Modelling of Coloured Metal Surfaces by Plasmonics Nanoparticles

Abstract

Metallic nanoparticles (NPs) dispersed in glass have been used since Romans times to color glasses [1]. With the recent development of metasurfaces, metallic and dielectric nanostructures have been proposed to color surfaces [2]. The excitation of resonant modes in the nanostructures is responsible for selective absorption of the incident light, thus causing the color creation. Top-down techniques based on lithography allow achieving highly saturated colors with a high resolution due to the deterministic patterning, but they are not suited for large-scale applications, such as the coloring of large surfaces. Furthermore, lithographic techniques are not suited to create metallic nanostructures on a substrate of the same metal. Metal nanostructures on metal can generate colors if their shape can support a localized surface plasmon resonance (LSPR). For example, this is valid for NPs of spherical shape slightly embedded on the substrate. In fact, when the embedding increases the resonance condition vanishes (an embedding increase corresponds to a transition from a spherical shape to a hemispherical shape) and the color disappears. This configuration has never been investigated theoretically. We recently proposed a bottom-up laser technique in the picosecond regime to create NPs on the metallic surface (laser-induced nanostructures) through a process of ablation and re-deposition, which is suited for mass production [3]. By tuning the laser properties, it is possible to control the NPs such that their size and density fall in the range of dimensions supporting LSPR, thus producing colors. This is shown in the palette realized on silver at the Royal Canadian Mint in Fig. 1a [3]. SEM images of these colored metallic surfaces reveal the presence of NPs of two sizes, i.e., medium and small, with radii R _m and R _s, respectively. Based on this information, we simulated the optical response of silver NPs distributed on a flat silver surface by using an in-house parallel 3D-FDTD code running on IBM BlueGene/Q (SOSCIP). Medium NPs were embedded by 30% of their radius, while small NPs were embedded by 0.5–3.5 nm. The simulation domain was discretized with a space-step from 0.125 to 0.5 nm to achieve convergent results, and we arranged the NPs following a hexagonal lattice in the xz-plane with a center-to-center inter-distance of D _m and D _s for medium and small NPs, respectively. In order to apply periodic boundary conditions, we needed D _m∕D _s to be an integer number. We modeled silver using the Drude+2CP model [4]. In Fig. 1b we show the field distribution at 390 nm for an xz-plane cut through the center of the small NPs. By averaging the reflectance over the embedding level of the small NPs, we obtained the average reflectance curves and the associated colors shown in Fig. 1c. The averaging washes out the effect of the small NPs, thus highlighting the major role in the color formation played by the medium NPs. The simulated palette in Fig. 1c reveals the same qualitative transition from blue to yellow observed in the experimental palette in Fig. 1a, thus identifying plasmonic resonances in arrangements of NPs as responsible for color creation.