Microscopic theory of optical properties of composite media with chaotically distributed nanoparticles

The boundary problem of light reflection and transmission by a film with chaotically distributed nanoinclusions is considered. Based on the proposed microscopic approach, analytic expressions are derived for distributions inside and outside the nanocomposite medium. Good agreement of the results with exact calculations and (at low concentrations of nanoparticles) with the integral Maxwell-Garnett effective-medium theory is demonstrated. It is shown that at high nanoparticle concentrations, averaging the dielectric constant in volume as is done within the framework of the effective-medium theory yields overestimated values of the optical film density compared to the values yielded by the proposed microscopic approach. We also studied the dependence of the reflectivity of a system of gold nanoparticles on their size, the size dependence of the plasmon resonance position along the wavelength scale, and demonstrated a good agreement with experimental data.