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.

No abstract

No abstract

In practical applications, the independent scattering approximation (ISA) is widely used to analyze light transfer in nanoparticle systems. However, the traditional independent scattering criterion is obtained under the assumption that the host medium surrounding particles is nonabsorbing, and thus may be invalid in certain circumstances. In this work, to explore the applicability of the ISA for small particles in absorbing host media, we calculate the extinction efficiency of particle clusters by direct solutions of macroscopic Maxwell equations. Using the far-field and distance-independent definitions of extinction, the computational efficiency multi-sphere method is applied for particle clusters in absorbing host, and its accuracy is verified with the discrete dipole approximation method. It is well known that for small particles, the dependent scattering in transparent host always enhances the extinction of the cluster and the criterion for the ISA is nearly independent of the particle refractive index and particle size. We show, however, that when the host medium is absorbing, the dependent scattering between particles can lead to a decreased or even negative extinction, and thus the ISA criterion depends on the particle refractive index, size, and host medium absorption index. In this result, the generalized criteria for absorbing host media may differ significantly from the conventional ones for transparent host media. The results can provide guidance in solving problems related to light transfer in nanoparticle systems, particularly in the presence of absorption in the host medium.

No abstract