Decay of dark and bright plasmonic modes in a metallic nanoparticle dimer

We develop a general quantum theory of the coupled plasmonic modes resulting from the near-field interaction between localized surface plasmons in a heterogeneous metallic nanoparticle dimer. In particular, we provide analytical expressions for the frequencies and decay rates of the bright and dark plasmonic modes. We show that, for sufficiently small nanoparticles, the main decay channel for the dark plasmonic mode, which is weakly coupled to light and, hence, immune to radiation damping, is of nonradiative origin and corresponds to Landau damping, i.e., decay into electron-hole pairs.

Figure 1

Sketch of a nanoparticle dimer formed by two spherical nanoparticles of radii $a_1$ and $a_2$ separated by a distance $d$, together with the coordinate system used in the text. The polarization $\widehat{\epsilon }$ of the localized surface plasmons forming an angle $\theta$ with the $z$ axis is also shown.

Figure 2

(a) Frequencies ${\omega }_{\pm }$ [Eq. (11)], (b) Landau damping linewidths ${\gamma }_{\pm }^{\mathrm{L}}$ [Eq. (22)], and (c) radiative damping linewidths ${\gamma }_{\pm }^{\mathrm{r}}$ [Eq. (26)] of the $+$ (solid lines) and $-$ (dashed lines) coupled plasmonic modes as a function of the polarization angle $\theta$ for ${\tilde{\omega }}_1/{\tilde{\omega }}_2=1$ (thin lines) and ${\tilde{\omega }}_1/{\tilde{\omega }}_2=1.05$ (thick lines). The bright (dark) modes for which the two LSPs are in phase (in antiphase) are represented by red/gray (black) curves. In the figure, the parameters are $a_1=a_2=a,d=3a,\hslash {\tilde{\omega }}_1/E_{\mathrm{F}}^{\left(1\right)}=1$, and spillout is neglected.

Figure 3

Landau damping (solid and dotted lines) and radiation damping (dashed-dotted and dashed lines) linewidths for transverse polarization $\theta =\pi /2$ as a function of nanoparticle radius $a$ of the bright ($+$, light gray/red lines) and dark ($-$, black lines) mode. (a) Homogeneous dimer composed of two Ag nanoparticles. The thin gray line in the figure corresponds to the absorption losses measured in Ref. [38]. (b) Heterogeneous Ag-Au dimer. In the figure, $d=3a$ and ${\epsilon }_{\mathrm{m}}=4$.