Nondipole light scattering by partially oriented ensembles. I. Numerical calculations and symmetries

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Abstract
We consider the elastic scattering of light by an ensemble of scatterers with radius of gyration greater than about one‐tenth of a wave; e.g., visible light scattered by an aqueous suspension of viruses or bacteria. We model the scattering molecule as an asymmetric rigid array of interacting point polarizabilities, and we include, as the source of anisotropy in the scattering ensemble, a permanent dipole moment on the molecule and a uniform electric field E° in the scattering cell. We calculate the entire Müller matrix M(θ, E○x, E○y, E○z), for scattering angles θ from 0° to 360° and for E○x, E○y, E○z nonzero one at a time, where z is the incidence axis, y is perpendicular to the scattering plane, and x is perpendicular to y and z. Our first major finding is that the nondipole elements of M are enormously more sensitive to partial orientation than are the dipole elements. The second major finding is a set of new symmetries governing the scattering matrix for the case of axially anisotropic scattering clouds. The Perrin reciprocity symmetries for isotropic clouds may be symbolized by M(θ)=PM(θ), where P stands for matrix transpose plus negation of third row and column (with double negation of element 3,3). Using this operator our new axial symmetries may be expressed as PM(+θ, 0, E○y, 0)=M(+θ, 0, −E○y,0)=M(−θ, 0, E○y, 0). The second symmetry may be generalized to fields in any direction as M(+θ,−E○x, −E○y, E○z)= M(−θ, E○x, E○y, E○z). We also show in Appendix A how the nonlocal polarizabilities used in the theory may be calculated by the inversion only of symmetric matrices, with a significant saving in calculation time when the number of subunits is large.