Effective medium theories for irregular fluffy structures: aggregation of small particles

We study the extinction efficiencies as well as scattering properties of particles of different porosity. Calculations are performed for porous pseudospheres with small size (Rayleigh) inclusions using the discrete dipole approximation. Five refractive indices of materials covering the range from $1.20+0.00i$ to $1.75+0.58i$ were selected. They correspond to biological particles, dirty ice, silicate, amorphous carbon and soot in the visual part of spectrum. We attempt to describe the optical properties of such particles using Lorenz-Mie theory and a refractive index found from some effective medium theory (EMT) assuming the particle is homogeneous. We refer to this as the effective model. It is found that the deviations are minimal when utilizing the EMT based on the Bruggeman mixing rule. Usually the deviations in extinction factor do not exceed $\sim 5%$ for particle porosity ${\cal P}=0 - 0.9$ and size parameters $x_{\rm porous} = 2 \pi r_{\rm s, porous}/\lambda \la 25$. The deviations are larger for scattering and absorption efficiencies and smaller for particle albedo and asymmetry parameter. Our calculations made for spheroids confirm these conclusions. Preliminary consideration shows that the effective model represents the intensity and polarization of radiation scattered by fluffy aggregates quite well. Thus, the effective models of spherical and non-spherical particles can be used to significantly simplify computations of the optical properties of aggregates containing only Rayleigh inclusions.