Investigation of the single scattering approximation through direct electromagnetic scattering simulation

Abstract

In this work, we investigate quantitatively the applicability conditions of single scattering approximation (SSA) through direct simulation of electromagnetic scattering by small volume elements filled with randomly distributed spherical particles. The influences of size parameter x, volume fraction fv, complex refractive index m and number N of particles on the nondimensional extinction cross section ηext and absorption cross section ηabs of particle groups are discussed. For non-absorbing particles with small size parameters (x = 0.1 and 0.2 in this study), due to the small phase shift across particles, the particle refractive index has almost no influence on the criteria for SSA. However, when the particle size increases or particle absorption is enhanced, the criteria for SSA will be closely related to the particle complex refractive index. Moreover, when the particle size is small, due to the weak multiple scattering between particles, the criteria for SSA can be regarded as the criteria for independent scattering approximation (ISA). But as the particles increase to relatively large sizes (x = 4.0 in this study), because of the enhancement of multiple scattering, the criteria for SSA and ISA should be treated differently. The widely used criteria obtained for bispheres may not be applicable to particle groups composed of lots of particles, and the optical thickness of dispersed media is not suitable for evaluating the applicability conditions of SSA. For particle groups composed of different particle numbers, due to the differences in dependent scattering and multiple scattering, the criteria for SSA are obviously different and the particle volume fraction should be small enough to make the SSA sufficiently accurate.