Transient optics of gold during laser irradiation: From first principles to experiment

Intense femtosecond laser pulses can induce dramatic changes on different properties of materials. Laser induced changes of the optical properties are particularly relevant, since they can lead to a modification of the amount of energy that the material absorbs from the laser pulse. In noble metals, changes of reflectivity upon femtosecond laser illumination are expected to be strong due to the excitation of $d$ electrons. In this work we perform measurements of the reflectivity of laser excited gold in the infrared and in the ultraviolet range, respectively. We find a remarkable dependence of the reflectivity on laser fluence, which is in turn different in both ranges of photon energy. In order to understand the behavior of the reflectivity in laser excited solids and to explain our measured reflectivity curves we develop a theoretical scheme in the framework of the two-temperature model with the electronic temperature as the key parameter. Our approach is based on all-electron calculations of the interband contribution to the reflectivity and a careful determination of the intraband, Drude-like terms and a realistic model for the space and time resolved energy transfer from a Gaussian laser pulse into the electronic system. We obtain very good agreement between experiment and theory and identify the main mechanisms for reflectivity changes as a function of laser fluence.

Figure 1

Models and parameters used in this work to relate an experimentally measured self-reflectivity to a calculated microscopic dielectric response.

Figure 2

DOS of the valence electrons of crystalline gold with the atomic shell configuration $\left[\mathrm{Xe}\right]4{\mathrm{f}}^{14}5{\mathrm{d}}^{10}6{\mathrm{s}}^1$ calculated at RT with wien2k. The broad $d$-band edge of $0.9\mathrm{eV}$ width is highlighted in gray. The Fermi-Dirac distribution for different $T_e$ is included and shifted by $\mathrm{\Delta }\mu \left(T_e\right)$. The obtained RT reflectivity is shown in the inset compared to the literature value from Johnson and Christy [22].

Figure 3

(a) Calculated reflectivity map $R(T_e,\hslash \omega )$ in dependence of the electronic temperature $T_e$ and photon energy $\hslash \omega$ obtained by DFT calculations using a temperature-dependent modification of the wien2k code. In (b) the DFT calculations are extended by the effect of eh collisions. Photon energies at 1.66 eV and 4.98 eV are marked with dotted lines at which the calculated results are compared to experiment.

Figure 4

Schematic picture of the nearly-Gaussian laser focus spot with experimental parameters. The enlargement shows the 2D-model geometry in cylindrical coordinates with the source term $S(r,z,t,T_e)$.

Figure 5

Single-shot self-reflectivity of gold measured at different incident pulse energies for laser pulses with $\hslash \omega =1.66\mathrm{eV}$ (IR) and $\tau =0.6\mathrm{ps}$ (diamonds in red and orange) in (a), $\hslash \omega =4.98\mathrm{eV}$ (UV) and $\tau =1.6\mathrm{ps}$ (circles in blue and pink) in (b), respectively, focused on a spot with $b=85\mu \mathrm{m}$ compared to simulations obtained by using temperature-dependent DFT calculations, combined with the effect of eh collisions. The literature values of Johnson and Christy for low temperatures are $R_{1.66\mathrm{eV}}^{\mathrm{Au}}=0.974$ (black bar) and $R_{4.98\mathrm{eV}}^{\mathrm{Au}}=0.340$ (gray bar) [22].