Experimental and Ab Initio Ultrafast Carrier Dynamics in Plasmonic Nanoparticles

Ultrafast pump-probe measurements of plasmonic nanostructures probe the nonequilibrium behavior of excited carriers, which involves several competing effects obscured in typical empirical analyses. Here we present pump-probe measurements of plasmonic nanoparticles along with a complete theoretical description based on first-principles calculations of carrier dynamics and optical response, free of any fitting parameters. We account for detailed electronic-structure effects in the density of states, excited carrier distributions, electron-phonon coupling, and dielectric functions that allow us to avoid effective electron temperature approximations. Using this calculation method, we obtain excellent quantitative agreement with spectral and temporal features in transient-absorption measurements. In both our experiments and calculations, we identify the two major contributions of the initial response with distinct signatures: short-lived highly nonthermal excited carriers and longer-lived thermalizing carriers.

Figure 1

(a) Map of the differential extinction cross section of colloidal gold nanoparticles as a function of pump-probe delay time and probe wavelength for a pump pulse of $68\mu \mathrm{J}/{\mathrm{cm}}^2$ energy density at 380 nm. At time 0, the pump pulse excites the sample. As the electrons thermalize internally, extinction near the absorption peak (533 nm) decreases (negative signal) while extinction in the wings to either side of the absorption peak increases (positive signal). After $\sim 700\mathrm{fs}$, the electrons began to thermalize with the lattice and the differential extinction decays. A contour line is drawn in black at zero extinction change. Differential extinction (b) as a function of probe wavelength at a set of times relative to the pump-probe delay time with maximum signal, $t_{\max }=700\mathrm{fs}$ and (c) as a function of pump-probe delay time at various probe wavelengths.

Figure 2

Difference of the predicted time-dependent electron distribution from the Fermi distribution at 300 K, induced by a pump pulse at 560 nm with intensity of $110\mu \mathrm{J}/{\mathrm{cm}}^2$. Starting from the carrier distribution excited by plasmon decay at $t=0$, electron-electron scattering concentrates the distribution near the Fermi level with the peak optical signal at $\sim 700\mathrm{fs}$, followed by a return to the ambient-temperature Fermi distribution and a decay of the optical signal due to electron-phonon scattering.

Figure 3

Comparison of measured and predicted differential cross sections at 530-nm probe wavelength for pump excitation at 560 nm with intensities of 21, 34, 68, and $110\mu \mathrm{J}/{\mathrm{cm}}^2$ as a function of time. Panel (a) compares absolute measurements (circles) and calculated values (solid lines) of the differential cross section, while the remaining panels are normalized by the peak value: (b) and (c) show measurements and predictions, respectively, over the full time range, while (d) and (e) focus on the initial rise period. Increased pump power generates more initial carriers, which equilibrate faster (shorter rise time) to a higher electron temperature (larger signal amplitude), which subsequently relaxes more slowly due to increased electron heat capacity. The ab initio predictions quantitatively match all these features of the measurements.

Figure 4

(a) Measured and (b) calculated differential cross sections normalized by peak value for 380-nm pump pulse with 34- and $110\text{−}\mu \mathrm{J}/{\mathrm{cm}}^2$ intensities, monitored at 560-nm probe wavelength. Contributions from the nonthermal electrons dominate at lower pump power, resulting in a fast signal rise and decay. [Correspondingly, smaller signals cause the higher relative noise in the measurements shown in (a).]

Figure 5

(a) Measured and (b) calculated differential cross sections for 560-nm pump pulse with $110\text{−}\mu \mathrm{J}/{\mathrm{cm}}^2$ intensity, normalized by peak value, for probe wavelengths of 480, 510, and 620 nm. Rise and decay are faster for probe wavelengths far from the interband resonance at 530 nm, where nonthermal effects are relatively more important.