Plasmonic interactions between a metallic nanoshell and a thin metallic film

The plasmonic interaction and optical properties of a metallic nanoshell near a metallic film are investigated theoretically and experimentally. The plasmon hybridization method is extended to include the screening effects mediated by dielectric backgrounds and a realistic description of the dielectric properties of the metal. We show that the plasmonic structure of the system depends strongly on the aspect ratio of the nanoshell (the ratio of inner to outer radius) and the thickness of the film. In the thin film limit, the plasmonic coupling between the nanoshell and the film induces a low-energy virtual state (VS) mainly consisting of delocalized thin film plasmons. We show that the energy and intensity of this state can both be controlled by the aspect ratio of the nanoshell and the thickness of the film. The theoretical results are found to agree well with experimental observations. Using finite-difference time-domain simulations, we show that the electromagnetic field enhancements induced by excitation of the VS can be very large and that the nanoshell/thin film system could serve as a tunable plasmonic substrate for surface enhanced spectroscopies.

Figure 1

(Color online) The geometry of the nanoshell-film system. Geometric variables $a$, $b$, $T$, and $Z_0$ represent the inner and outer radii of the nanoshell, the metallic film thickness, and the shell-film separation, respectively. $C_{lm}$, $S_{lm}$, $P_{\vec{k}}$, and $Q_{\vec{k}}$ are the amplitudes of the primitive nanoshell cavity, sphere plasmons, and the film plasmons on both sides. ${ϵ}_C$, ${ϵ}_S$, ${ϵ}_1$, ${ϵ}_2$, and ${ϵ}_F$ are the background dielectric constants of the nanoshell core, the nanoshell metallic layer, the embedding media above and below the film, and the metallic film, respectively. The effects of varying the dielectric background constants are investigated in Fig. 4.

Figure 2

(Color online) [(a)–(c)] Schematic illustration of the nanoshell-metallic film interaction as the aspect ratio $(x=a∕b)$ of the nanoshell increases. The light blue area to the left represents the plasmonic density of states of the film $\rho \left(\omega \right)$. The dark blue area represents the effective continuum $\rho V_{l=1}^2\left(\omega \right)$. The right part illustrates the geometry and energy of the discrete nanoshell plasmon. The black curves depict the absorption spectrum resulting from the plasmonic interaction between the nanoshell and the film.

Figure 3

Optical absorption spectra of the Au nanoshell-thin film system in geometries corresponding to Fig. 2. The solid lines are dipolar optical absorption as a function of frequency for a nanoshell of outer radius $b=50\mathrm{nm}$ and different inner radii $a=20\mathrm{nm}$ [panel (a)], $a=40\mathrm{nm}$ [panel (b)], and $a=45\mathrm{nm}$ [panel (c)]. The center of the nanoshell is at a position $Z_0=53\mathrm{nm}$ outside a metallic film of thickness $T=12\mathrm{nm}$. The gold metal is modeled using Johnson-Christy data (Ref. 49) and ${ϵ}_C=2.04$ $\left(\mathrm{Si}{\mathrm{O}}_2\right)$, ${ϵ}_1=1$ (air), and ${ϵ}_2=2.25$ (glass). The dotted lines are the absorption spectra for the individual nanoshells. The peaks labeled “VS” are the virtual states. The peaks labeled “B” and “AB” are the discrete dipolar bonding and antibonding nanoshell peaks, respectively. The antibonding peaks are strongly damped and broadened due to interband transitions.

Figure 4

Effect of the background dielectric on the optical absorption of a nanoshell near a metallic film for perpendicular polarization $m=0$. The nanoshell has $a=40\mathrm{nm}$, $b=50\mathrm{nm}$, and $Z_0=53\mathrm{nm}$. The film thickness is $T=8\mathrm{nm}$. Panel (a) shows the spectra for the film in vacuum. Panel (b) shows the spectra for ${ϵ}_1=1$ and ${ϵ}_2=5$. Panel (c) is for ${ϵ}_1=5$ and ${ϵ}_2=1$. Panel (d) is for ${ϵ}_1={ϵ}_2=5$.

Figure 5

(Color online) Extinction spectra (left panels) and local electric field enhancements (right panels) calculated by FDTD for the gold nanoshell/slab system for perpendicular polarization $m=0$. The slab has a thickness $T=8\mathrm{nm}$ and lateral dimensions $300\times 300{\mathrm{nm}}^2$. It is covered by a PVP spacer layer $(ϵ=2.25)$ of thickness $3\mathrm{nm}$ and placed on a glass substrate $({ϵ}_2=2.25)$ of thickness $100\mathrm{nm}$. The nanoshell has an outer radius $b=50\mathrm{nm}$ and a silica core $({ϵ}_C=2.04)$. The inner radii are (a) $a=20\mathrm{nm}$, (b) $a=40\mathrm{nm}$, and (c) $a=45\mathrm{nm}$. The dotted lines are the absorption spectra calculated using the PH method. The arrows indicate the energies for which the electric field enhancements were calculated. The maximum field enhancement factor in each structure is 120.8, 177.2, and 244.3 for panels (a), (b), and (c), respectively.

Figure 6

SEM image of a representative sample of a thin Au layer on which Au nanoshells have been dispersed. The Au film thickness is $4\mathrm{nm}$ and the nanoshell has a $60\mathrm{nm}$ radius core made from $\mathrm{Si}{\mathrm{O}}_2$ and a shell thickness of $10\mathrm{nm}$. The Au film is thermally evaporated onto a clean glass slide at base pressure of ${10}^{-6}\text{torr}$. A thin Ti film with $1.5\mathrm{nm}$ thickness is used as an adhesion layer between the gold film and the glass substrate. A spacer layer of $(3.5\pm 0.5)\mathrm{nm}$ is formed by depositing polyvinylpyridine (PVP) from a 1% ethanol solution for $8\mathrm{h}$.

Figure 7

(Color online) Experimental extinction spectra of the nanoshell/film system with film thickness of $12\mathrm{nm}$. The spectra are taken using $p$-polarized light at varying incident angles.

Figure 8

(Color online) Extinction spectra for perpendicular polarization $m=0$ measured for (a) air-ambient and (b) PVP-coated samples. In each panel, the measurement is performed for four different film thicknesses, $T=4,8,12$, $16\mathrm{nm}$, respectively. The inset in panel (b) is the magnified low-energy part of the $T=4\mathrm{nm}$ curve for identifying the VS.

Figure 9

(Color online) Comparison of experimentally obtained energies of the $m=0$ VS with the results from PH as a function of film thickness for different dielectric constants of the embedding medium ${ϵ}_1$. The curves are the theoretical calculations with ${ϵ}_1$ increasing from 1.0 to 5.0. The blue and red symbols are the experimental measurements for air-ambient and PVP-overcoated samples, respectively.

Figure 10

(Color online) Comparison of experimentally obtained energies of the $m=1$ VS with the results from PH as a function of film thickness for different dielectric constants of the embedding medium ${ϵ}_1$. The lines and the symbols refer to the same structures as in Fig. 9.