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Effective permittivity of random 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 ϕ, a microstructure parameter κrelated to the static structure factor and particle radius a is studied. In the electrostatic limit, the upper and lower bounds of κcorrespond to Maxwell-Garnett and Bruggeman EMTs respectively. Finite size effects are significant when |β^2(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 non-linear dependence of ε_eff on ϕ, and Fano resonance in ε_eff.