Surface-Plasmon-Enhanced Optical Forces in Silver Nanoaggregates

We use extended Mie theory to investigate optical forces induced by and acting on small silver nanoparticle aggregates excited at surface plasmon resonance. It is shown that single molecules can be trapped at junctions between closely spaced nanoparticles, which are simultaneously pulled together by optical forces. These effects could significantly influence surface-enhanced Raman scattering and related spectroscopies under normal experimental conditions and contribute to single-molecule sensitivity.

Figure 1

(a) Wavelength dependence of the molecular polarizability [10]; (b),(c) variation in optical potential $U(\lambda )$ in units of $k_{B}T$ ($T=300\mathrm{K}$) at the junction between Ag particles ($d=1\mathrm{n}\mathrm{m}$) for a three-sphere and a two-sphere system in water illuminated with a plane wave polarized parallel to the symmetry axes.

Figure 2

(a) Spatial variation of optical potential $U$ in units of $k_{B}T$ ($T=300\mathrm{K}$) around a three-sphere system ($R=25\mathrm{n}\mathrm{m}$, $d=1\mathrm{n}\mathrm{m}$, $I_0=10\mathrm{m}\mathrm{W}/\mu {\mathrm{m}}^2$) in water excited at a collective surface plasmon resonance [$\lambda =760\mathrm{n}\mathrm{m}$, see Fig. 1b]. (b) The conservative (gradient) force and the dissipative force along the $x$ axis through a dimer gap (see inset, $R=45\mathrm{n}\mathrm{m}$, $d=1\mathrm{n}\mathrm{m}$, $\lambda =550\mathrm{n}\mathrm{m}$). The intensity enhancement factors $M_1$ in the gap are $9.2\times {10}^5$ in (a) and $1.7\times {10}^5$ in (b). Molecular polarizability according to Fig. 1a.

Figure 3

(a) Variation in optical potential in a nanogap for a trimer system as a function of particle radius $R$ and interparticle separation $d$. (b) Variation in optical potential in nanogaps ($d=1\mathrm{n}\mathrm{m}$) at SPR as a function of the number of multipoles $L$ included in the Mie expansion.

Figure 4

(a) Polar plot of the optical force per area unit, ${}^{10}\log (⟨\mathbf{T}·\mathbf{n}⟩·\mathbf{n})$, for the lower particle in a dimer (see inset, $I_0=1\mathrm{m}\mathrm{W}/\mu {\mathrm{m}}^2$, $\lambda =514.5\mathrm{n}\mathrm{m}$, $R=45\mathrm{n}\mathrm{m}$, $d=1\mathrm{n}\mathrm{m}$); (b) interparticle optical potential $U(d,R)$ for dimers in water ($T=300\mathrm{K}$, polarization configuration shown in inset).