Y.-L. Xu

Electromagnetic scattering by an aggregate of spheres

We present a comprehensive solution to the classical problem of electromagnetic scattering by aggregates of an arbitrary number of arbitrarily configured spheres that are isotropic and homogeneous but may be of different size and composition. The profile of incident electromagnetic waves is arbitrary. The analysis is based on the framework of the Mie theory for a single sphere and the existing addition theorems for spherical vector wave functions. The classic Mie theory is generalized. Applying the extended Mie theory to all the spherical constituents in an aggregate simultaneously leads to a set of coupled linear equations in the unknown interactive coefficients. We propose an asymptotic iteration technique to solve for these coefficients. The total scattered field of the entire ensemble is constructed with the interactive scattering coefficients by the use of the translational addition theorem a second time. Rigorous analytical expressions are derived for the cross sections in a general case and for all the elements of the amplitude-scattering matrix in a special case of a plane-incident wave propagating along the z axis. As an illustration, we present some of our preliminary numerical results and compare them with previously published laboratory scattering measurements.

Electromagnetic scattering by an aggregate of spheres: far field.

In electromagnetic multisphere-scattering calculations the reexpansion method for seeking a single-field representation of the total scattered field is found impracticable because of severe numerical problems. We present a simple single-field expansion of the total scattered far field based on an asymptotic form of vector translational addition theorems. With this asymptotic expansion of the far field, we derive analytical expressions for the scattering properties of an arbitrary aggregate of spheres. Resulting formulas are free from numerical problems in practical applications. Theoretical predictions from this far-field solution for various aggregates of spheres that we tested agree favorably with laboratory microwave scattering measurements. Some numerical results are presented and compared with experimental data.

A generalized multiparticle Mie-solution: further experimental verification

Abstract We further test our electromagnetic multisphere-scattering solution developed earlier by comparing theoretical predictions from the theory with a set of laboratory measurements of microwave analog to light scattering by aggregated spheres. This solution is an extension of Mie theory to the multisphere case, generally applicable to an arbitrary aggregate of spherical and/or nonspherical particles. It is demonstrated once again that the theory is in a uniform agreement with experiment, convincingly confirming the veracity of the multiparticle-scattering formulation. The computer code for the calculation of the scattering by an aggregate of spheres in a fixed orientation and the experimental data havebeen made publically available.

Orientation-averaged radiative properties of an arbitrary configuration of scatterers

We discuss both analytical and numerical methods in calculating radiative scattering parameters of a randomly oriented ensemble of particles. There exist two approaches to rigorously solving multiparticle scattering. One is the generalized multiparticle Mie-solution (GMM) and the other is cluster T-matrix approach (CTM). We show that, the same as in the case of fixed-orientation scattering, the random-orientation formulations of GMM and CTM have a remarkable contrast in capability of handling the overall dimension of an ensemble of particles in practical applications. We also show that the use of a standard scheme of numerical quadrature could be more efficient than straightforwardly taking an unweighted arithmetic average in discrete orientational averaging.

Comparison between Multisphere Light-scattering Calculations: Rigorous Solution and Discrete-Dipole Approximation

We present the comparison of light-scattering calculations between a rigorous solution and the discrete-dipole approximation (DDA) for two-sphere aggregates. We also compare theoretical predictions with laboratory scattering measurements to examine the validity of the numerical solutions. It is found that there are cases in which the DDA solution, while satisfying the validity criterion for interdipole spacing to be small compared with the wavelength of incident radiation, deviates significantly from the rigorous solution and the experimental results. We show that the DDA works reasonably well for small-volume structures and that its validity is challenged, at least as it is currently implemented, when used on larger structures. We also show that, besides its advantages in reliability, the rigorous solution approach is far superior to the approximation method in computing efficiency as well.

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 Cruzans original research on the vector addition theorems [Q. Appl. Math. 20, 33-40 (1962)] is correct, although many authors believe that Cruzans formulation contains an overall-sign error.

Photophoresis of micrometer-sized particles in the free-molecular regime

The photophoretic force in the free-molecular regime has been calculated for a spherical particle using the Lorenz‐ Mie solution to the electromagnetic field within the particle. The temperature distribution on the surface of the suspended particle is calculated using a finite diAerence method. The eAect of the complex refractive index ma na ik and the normalized size parameter defined as aa 2pa=k on the photophoretic force and particle velocity are also examined. We show that for a 1 solar constant illumination, the photophoretic forces might be as high as 20% of the weight of the particles considered. ” 2001 Published by Elsevier Science Ltd.

Interactions with Electromagnetic Radiation: Theory and Laboratory Simulations

At the time of the most recent major book on interplanetary dust (McDonnell 1978), most theoretical studies were confined to homogeneous and spherical dust models. Only microwave analogue experiments were used to explore the scattering by more realistic structures representing either the first stratospheric collections of interplanetary dust particles or complex aggregates of interstellar grains proposed on theoretical grounds. Advances in computing power, light scattering theory, and in experimental capabilities have since allowed the implementation of powerful and flexible theoretical solutions, more sophisticated solutions for the calculation of scattering by interacting particles based on classical methods, and have led to multi-wavelength microwave analogue investigations of structures in the size range of interplanetary dust. We attempt to summarize these advances, place them into context, and suggest a framework for models of interplanetary dust that facilitates systematic studies. The electromagnetic scattering sections apply to a broad range of natural and artificial terrestrial and cosmic dust or aerosols as well as to interplanetary dust.