The scattering matrix for randomly oriented particles

Abstract

An efficient numerical method is derived for evaluation of the scattering properties of randomly distributed particles described by the coupled dipole approximation. An exact analytic average for these properties is also derived. All elements of the scattering matrix for a collection of randomly oriented particles can be obtained by either method. The results are applicable to model calculations of the scattering matrix for realistic particles. The analytic average also allows qualitative interpretation of the dependence of the matrix elements on dipolar interactions.

The discrete dipole approximation: An overview and recent developments

“…Singham et al [136] noted that the set of problems described above is physically equivalent to a fixed orientation of the particle and different incident and scattering directions. The latter are determined by transformation of the laboratory reference frame to the reference frame associated with the particle.…”

“…If or its LU decomposition is obtained [75,136], a single solution for any right part y can be obtained in n 1 −…”

“…Moreover, Singham et al [136] and McClain and Ghoul [138] independently proposed an analytical way of averaging the scattering matrix at any scattering angle, which requires O(n 2 ) operations once is known. Khlebtsov [139] extended this technique to averaging of extinction and absorption cross sections.…”

On the concept of random orientation in far-field electromagnetic scattering by nonspherical particles

“…As a result, we have provided the rigorous (and long overdue) justification of the main premises implicit in Refs. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and numerous related publications. The laboratory, Oxyz, and particle, Ox′y′z′, reference frames having a common origin.…”

Polarized light scattering as a probe for changes in chromosome structure

“…They applied the coupled dipole approximation to a variety of structures for single particles 41 and for an orientation average. 42 They showed that a helix modelled by spherical or prolate spheroidal subunits is equivalent as long as the thickness of the subunits are the same and Maxwell-Garnett theory 40 is used to determine the polarizability of the dipole representing the subunit. 43 In the same publication this group did a preliminary investigation of the necessity of including dipolar interactions.…”