Notes on Rayleigh's hypothesis and the extended boundary condition method.

Regarding wave scattering on a three-dimensional nonspherical obstacle, the Rayleigh hypothesis states that the scattered field can be expanded everywhere outside the obstacle using only outgoing eigensolutions of the underlying Helmholtz equation. However, the correctness of this assumption has not yet been finally clarified, although it is important for the near-field analysis of scattering processes and for multiple scattering. To circumvent this uncertainty, Waterman introduced the extended boundary condition to develop his T-matrix method. This approach leads to the restriction that, when modeling multiple scattering processes using this T-matrix, the smallest circumscribing spheres of the individual obstacles must not overlap. The purpose of this paper is to provide a justification of the correctness of Rayleigh's hypothesis and clarify its implications for modeling multiple scattering. We show that Waterman's T-matrix can in fact be used inside the critical region between the surface of the obstacle and its smallest circumscribing sphere to represent the near-field and that one does not necessarily have to exclude an overlap of these spheres in the multiple scattering modeling. The theoretical considerations in the first part of this paper are supplemented by a numerical study of a benchmark configuration for multiple scattering in the last part.

Convergence of the iterative T-matrix method.

Among the various methods for computing the T-matrix in electromagnetic and acoustic scattering problems is an iterative approach that has been shown to be particularly suited for particles with small-scale surface roughness. This method is based on an implicit T-matrix equation. However, the convergence properties of this method are not well understood. Here, a sufficient condition for the convergence of the iterative T-matrix algorithm is derived by applying the Banach fixed point theorem. The usefulness of the criterion is illustrated by applying it to predicting, as well as to systematically improving the convergence of the iterative method.

A numerical study of acoustic scattering by Janus spheres.

Recently Janus particles have become important in several technological fields because they have interesting properties compared with homogeneous particles. The interaction of Janus particles with sound waves is of particular interest for diagnostic purposes, and also in applications in micro- and nanotechnology. In this paper the authors demonstrate that a method of fundamental solution combined with a T-matrix that is computed from far-field information can be applied with benefit to analyse the scattering of sound waves by a particular type of Janus sphere. Moreover, it is shown that this method converges faster than the conventional T-matrix method introduced by Waterman [(1969). J. Acoust. Soc. Am. 45, 1417-1429]. This is of special importance if orientation averaged scattering quantities are required, or if multiple scattering processes on Janus spheres are considered. This method is used to demonstrate the interesting phenomenon of an enhanced side scattering intensity that is larger than the forward scattering intensity, and that this effect can be strengthened using a particular configuration of two identical Janus spheres. Finally, the authors discuss a useful approximation that can be readily applied for two or more Janus spheres.

Modeling optical properties of particles with small-scale surface roughness: combination of group theory with a perturbation approach.

A T-matrix method for scattering by particles with small-scale surface roughness is presented. The method combines group theory with a perturbation expansion approach. Group theory is found to reduce CPU-time by 4-6 orders of magnitude. The perturbation expansion extends the range of size parameters by a factor of 5 compared to non-perturbative methods. An application to optically hard particles shows that small-scale surface roughness changes scattering in side- and backscattering directions, and it impacts the single-scattering albedo. This can have important implications for interpreting remote sensing observations, and for the climate impact of mineral aerosols.

Case study about the accuracy behavior of three different T-matrix methods.

In this paper we discuss the influence of two different sets of weighting functions on the accuracy behavior of T-matrix calculations for scalar scattering problems. The first set of weighting functions is related to one of Waterman's original approaches. The other set results into a least-squares scheme for the transmission problem. It is shown that both sets of weighting functions produce results with a converse accuracy behavior in the near and far fields. Additional information, such as reciprocity and the fulfillment of the boundary condition, are needed to choose the set of weighting functions that is most appropriate for a certain application. The obtained criteria are applied afterward to an iterative T-matrix approach we developed to analyze scattering on regular particle geometries with an impressed but slight surface irregularity. However, its usefulness is demonstrated in this paper by analyzing the far-field scattering behavior of Chebyshev particles of higher orders.

Scattering database for spheroidal particles.

We present a database containing light scattering quantities of randomly oriented dielectric spheroidal particles in the resonance region. The database has been generated by using a thoroughly tested T-matrix method implementation. The data possess a defined accuracy so that they can be used as benchmarks for electromagnetic and light scattering computations of spheroids. Within its parameter range the database may also be applied as a fast tool to investigate the scattering properties of nonspherical particles and to verify assumptions or statements concerning their scattering behavior. A user interface has been developed to facilitate the data access. It also provides some additional functionalities such as interpolations between data or the computation of size-averaged scattering quantities. A detailed description of the database and the user interface is given, followed by examples illustrating their capabilities and handling. On request, the database including the documentation is available, free of charge, on a CD-ROM.

Light scattering on Chebyshev particles of higher order.

We present what we believe to be the first results of a light-scattering analysis on several Chebyshev particles characterized by higher orders. Chebyshev particles of comparatively lower orders were used in the past to study the effects of nonspherical but concave geometries in remote sensing applications. We will show that, based on the developed methodology, accurate results can also be obtained for particles of higher orders exhibiting a more pronounced surface waviness. The achieved results demonstrate that higher-order Chebyshev particles can be used to estimate the influence of a weak surface roughness on the light-scattering behavior of the underlying smooth scatterer. The effects obtained correspond with the results of other approaches and with the theoretical expectations of a weak surface roughness. In contrast to what is known for regular particles, there can be observed an essential difference between the phase functions of the underlying spherical scatterer and the corresponding higher-order Chebyshev particle if a higher absorptivity of the scattering medium is considered. This paper demonstrates additionally that Chebyshev polynomials can be simply combined with smooth geometries other than spheres.

Two software tools for plane-wave scattering on nonspherical particles in the German Aerospace Center's Virtual Laboratory.

We present the methodological background, the range of applicability, and the on-line usage of two software packages, MIESCHKA and CYL, which we have developed for light-scattering analysis on nonspherical particles. MIESCHKA solves Maxwell's equations in a rigorous way but is restricted to axisymmetric geometries, whereas CYL is an approximation for finite columns with nonspherical cross sections. We have established an easy on-line access to both of these programs through the Virtual Laboratory. Its generic software infrastructure was designed to simplify the web-based usage and to support the intercomparability of scientific software.