Nondipole light scattering by partially oriented ensembles. II. Analytic algorithm

Abstract

We consider the elastic single scattering of light from an ensemble of identical particles with nonrandom orientational distribution. The particle is modeled as an arbitrary rigid array of N dipole polarizabilities, and the polarizabilities within each particle interact through the retarded dipole–dipole tensor. We consider the scattering ensemble to be an ‘‘optical element’’ in the Müller formalism; thus its polarized scattering properties, both dipole and nondipole, are specified completely by a four-by-four Müller matrix M(ψ), where ψ is the scattering angle. In a previous work on orientationally random ensembles, the slow convergence of the nondipole elements suggested that they might be particularly sensitive to small orienting forces. This was confirmed by numerical calculations, which, however, also demonstrated the need for a faster analytic averaging algorithm. In this paper we extend the uniform distribution analytic algorithm to cases in which the orientation of the particles is specified by a general nonuniform distribution. We then specialize the general formula to the case of axially nonrandom orientation, such as might be caused by an external static electric field E operating on a permanent electric dipole of the model particle. We present an explicit algorithm for M(ψ,E) for this special case, together with an estimate of its computability. For models with just a few subunits, it should be computable by a desktop machine with four megabytes of memory. For more realistic models using 1000 subunits, the job can easily rise into the supercomputer range.