Angular reflectance of suspended gold, aluminum and silver nanospheres on a gold film: Effects of concentration and size distribution

In this article, we describe a parametric study of the effects of the size distribution (SD) and the concentration of nanospheres in ethanol on the angular reflectance. Calculations are based on an effective medium approach in which the effective dielectric constant of the mixture is obtained using the Maxwell–Garnett formula. The detectable size limits of gold, aluminum, and silver nanospheres on a 50-nm-thick gold film are calculated to investigate the sensitivity of the reflectance to the SD and the concentration of the nanospheres. The following assumptions are made: (1) the total number of particles in the unit volume of suspension is constant, (2) the nanospheres in the suspension on a gold film have a SD with three different concentrations, and (3) there is no agglomeration and the particles have a log-normal SD, where the effective diameter, d _eff and the effective variance, ν _eff are given. The dependence of the reflectance on the d _eff, ν _eff, and the width of the SD are also investigated numerically. The angular variation of the reflectance as a function of the incident angle shows a strong dependence on the effective size of the metallic nanospheres. The results confirm that the size of the nanospheres (d _eff <100 nm) can be detected by reflected light from the bottom surface of a gold film with a reasonable sensitivity if a proper angle of incidence is chosen based on the type of metallic particles on a gold thin film at λ = 632 nm. We show that the optimum incident angle to characterize the size of nanospheres on a gold film is between 70° and 75° for a given concentration with a particular SD.