Detailed comparison of recent-and dissimilar-effective-medium models incorporating dependent scattering.

Abstract

We compare the predictions of two recently derived effective-medium models for the effective refractive index of a turbid suspension of particles. The two formulas are notoriously dissimilar; both are based on the quasi-crystalline approximation, but the approximations used beyond this point are entirely different. Nevertheless, for dilute suspensions both reduce to the well-established van de Hulst formula. The dissimilarities between the formulas are evident for dense suspensions, where dependent-scattering effects are important. When they might coincide is, therefore, not clear. The purpose of this work is to explore the range of particle parameters and volume fractions for which both models are applicable. Our results show that, rather surprisingly, the models produce very similar curves of the real and imaginary parts of the effective refractive index for volume fractions up to 0.4 and for particles comparable to, and larger than, the wavelength, as well as for a fairly large range of refractive-index contrasts between the particles and the surrounding medium. These results significantly increase our confidence in the validity of both models.