Modeling the optical properties of nanocomposite media using effective transfer matrices

In this study we suggest an effective matrix method (EMM) for the optical modeling of nanocomposite media. We show that an effective transfer matrix of a nanocomposite medium, comprising an assumed periodic arrangement of nanoparticles embedded in a surrounding matrix, can be extracted from a rigorous finite element simulation of the structure. The effective matrix of the nanocomposite can then be used in a standard transfer matrix calculation to forward-calculate the optical spectra of arbitrary stratified structures that contain the nanocomposite. The computational complexity of this approach is significantly less than a rigorous electromagnetic simulation of such arbitrary stratified structures, while its accuracy is practically the same. We compare this EMM to various effective medium approximations based on analytical formulas and numerical retrieval techniques. We show that the proposed EMM can be successfully applied to certain nanocomposites that cannot be described with an effective refractive index.