Reducing shape errors in the discrete dipole approximation using effective media.

The discrete dipole approximation (DDA) simulates optical properties of particles with any given shape based on the volume discretization. These calculations cost a large amount of time and memory to achieve high accuracy, especially for particles with large sizes and complex geometric structures, such as mixed black-carbon aerosol particles. We systematically study the smoothing of the DDA discretization using the effective medium approximation (EMA) for boundary dipoles.

Reproducing the morphology-dependent resonances of spheres with the discrete dipole approximation.

During the development and application of a scattering algorithm, its accuracy is normally validated by comparing with results of spherical particles given by the exact Mie theory. Being the simplest shape, sphere supports morphology-dependent resonances (MDRs), which cause sharp variations of the scattering properties in narrow size ranges. We show that MDRs may mislead the validation of any volume- or surface-discretization methods, including the discrete dipole approximation (DDA) and, thus, should be explicitly avoided.

Scattering of a damped inhomogeneous plane wave by a particle in a weakly absorbing medium.

We use the volume integral equation formulation to consider frequency-domain electromagnetic scattering of a damped inhomogeneous plane wave by a particle immersed in an absorbing medium. We show that if absorption in the host medium is sufficiently weak and the particle size parameter is sufficiently small, then (i) the resulting formalism (including the far-field and radiative-transfer regimes) is largely the same as in the case of a nonabsorbing host medium, and (ii) one can bypass explicit use of sophisticated general solvers of the Maxwell equations applicable to inhomogeneous-wave illumination. These results offer dramatic simplifications for solving the scattering problem in a wide range of practical applications involving absorbing host media.

Additivity of integral optical cross sections for a fixed tenuous multi-particle group.

We use the volume integral equation formulation of frequency-domain electromagnetic scattering to settle the issue of additivity of the extinction, scattering, and absorption cross sections of a fixed tenuous group of particles. We show that all the integral optical cross sections of the group can be obtained by summing up the corresponding individual-particle cross sections, provided that the single-scattering approximation applies.

Addendum to “Impressed sources and fields in the volume-integral-equation formulation of electromagnetic scattering by a finite object: A tutorial” [J. Quant. Spectrosc. Radiat. Transfer 214 (2018) 158–167].

Our recent tutorial referred to in the title has summarized a general theoretical formalism of electromagnetic scattering by an arbitrary finite object in the presence of arbitrarily distributed impressed currents. This addendum builds on the tutorial to provide a streamlined discussion of specific far-field limits and the corresponding reciprocity relations by introducing appropriate far-field operators and linear maps and deriving the reciprocity relations through the pseudo adjoint of these maps. We thereby extend the compact operator calculus used previously to consider the fields and sources near or inside the scattering object.