Effective properties of resonant nanoparticle suspensions: Impact of the elementary volume shape and eigenmodes analysis

Abstract

The study of the effective properties of random particulate materials is a storied subject, which gave rise to several effective-medium theories establishing a link between the microstructure and the macroscopic properties of inhomogeneous materials. This link is typically provided by the effective refractive index. However, effective-medium theories are defective when resonant interactions between the particles take place. Homogenization must then be performed via Maxwell’s equations from the rigorous calculation of the electromagnetic fields averaged over a statistical ensemble of realizations of the random medium in a finite domain, i.e., different configurations of the geometrical particle distribution. In even more restricted regimes originating from interparticle coupling, one observes markedly high field intensities at the surface of the particles or in localized regions of the agglomerate, casting doubts on the representativeness of the calculated mean field to extract an effective refractive index. Here we show that the value of the extracted effective refractive index may strongly depend on the shape of the ensemble’s configurations, irrespective of the statistical fluctuations of the states. This result is obtained by performing homogenization on systems of particles arranged in the shape of elliptic domains, with different eccentricities. The impact of the boundary effects on the effective refractive index is analyzed through the calculation of the quasinormal modes of the particulate systems, evidencing either strong fluctuations of the eigenfrequencies in the complex plane or Mie-type eigenmodes.