Broadband measurements of the transient optical complex dielectric function of a nanoparticle/polymer composite upon ultrafast excitation

We determined experimentally the complex transient optical dielectric function of a well-characterized polyelectrolyte/gold-nanoparticle composite system over a broad spectral range upon short pulse laser excitation by simultaneously measuring the time-dependent reflectance and transmittance of white light pulses with femtosecond pump-probe spectroscopy. We extracted directly the ultrafast changes in the real and imaginary parts of the effective dielectric function, ${\epsilon }_r^{\text{eff}}(\omega ,t)$ and ${\epsilon }_i^{\text{eff}}(\omega ,t)$, from the experiment. This complete experimental set of information on the time-dependent complex dielectric function challenges theories modeling the transient dielectric function of gold particles and the effective medium.

Figure 1

Transmittance and reflectance spectra at normal incidence (black solid lines) together with the real and imaginary parts of the static dielectric function (red dashed lines) derived from these measurements.

Figure 2

The contour plots (b) and (c) show the simultaneously measured transient spectra of the reflectance and transmittance, respectively. Transient changes of reflectance (a) and transmittance (d) for three single energies from horizontal cuts through (b) and (c). Three difference spectra [vertical cuts through (b) and (c)] are presented in panels (e) and (f).

Figure 3

Calculated change in (a) reflectance and (b) transmittance at 543 nm for the assumed sets of values of the real and imaginary parts of the effective dielectric function. The functions $\Delta R({\epsilon }_r^{\text{eff}},{\epsilon }_i^{\text{eff}})$ and $\Delta T({\epsilon }_r^{\text{eff}},{\epsilon }_i^{\text{eff}})$ are calculated individually for each probe-wavelength.

Figure 4

Transient complex dielectric function determined from simultaneous measurements of the reflectance and transmittance. Temporal and spectral projections are again chosen for 2.06, 2.28, and 2.48 eV and for 1, 3, and 5 ps after excitation.

Figure 5

Coefficients $r_{1,2}\left(\omega \right)$ and $t_{1,2}\left(\omega \right)$ from Eqs. (1) and (2) determined from Figs. 2 and 4. These coefficients yield an excellent match for all delay times simultaneously.

Figure 6

Trajectories of the complex dielectric function at five selected spectral positions. They show the different evolution of changes in the real and imaginary parts after laser-induced heating of the gold particles.