Inhomogeneity structure and the applicability of effective medium approximations in calculating light scattering by inhomogeneous particles

Abstract Atmospheric aerosols commonly occur as inhomogeneous particles with significant internal variations of refractive indices. For the purpose of light-scattering calculations, effective medium approximations (EMAs) have been developed that seek to model an inhomogeneous particle with an internal variation of refractive index using a homogeneous particle with a single “effective” refractive index, one whose value is expected to yield approximately the same scattering properties. Here the applicability of four EMAs is investigated in the relatively simple case that the particle is a mixture of materials having just two different indices of refraction, and consideration is given to the effects of the spatial arrangement of these on the reliability of results obtained using the EMAs. The EMAs considered are based on the Bruggeman theory, the Maxwell–Garnett theory, and two different Wiener bounds. The mixing states considered are relatively regular forms of “layering,” as well as states that involve varying degrees of more irregular “mixing.” Just two overall particle shapes are considered: spheres and spheroids. For each inhomogeneous particle two sets of scattering calculations are performed: calculations treating the inhomogeneous particle itself exactly, and calculations treating an effective homogeneous particle with the same shape and size but a single refractive index determined using one of the EMAs. The first kind is done using the core–mantle Mie theory in the case of stratified composition and the pseudo-spectral time-domain method in the more irregular mixing cases. The second kind of calculation is done using the Lorenz–Mie or T-matrix method. Calculated values of extinction efficiencies, asymmetry factors, and phase matrices of both a single particle and an ensemble of particles are compared. In comparisons of the EMAs with each other, the Bruggeman model and Maxwell–Garnett model give similar results, results which differ by small but noticeable amounts from the results obtained from the Wiener bounds. This suggests that the particular choice of one of the EMAs over another is not critical in calculating the scattering properties of atmospheric particles, especially the bulk-scattering properties. Comparison with the numerically exact results shows that the applicability of the EMAs is largely independent of the particle shape, size, or volume fraction of the components, but is significantly affected by different mixing states. It is found that the Bruggeman and Maxwell–Garnett theories can only give accurate approximations for the optical properties of well-mixed particles, ones for which the scale characterizing the index variation is no larger than about 0.4 / π times the wavelength of the incident light, and that applicability of EMAs for stratified and weakly mixed particles is very limited. These results must of course be viewed with some caution, given the great number of combinations of particle geometries, mixing states, and refractive indices that are possible compared to the few idealized ones we examine.