Plasmon lifetime enhancement in a bright-dark mode coupled system

Metallic nanoparticles can localize the incident light to hot spots as plasmon oscillations, where the intensity can be enhanced by up to four orders of magnitude. Even though the lifetime of plasmons is typically short, it can be increased via interactions with quantum emitters, e.g., spaser nanolasers. However, molecules can bleach in days. Here, we study the lifetime enhancement of plasmon excitations due to the coupling with longer-lifetime dark plasmon modes. We apply an analytical model based on harmonic oscillators to demonstrate that a coupled system of bright and dark plasmon modes decays more slowly than the bright mode alone. Furthermore, exact solutions of the three-dimensional Maxwell equations, i.e., finite-difference time domain, demonstrate that the lifetime of the coupled system significantly increases at the hot spot, which is not predictable by far-field response. The decay of the overall energy of such a coupled system, which can be extracted from experimental absorption measurements, is substantially different from the decay of the hot spot field. This observation enlightens the plasmonic applications in which the hot spot intensity enables the detection of the optical responses.

Figure 1

Description of the coupled plasmonic system: a metal nanosphere supporting a bright plasmon mode and a metal nanorod dimer supporting a dark plasmon mode, which cannot be excited directly by the incident light. The graph shows representative optical responses of the individual and coupled systems; the dark mode appears when it is coupled to the bright mode.

Figure 2

Normalized lifetime of the coupled system, defined by Eq. (4), as a function of the coupling constant $f$ for (a) ${\gamma }_2=0.001\omega$ and (b) ${\gamma }_2=0.01\omega$. In both cases, ${\omega }_1=1.0\omega$, and ${\gamma }_1=0.1\omega$.

Figure 3

Plasmon intensity for the uncoupled (dashed line) and coupled plasmon modes for ${\omega }_1=1.0\omega ,{\omega }_2=0.9\omega ,{\gamma }_1=0.1\omega ,{\gamma }_2=0.01\omega$, and $f=0.025\omega$, where the timescale is determined by considering an excitation frequency $\omega$ corresponding to a wavelength of 500 nm. In the inset, the axes are zoomed in at a later timescale.

Figure 4

Scattering cross section of a single nanorod and that of a nanorod dimer, obtained by FDTD simulations. The inset shows the schematics of the system with the given parameters: $a=20$ nm, $b=80$ nm, $w=10$ nm. The incident plane wave is normally incident and polarized along the nanorod axis.

Figure 5

Plasmon modes of (a) a single nanorod and (b) a nanorod dimer, excited by local dipole sources: red: in the middle, oriented along the nanorod axis; blue: in the middle, oriented perpendicular to the nanorod axis; and black: in the end, oriented along the nanorod axis. The distance between the dipole source and the nanostructure is 20 nm in each case; the geometrical parameters are the same as the ones in Fig. 4, i.e., nanorod length of 80 nm, with a cross section of $20\times 20{\mathrm{nm}}^2$, and the separation between the nanorods in the dimer configuration is 10 nm.

Figure 6

Scattering cross section spectra of the Pt nanosphere with a 75-nm radius (black dashed line) and the coupled systems with different interstructure distances $d$. The source is a plane wave at normal incidence, polarized perpendicular to the dimer axis, as shown in the inset. Nanorod length is 80 nm, with a cross section of $20\times 20{\mathrm{nm}}^2$, and the separation between the nanorods is 10 nm.

Figure 7

Lifetime of the coupled system, defined by the exponential decay fit, that is applied to the electric field intensity over time for different interstructure distances. The inset shows the electric field intensity for $d=10$ nm and $d=50$ nm (solid lines), and the peaks of the oscillating field are shown by the dashed lines. The formula given in the inset is the fit formula to obtain $\tau$.