivity analysis (CDSA), in conjunction with the virtual work principle, equations have been derived for calculating forces without the need to solve the adjoint system. The resultant expressions are similar to the Maxwell stress tensor, but have the important advantage of the integration taking place on the surface of material rather than in the air outside. Implementation of the scheme leads to efficient calculations and improved accuracy.     

Error growth in transient large displacement calculations

Nonlinear problems are widely acknowledged as being more difficult to solve numerically than linear problems. Various kinds of errors contribute to this difficulty and in this paper some of these errors will be described and illustrated by solving certain large displacement problems using eight-noded isoparametric brick elements in space and an explicit integration method in time. First, approximation errors in time integration are illustrated, with violation of energy conservation being used as an indicator of the increased difficulties encountered in solving large displacement problems. Next, round-off errors and order of operations are discussed and illustrated for the case of a cube that is impulsively set in rotation about its centre of mass. Simple tests of invariance with respect to translation and rotation are shown to be interesting and potentially useful. Finally, approximation errors in spatial discretization, especially those associated with incomplete or inconsistent integration over the element volume, are illustrated for a large deflection beam problem.     

Analytical light-scattering solution for Chebyshev particles

We develop a modification of the T-matrix method that allows for fast calculations of scattering properties of particles with irregular shapes. This modification uses the so-called Sh matrices, the elements of which depend on the shape of particles and do not depend on the particle size or optical constants; i.e., the introduction of Sh matrices makes possible the separation of these parameters within the T-matrix algorithm. For a given shape of a scattering object we calculate the Sh matrices only once and then can quickly calculate the T-matrix elements for a number of sizes and refractive indices. This, in particular, can provide rapid particle-size and refractive index averaging in a particle ensemble. This separation is useful for the derivation of an analytical light-scattering solution for Chebyshev particles.