Electron- and Lattice-Temperature Dependence of the Optical Response of Gold Nanoparticles

Abstract

Transient absorption spectroscopy is routinely used to study the electron dynamics in plasmonic gold nanoparticles. Typically, the transient absorption bleach is analyzed as measure for the electron temperature. However, the implicitly assumed linear dependence between bleach intensity and temperature has not been systematically studied. Similarly, the influence of lattice heating also lacks a detailed analysis. Here, we solve momentum-resolved metal Boltzmann-Bloch equations for a semi-analytic access to the temperature-dependent gold nanoparticle absorption. We confirm the theory with steady state and transient absorption experiments, define regions of linear correlation between transient absorption bleach intensity and electron temperature and reveal a strong impact of the lattice temperature on the TA bleach intensity.

Figures (7)

• Figure 1: Inverse two-temperature relaxation rate $\gamma^{-1}(T_e,T_l)=(\gamma^{(ep)}_{k_F}(T_e,T_l) + \gamma_S)^{-1}$ for selected phonon temperatures $T_l$. The dashed line represents the rate at $T_e=T_l$.
• Figure 2: Temperature--dependent absorption spectra of AuNP. The spectra were normalized such that the relative ratios are preserved.
• Figure 3: (a) Differential steady--state absorption spectra from the data plotted in Fig. \ref{['Paper:fig:cw-abs']}. The spectra are referenced to the $T_{eq}=200$ K spectrum. (b) Calculated differential absorption spectra for the same temperatures as for (a). The spectra in (a) and (b) are scaled by a factor defined by the absolute value of the most intense $\Delta A$. The dashed lines represent the baseline of the $200$ K reference. (c) Experimental and calculated differential absorption bleach versus equilibrium temperature increase $\Delta T_{eq}$ relative to $200$ K. Note that the theory curve consists of individual data points and is not a fit to the experimental values.
• Figure 4: (a) Pump–probe TA bleach dynamics at $T_{eq,0} = 295$ K for different pump fluences. (b) Experimental (${-}$) and theoratical (${--}$) TA spectra at $25$ ps delay, as highlighted in (a). The calculated spectra are scaled such that the bleach intensities at $\Delta T_{eq}= 37$ K match.
• Figure 5: Transient absorption spectra recorded at the delay time of maximum bleach contrast for equilibrium lattice temperatures $T_l = T_{eq}$. At each temperature, spectra are shown for four excitation energies labeled by the corresponding initial electron temperature rise $\Delta T_e$ (i.e., different pump fluence). Dashed curves show calculated TA referenced to the equilibrium spectrum and scaled so that the bleach minimum matches the experimental minimum.