Infrared plasmonics: STEM-EELS characterization of Fabry-Pérot resonance damping in gold nanowires

Materials possessing strong midinfrared responses are of current interest because of their potential application to long-wavelength metamaterials, photonic devices, molecular detection, and catalysis. Here, we utilize high-energy resolution (80 ${\mathrm{cm}}^{-1}$, 10 meV) electron-energy-loss spectroscopy (EELS) in a monochromated and aberration-corrected scanning transmission electron microscope (STEM) to resolve multipolar surface plasmon resonances (SPRs), sometimes called Fabry-Pérot (FP) resonances, in gold nanowires with mode energies spanning from $\sim 1000$ to $8000{\mathrm{cm}}^{-1}$. STEM-EELS provides access to these mid- to near-IR responses in a single acquisition, avoiding the difficulties inherent in obtaining the same data using near-field optical techniques. The experimentally measured FP resonance energies and linewidths, together with analytical modeling and full-wave numerical electrodynamics simulations, provide a comprehensive picture of the radiative and intrinsic contributions to the total damping rates. We find some FP modes with dephasing times $>60\mathrm{fs}$, which is almost twice the longest previously reported plasmon dephasing time for individual Au nanoparticles in the infrared. The long dephasing times and the broad tunability of the FP resonance energies throughout the infrared region suggest additional opportunities for harnessing infrared plasmonic energy before dephasing occurs.

Figure 1

Comparison of experimentally measured (left) and simulated EEL spectra (right) of Au nanowires. (a) STEM-EELS spectra of Au nanowires with lengths ranging from 0.52 to $9.8\mu \mathrm{m}$. The spectra were acquired with an electron probe impact parameter of 10 nm outside the nanowire, along the long axis. The FP modes up to order $m=5$ are indicated by a colored vertical bar. (b) Simulated EEL and CL spectra of the same nanowires obtained at the same impact parameter.

Figure 2

Experimentally measured FP resonance energies as a function of Au nanowire length. $m$ indicates the order of the FP mode. The dashed black lines are added only to guide the eye.

Figure 3

Comparison of experimental, theoretical, and simulated FP dispersion curves, mode energies, and mode linewidths. (a) Dispersion curve for dipolar ($m=1$) FP mode. The red shading denotes the extinction coefficient of the dipolar FP mode calculated from the analytic model. The experimental (green dots) and simulated (purple dots) track well with the analytical extinction coefficient. The vacuum light and quasistatic dipolar mode dispersion curves are shown for comparison. (b) Experimental and simulated FWHMs for all FP modes obtained from the EEL spectra in Fig. 1 as a function of nanowire length. The experimental (solid green) and simulated (solid purple) FWHMs for the dipolar ($m=1$) FP modes are compared to the FWHM obtained from the analytical model. The FWHM decreases as $L$ increases, with the analytic value eventually falling below the Drude linewidth (dashed line) near $L=2.5\mu \mathrm{m}$. The FWHMs of higher-order FP modes ($m>1$, gray dots) are presented for comparison. The inset shows the FWHM behavior for small nanowire lengths.

Figure 4

Induced potential and electric field of a gold prolate spheroid placed in a uniform $z$-polarized field (a). Evolution of the induced electric field along the applied field polarization axis $(0,0,z)$ (b) and perpendicular to the applied field polarization axis $(x,0,0)$ (c), clearly showing the increasing spill-out and decreasing internal magnitude of the induced field with increasing spheroid aspect ratio.

Figure 5

(a) Experimental plasmon dephasing times for Au nanowires of selected lengths. The dashed lines are provided to guide the eye. The first three FP modes are labeled according to $m=1,2,3$. (b) Radiative damping weights determined from the intensity ratio of the simulated CL/EEL spectra shown in Fig. 1. Data from the same nanowire are connected by dashed lines to guide the eye.