Coupled plasmon resonances in monolayers of metal nanoparticles and nanoshells

We report on the coupled plasmon resonances in a monolayer consisting of metal or metallodielectric nanoparticles with the dipole and quadrupole single-particle resonances. The theoretical models included spherical gold and silver particles and also gold and silver nanoshells on silica and polystyrene cores forming two dimensional random clusters or square-lattice arrays on a dielectric substrate (glass in water). The parameters of the individual particles were chosen so that a quadrupole plasmon resonance could be observed along with the dipole-scattering band. By using an exact multipole cluster-on-a-substrate solution, we showed that particle-substrate coupling can be neglected in the calculation of the monolayer-extinction spectra, at least for the glass-in-water configuration. When the surface particle density in the monolayer was increased, the dipole resonance became suppressed and the spectrum for the cooperative system was determined only by the quadrupole plasmon. The dependence of this effect on the single-particle parameters and on the cluster structure was examined in detail. In particular, the selective suppression of the long-wavelength extinction band was shown to arise from the cooperative suppression of the dipole-scattering mode, whereas the short-wavelength absorption spectrum for the monolayer was shown to be little different from the single-particle spectrum. For experimental studies, the silica/gold-nanoshell monolayers were fabricated by the deposition of nanoshells on a glass substrate functionalized by silane-thiol cross-linkers. The measured single-particle and monolayer-extinction spectra are in reasonable agreement with simulations based on the nanoshell geometrical parameters (scanning electron microscopy data). Finally, we evaluated the sensitivity of the coupled quadrupole resonance to the dielectric environment to show a universal linear relation between the relative shift in the coupled-quadrupole-resonance wavelength and the relative increment in the environment refractive index.

Figure 1

(Color online) The coordinate system for the exact CSS solution. The incident light propagates in the $+z$ direction from a half-infinite substrate (the dielectric function ${\epsilon }_s$) to a half-infinite homogeneous medium $\left({\epsilon }_m\right)$ surrounding two-layered 2D-cluster particles.

Figure 2

(Color online) Extinction spectra for $\mathrm{Si}{\mathrm{O}}_2∕\mathrm{Au}$-type nanoshells with gold-shell thicknesses of 15, 20, and $25\mathrm{nm}$ and with core diameters of 50, 100, and $150\mathrm{nm}$.

Figure 3

(Color online) Extinction spectra of a $6\times 6$ lattice array of $100\mathrm{nm}$ silver spheres assembled on a glass substrate $(n_s=\sqrt{{\epsilon }_s}=1.48)$ in water and separated by $50\mathrm{nm}$ distances. Calculations are by the exact CSS solution and without the substrate (the same array in water). The single-particle spectrum is shown for comparison.

Figure 4

(Color online) Extinction spectra for $4\times 4$ lattice clusters built up from $\mathrm{Si}{\mathrm{O}}_2∕\mathrm{Au}$-type nanoshells with sizes of (a) $160∕20\mathrm{nm}$ and (b) $190∕25\mathrm{nm}$. The relative interparticle-distance parameter $s$ was varied from 1 to 0.1.

Figure 5

(Color online) Extinction spectra for $N\times N$ lattice clusters built up from [(a) and (b)] $\mathrm{Si}{\mathrm{O}}_2∕\mathrm{Au}$ nanoshells $(140∕20\mathrm{nm})$ and (c) silver $100\mathrm{nm}$ nanospheres. $N=1$, 2, 4, and 6. The interparticle-distance parameter $s$ is 0.1 (a), 0.2 (b), and 0.5 (c).

Figure 6

(Color online) Comparison of the extinction spectra for lattice and random clusters made up of $\mathrm{Si}{\mathrm{O}}_2∕\mathrm{Au}$ $(160∕20\mathrm{nm})$ nanoshells with particle numbers of (a) 16 and (b) 36. Also shown are the spectra for isolated particles $(N=1)$. The interparticle-distance parameter is 0.1, 0.2, and 0.35 for the lattice clusters and 0.1 for the random clusters. The average particle density for the random clusters is (a) 0.415 and (b) 0.36 for 16 and 36 particles, respectively.

