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A method for calculating the extinction, absorption, and scattering cross sections of clusters of neighboring spheres for both fixed and random orientations is developed. The analysis employs the superposition formulation for radiative interactions among spheres, in which the total field from the cluster is expressed as a superposition of vector spherical harmonic expansions about each of the spheres in the cluster. Through the use of addition theorems a matrix equation for the expansion coefficients is obtained. Further application of addition theorems on the inverse of the coefficient matrix is shown to yield analytical expressions for the orientation-averaged total cross sections of the sphere cluster. Calculations of the cross sections of pairs of spheres and fractal aggregates of several spheres are presented. It is found that a dipole representation of the field in each sphere does not adequately predict the absorption cross section of clusters of small-size-parameter spheres when the spheres are highly conducting. For this situation several multipole orders are required for an accurate calculation of the absorption cross section. In addition, the predicted absorption of sphere clusters can be significantly greater than that estimated from the sum of the isolated-sphere cross sections.

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We use the numerically exact superposition T-matrix method to perform extensive computations of electromagnetic scattering by a 3D volume filled with randomly distributed wavelength-sized particles. These computations are used to simulate and analyze the effect of randomness of particle positions as well as the onset and evolution of various multiple-scattering effects with increasing number of particles in a statistically homogeneous volume of discrete random medium. Our exact results illustrate and substantiate the methodology underlying the microphysical theories of radiative transfer and coherent backscattering. Furthermore, we show that even in densely packed media, the light multiply scattered along strings of widely separated particles still provides a significant contribution to the total scattered signal and thereby makes quite pronounced the classical radiative transfer and coherent backscattering effects.

An analysis of radiative scattering for an arbitrary configuration of neighbouring spheres is presented. The analysis builds upon the previously developed superposition solution, in which the scattered field is expressed as a superposition of vector spherical harmonic expansions written about each sphere in the ensemble. The addition theorems for vector spherical harmonics, which transform harmonics from one coordinate system into another, are rederived, and simple recurrence relations for the addition coefficients are developed. The relations allow for a very efficient implementation of the ‘order of scattering’ solution technique for determining the scattered field coefficients for each sphere.

An analysis of radiative absorption and scattering by clusters of spheres in the Rayleigh limit is developed with an electrostatics analysis. This approach assumes that the largest dimension of the cluster is significantly smaller than the wavelength of the radiation. The electric field that is incident upon and scattered by the cluster can then be represented by the gradient of a potential that in turn satisfies Laplace's equation. An analytical solution for the potential that exactly satisfies the boundary conditions at the surfaces of the spheres is obtained with a coupled spherical harmonics method. The components of the polarizability tensor and the absorption, scattering, and depolarization factors are obtained from the solution. Calculations are performed on fractallike clusters of spheres, with refractive-index values that are characteristic of carbonaceous soot in the visible and the IR wavelengths. Results indicate that the absorption cross sections of fractal soot clusters can be significantly larger in the mid-IR wavelengths than what is predicted for Rayleigh-limit spheres that have the same total volume. The absorption cross section (relative to a sphere of the same volume) is dependent on the number of spheres in the aggregate for aggregates with up to approximately 100 primary spheres, and for larger aggregates the relative absorption becomes constant. The predicted spectral variation of soot absorption in the visible and the mid-IR wavelengths is shown to agree well with experimental measurements.

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