Modeling Optical Materials at the Single Scatterer Level: The Transition from Homogeneous to Heterogeneous Materials

Materials that contain distinct scatterers, for example, nanoparticles, with sizes exceeding 100 nm scatter light heavily and are heterogeneous. In contrast, the atomic or molecular scatterers in conventional optical materials form a homogeneous distribution on the scale of the wavelength. In this paper, the transition between homogeneous and heterogeneous materials is investigated. To this end, a procedure is introduced that allows for retrieving reliable refractive index values from full wave optical numerical simulations of the underlying multibody scattering problem. Using this procedure, it is shown that the concept of an effective refractive index breaks down on multiple levels as a material transitions out of the homogeneous regime. These findings allow for quantifying how novel dispersion-engineered nanocomposites for bulk optical applications must be designed and show that Maxwell-Garnett-type effective medium theories are accurate tools for the design of nanocomposites. The procedure can be readily generalized to other types of scatterers, including atoms and molecules and hence guide the design of different kinds of novel materials.