Nonlinear absorption in Au films: Role of thermal effects

The effective nonlinear optical absorption coefficient ${\beta }_{\mathrm{eff}}$ is measured for $20\text{−}\mathrm{nm}$-thick Au films at $630\mathrm{nm}$ as a function of pulse width. The $z$-scan measurements show that ${\beta }_{\mathrm{eff}}$ increases from $6.8\times {10}^{-7}$ to $6.7\times {10}^{-5}\mathrm{cm}{\mathrm{W}}^{-1}$ as the pulse width is varied from $0.1\text{to}5.8\mathrm{ps}$. To help interpret this $\sim 100\times$ increase, differential transmission and reflectivity measurements are performed using $775\mathrm{nm}$ pump and $630\mathrm{nm}$ probe pulses. All experiments are simulated with a two-temperature model for electrons and lattice. The pulse width dependence of ${\beta }_{\mathrm{eff}}$ is consistent with thermal smearing of $d$-band to conduction-band transitions, with ${\beta }_{\mathrm{eff}}$ arising from changes in the linear $\left(\mathrm{Im}{\chi }^{\left(1\right)}\right)$ absorption coefficient.

Figure 1

(Color online) Pulse width $\left({\tau }_p\right)$ dependence of nonlinear absorption coefficient ${\beta }_{\mathrm{eff}}$ (squares) extracted from the $z$-scan experiments and simulated values ${\beta }_{\mathrm{sim}}$ (circles) calculated from thermally induced changes to the linear absorption coefficient using the TTM. The line is a guide to the eyes.

Figure 2

(Color online) Time-dependent differential reflection (red) and transmission (blue) for a thin Au film pumped with a $200\mathrm{fs}$, $775\mathrm{nm}$ pulse of fluence $5.3\mathrm{mJ}{\mathrm{cm}}^{-2}$ and probed with $200\mathrm{fs}$, $630\mathrm{nm}$ pulses. The inset shows the correlation between the ${(\Delta T∕T)}_{\max }$ measured experimentally (dots) for different excitation pulse fluences and the peak electron temperature at the Au front surface determined theoretically from the TTM.

Figure 3

(Color online) Simulated time-resolved transmissivity from two-temperature model calculations for a $630\mathrm{nm}$, $600\mathrm{fs}$ pulse with $100\mathrm{nJ}$ energy and variable spot size. The focal spot diameter (FWHM) are $w_1=40\mu \mathrm{m}$, $w_2=60\mu \mathrm{m}$, $w_3=80\mu \mathrm{m}$, and $w_4=100\mu \mathrm{m}$. The inset shows an experimental $z$-scan trace (open circles) for the same pulse with corresponding fit (solid curve) using Eq. (1); the integers 1–4 in the inset correspond to the different beam diameters and indicate how a $z$-scan trace can be reconstructed from calculated thermally induced changes in optical properties.

Figure 4

(Color online) (a) Calculated ${\beta }_{\mathrm{sim}}$ as a function of pulse width for a pulse energy of $100\mathrm{nJ}$, and a beam diameter of $40\mu \mathrm{m}$. The shaded area indicates the range of conditions for which the experiments are performed. (b) ${\beta }_{\mathrm{sim}}$ as a function of peak pulse intensity for $500\mathrm{fs}$ pulses with a beam diameter of $40\mu \mathrm{m}$. The intensity at which the $z$-scan was taken for this pulse length is shown with an arrow. The behavior of the peak electron temperature $T_{\max }^{\left(e\right)}$, as a function of both parameters is plotted with the dashed line.