Figure 7

(Color online) Extinction, scattering, and absorption spectra for random clusters made up of thirty-six $100\mathrm{nm}$ diameter silver particles. The minimal-distance parameter $s$ is 0.05, and the average particle densities are (a) 0 (a single particle), (b) 0.06, (c) 0.12, (d) 0.25, (e) 0.35, and (f) 0.4. The calculated results were averaged over five statistical realizations.

Figure 8

(Color online) Extinction, scattering, and absorption spectra for random clusters made up of 36 PS/Ag-type silver nanoshells (core diameter of $110\mathrm{nm}$; shell thickness of $20\mathrm{nm}$). The minimal-distance parameter $s$ is 0.05, and the average particle densities are (a) 0 (a single particle), (b) 0.06, (c) 0.12, (d) 0.25, (e) 0.35, and (f) 0.4. The calculated results were averaged over five statistical realizations.

Figure 9

(Color online) Same as in Fig. 7 but for PS/Au-type gold nanoshells (core diameter of $110\mathrm{nm}$; shell thickness of $35\mathrm{nm}$).

Figure 10

(Color online) Same as in Fig. 8 but for gold nanoshells with a core diameter of $200\mathrm{nm}$ and a shell thickness of $20\mathrm{nm}$.

Figure 11

(Color online) Dark-field microscopic images of glass-adsorbed $180\mathrm{nm}$ gold nanoshells. Incubation times: (a) $10\min$, (b) $15\min$, (c) $20\min$, (d) $30\min$, and (e) $60\min$. (f) AFM image of a monolayer portion showing closely packed particles (incubation time of $12\mathrm{h}$).

Figure 12

SEM image of a monolayer portion showing self-assembled silica/gold nanoshells on a silane-functionalized quartz substrate. The average nanoparticle diameter is $245\pm 12\mathrm{nm}$ (standard deviation, SEM data), and the average silica-core diameters are $200\pm 10\mathrm{nm}$ (SEM data) and $212\pm 5\mathrm{nm}$ (DLS data).

Figure 13

(Color online) Normalized experimental and theoretical extinction spectra (a) for a gold-nanoshell suspension and (b) for a monolayer on a silane-functionalized glass substrate in water. The theoretical shell thickness $\left(17\mathrm{nm}\right)$ was chosen from the best agreement between the suspension spectra and is close to the experimental value ($20\mathrm{nm}$, DLS data). The monolayer theoretical spectra were averaged for five independent generations of random arrays $(N=36)$, with the average surface particle densities $\rho =0.25$ and 0.4 ($s$ parameter of 0.05).

Figure 14

(Color online) Normalized experimental and theoretical extinction spectra for a suspension of $\mathrm{Si}{\mathrm{O}}_2∕\mathrm{Au}$ nanoshells ($200∕20\mathrm{nm}$, SEM data) and for a monolayer on a silane-functionalized quartz substrate in water. The experimental monolayer extinction was multiplied by 6 before normalization, according to Eq. (22). The monolayer theoretical spectra were averaged for five independent generations of random arrays $(N=36)$, with the average surface particle density $\rho =0.25$ (the $s$ parameter equals 0.05). The fitting average core diameter and gold-shell thickness are 230 and $15\mathrm{nm}$, respectively.

Figure 15

(Color online) (a) Experimental (circles) and theoretical (crosses) dependences of the normalized quadrupole-resonance wavelength shift $\Delta {\lambda }_q∕{\lambda }_q$ on the normalized external-medium refractive index increment $\Delta n_m∕n_m$. Calculations and measurements for $\mathrm{Si}{\mathrm{O}}_2∕\mathrm{Au}$ $(190∕25\mathrm{nm})$ nanoshell monolayer in air, water, ethyl alcohol, hexane, and carbon tetrachloride. (b) Experimental dependence of $\Delta {\lambda }_q∕{\lambda }_q$ on $\Delta n_m∕n_m$ for the same monolayer placed in water and solutions of $m$-cresol (0%, 20%, 40%, 60%, and 80%). The straight lines show a linear approximation of the (a) theoretical and (b) experimental data.