Effective permittivity of dense random particulate plasmonic composites

An effective-medium theory (EMT) is developed to predict the effective permittivity ε _eff of dense random dispersions of high optical-conductivity metals such as Ag, Au, and Cu. Dependence of ε_eff on the volume fraction ø, a microstructure parameter-related to the static structure factor and particle radius a, is studied. In the electrostatic limit, the upper and lower bounds of k correspond to Maxwell-Garnett and Bruggeman EMTs, respectively. Finite size effects are significant when jβ²(ka/n)³ becomes O(1), where β, k, and n denote the nanoparticle polarizability, wavenumber, and matrix refractive index, respectively. The coupling between the particle and effective medium results in a red-shift in the resonance peak, a nonlinear dependence of εeff on ø, and Fano resonance in εeff .