Shermila Brito Singham

Backscattering by nonspherical particles: A review of methods and suggested new approaches

Scattering of electromagnetic radiation near the backward direction is more sensitive to particle shape than scattering near the forward direction. Mie theory is therefore of dubious applicability to predicting backscattering by atmospheric particles known to be irregular or to inverting measurements on such particles. An irregular particle is one with an uncertain shape. In the face of uncertainty one must adopt a statistical approach in which scattering properties of ensembles are determined. To obtain ensemble averages, a basis is needed for averaging over a set of electromagnetic microstates. Ensemble averages based on the Rayleigh theory for small ellipsoids and on the T matrix method for spheroids agree better with measurements than Mie theory does. The coupled-dipole method also provides a basis for ensemble averaging. This method also leads to a simple physical interpretation of why backscattering is so sensitive to particle shape and can be used to calculate scattering by one- and two-dimensional analogs to three-dimensional irregular particles.

Evaluation of the scattering matrix of an arbitrary particle using the coupled dipole approximation

The coupled dipole approximation is applied to the calculation of the scattering matrix of an arbitrary particle. Both isotropic and anisotropic dipoles are used in the calculations. The forms of the matrices obtained for several types of scatterers are found to be in exact agreement with those predicted by symmetry. The method is tested quantitatively by comparison with Mie predictions for solid and coated spheres and good agreement is observed. This comparison is also used to establish appropriate magnitudes for anisotropic dipolar polarizabilities.

Light scattering by an arbitrary particle: the scattering-order formulation of the coupled-dipole method

The field scattered by an arbitrary particle modeled as an array of coupled dipoles can be expressed as an infinite series in terms of scattering orders. The fields of a given scattering order can be calculated from those of the previous order. When the series converge, the approximate method agrees well with the exact theory for a sphere. The maximum size of the dipolar array that can be used with the method as well as the number of terms required for convergence depends on the relative refractive index and the shape of the particle.

Light scattering by an arbitrary particle: a physical reformulation of the coupled dipole method

The coupled dipole model of scattering by an arbitrary particle has been reformulated in terms of internal scattering processes of all orders. This formalism readily permits physical interpretation of observables and provides a rational basis for making computations more efficient. The calculation of scattering parameters can be simplified by appropriately terminating the infinite series at any order as well as by restricting the summations over the dipolar interaction terms within each order. Large particles can be partitioned into segments so that the scattered field is a superposition of the fields from the segments together with fields due to interactions among dipoles in different segments.

The scattering matrix for randomly oriented particles

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.

Intrinsic optical activity in light scattering from an arbitrary particle

Abstract The coupled-dipole method is extended to include intrinsic optical activity in the material of an arbitrarily shaped particle. The dipolar subunits used in the method are spherical or ellipsoidal. Good agreement is obtained on comparison with the exact theory for an optically active sphere.

Hybrid method in light scattering by an arbitrary particle

A hybrid method for light scattering by an arbitrary particle using the scattering-order formulation of the coupled dipole method is described. An arbitrary particle is divided into two or more segments, and the field scattered by the particle is obtained from the fields scattered by each segment together with the field due to interactions among segments. An exact or approximate theory is used to calculate the scattered field from each segment, and interactions are included using the scattering-order formulation of the coupled dipole method. Calculations show that for certain particles, this hybrid approach can require fewer computations and give more accurate results than the scattering-order method.

Polarizabilities for light scattering from chiral particles

The coupled dipole method is used to calculate the circular intensity differential scattering (CIDS) from chiral particles. The particles are described by a collection of spherical or ellipsoidal dipoles. In the case of ellipsoidal dipoles, it is shown that triaxial polarizabilities have to be used to quantitatively describe the scattering matrix of the particle. For certain collections of ellipsoidal dipoles, the dipolar interactions may be neglected in calculating CIDS from the structure. The coupled dipole approximation also provides a convenient method for calculating CIDS from a one dimensional helical crystal.

Phase differential scattering from microspheres

Differential phase measurements on scattered light are possible using the two-frequency Zeeman effect laser. We refer to such measurements as phase differential scattering (PDS) in contrast to conventional intensity differential scattering measurements. PDS has certain significant experimental advantages for light scattering studies, most notably its simplicity. We find good agreement between experiment and theory for PDS from aqueous suspensions of polystyrene microspheres. The data show a strong dependence on concentration when the microspheres are larger than dipoles.

Theoretical factors in modeling polarized light scattering by arbitrary particles

The coupled dipole method has been used to model the S(34) scattering matrix element for particles of arbitrary shape. Comparison of the results of the approximate method with the exact theory for a sphere shows that the size of the units required for S(34) is much smaller than the size required for calculating S(11) with similar accuracy. Model calculations for chiral particles show that the S(34) matrix element depends sensitively on the exact shape, size and optical properties of the scatterer.