Refractive index of sparse layers of adsorbed gold nanoparticles

Measurements are presented of the effective complex refractive index of a layer of gold nanoparticles adsorbed to a silicon wafer at low coverages. The measurements were made by means of variable-angle ellipsometry, and correlated with nanoparticle coverage determined from atomic force microscope images. The analysis establishes the effective refractive index of a uniform layer whose thickness equals the nanoparticle diameter. A simple empirical relationship is obtained for real component of refractive index as a function of the fractional nanoparticle coverage regardless of the nanoparticle size. The imaginary component also follows a simple relationship but only up to a certain coverage, above which it increases rapidly. These relationships may be useful in other contexts such as chemical or biosensors in which the nanoparticle coverage could be inferred from optical measurements such as ellipsometry, surface plasmon resonance spectroscopy, reflectometry, or interferometry.