Using a New Scattering Order Formulation of the Discrete Dipole Approximation to Calculate Scattering by Irregularly Shaped Aerosols

The discrete dipole approximation (DDA) or coupled dipole method is an approach to modeling the scattering of electromagnetic radiation that has become popular due to its extreme flexibility in terms of the shape of the scatterer or “target”. At least three publicly available models exist, DDSCAT, ADDA, and OpenDDA, each of which has been updated and documented extensively. The concept of the DDA is to break up a target into a three-dimensional grid of polarizable points. These points are attributed a size that is small enough compared to the wavelength of the incident radiation that the electromagnetic fields associated with them are dipole fields, whose expressions both in the near field and far field are well known. The near field dipole fields dictate the radiative interactions among the polarizable points, while the far field dipole fields dictate the total radiance of radiation scattered by the target. In conventional implementations of the DDA, the system of equations relating the field of the incident electromagnetic wave to the fields of the polarizable points is transformed into a matrix equation for the polarization (the dipole moment per unit volume) at each point. Once the dipole moment per unit volume at each point is known, the scattered radiance as a function of angle, the scattering, absorption, and extinction cross sections, and all parameters derived from these may be calculated. In the current study, we revisit a complementary DDA formulation called the scattering order formulation of the discrete dipole approximation (SOF-DDA), which is particularly useful for handling highly complex particle morphologies in which an irregularly spaced grid of dipoles and/or very high dipole resolution is necessary to resolve fine features of internal and external scatterer inhomogeneities. In the SOF-DDA, not only may the dipoles be placed with arbitrary spacing, there is no system of coupled equations to solve, no matrix to invert, and no two-dimensional arrays to store. Dipoles may be concentrated where the highest spatial resolution is necessary, with their size and shape defined correspondingly, with no loss of efficiency. No grid points need to exist where there is no material (in voids), and no boolean variable need be defined at such points. Most importantly, the SOF-DDA, as it name suggests, follows the succession of radiative interactions (orders of scattering) among the dipoles and as such has the potential to provide more physical insight into the process of scattering than conventional DDA models. One intriguing drawback of the SOF-DDA is that for a large collection of dipoles, particularly in a larger compact scatterer, the series solution over orders of scattering may diverge rather than converge. We will show the results of a new SOF-DDA "marching" scheme that overcomes this obstacle and predicts a finite cross section even for larger compact scatterers. We will also show preliminary results of our SOF-DDA scheme for aerosols with fine scale irregularities.