Influence of surface roughness on the optical properties of plasmonic nanoparticles

For plasmonic nanoparticles, we investigate the influence of surface roughness inherent to top-down fabrication on the optical properties and find that it has a surprisingly small influence on the position and width of the plasmon peaks. Our experimental observation is supported by simulations based on the boundary element method approach. Using a perturbation approach, suitable for metallic nanoparticles with a moderate degree of surface roughness, we demonstrate that the reason for this lies in motional narrowing where the plasmon averages over the random height fluctuations. Surface roughness in large arrays of identical nanoparticles, such as that encountered in the context of metamaterials, is thus expected to not constitute a major roadblock.

Figure 1

(a) Scattering spectra of four individual gold nanorods excited with a polarization parallel to the particles long axis. Since the repeatability of the scattering intensity is only within $~$20%, the spectra are normalized to facilitate the spectral comparison. (b) Spectra simulated within our BEM approach, using the gold dielectric function of Ref. 14 and a refractive index of $n_b=1.65$ for the substrate, for the particle shapes extracted from the SEM images reported in panel (c). The particle height is $45\hspace{0.5em}\mathrm{nm}$. The lengths of the scale bars in the lower panels are $100\hspace{0.5em}\mathrm{nm}$.

Figure 2

(a) Simulated spectra for nanorods with a diameter of 30 nm and for height-to-diameter ratios of 2:1, 3:1, and 4:1. In our simulations we use a dielectric function representative for gold[14] and a homogeneous dielectric background ($n_b=1.5$), and add stochastically surface roughness according to the prescription of Eq. (1) with ${\sigma }_h=3$ nm and for different $\Delta h$ values, which determine the height variations of surface roughness. Each spectrum is averaged over 100 randomly generated nanoparticles. The solid lines report the spectra of the smooth nanorods in the panel for $\Delta h=2$ nm, and the mean values of the spectra otherwise. The thick gray lines report results for rippled rods, as discussed in the text. The spectra for ratios 2:1 and 3:1 have been magnified by factors of 15 and 2, respectively. (b) Surface charge distributions ${\sigma }_a$ for the optically active plasmon modes for the smooth (left), rippled (middle), and rough (right) nanorods.

Figure 3

Comparison of full simulations and perturbation theory of Eq. (6), for the positions of the resonance energies of the optically active surface plasmon modes with polarization along the long axis of the rod. The open and solid symbols report results obtained within first- and second-order perturbation theory, respectively. In the inset we show a blow-up for the nanorod with a height-to-diameter ratio of 4:1.