Electron and lattice dynamics following optical excitation of metals

Spectroscopic study of optically induced ultrafast electron dynamics in gold

“…͑6͒, assuming first that the transient reflectivity is proportional to the electron temperature, and second a value of 71 J m 3 K 2 for the constant A e . 16 The fitted curves are shown in Fig. 3.…”

“…In order to directly determine its real and imaginary parts, one can simultaneously measure the reflectivity and transmission of the sample, [13][14][15][16][17][18][19] if it is thin enough and deposited upon a transparent substrate. Since the real and imaginary parts of the dielectric function are related via Kramers-Kronig relations, each of them can be reconstructed from the other if the latter is measured over a sufficiently broad spectral range.…”

“…26 Since the measured film is thin compared to the ballistic electron range, 15,16 and because the pump spot size is much greater than the film thickness, the transient temperature gradients are small and so we can neglect heat transport. The modified two temperature model equations can then be written as…”

“…This equation describes an initial linear decay of the transient temperature in the high perturbation limit, 16 and an exponential decay at longer time delays corresponding to the low perturbation limit. It may be used to fit the decay of the transient reflectivity signal once additional assumptions are made to relate the signal to the electron temperature.…”

“…Often, the transient signal is analyzed by assuming that it depends linearly upon either the transient electron ͑and lattice͒ temperature, 6,10 or the transient excess total electron energy, 11 or the transient electron occupation number. 12 However, such an assumption ͑referred to as the "linearity assumption" from hereon͒ is not self-consistent since transient reflectivity and transmission signals appear to have a different temporal shape, [13][14][15][16][17][18] and hence cannot be both proportional to the same function of time, e.g., the transient electron temperature. As has been known since the early optical thermomodulation studies of metals, 19 rigorous analysis instead requires the transient reflectivity and transmission to be properly calculated from the dependence of the complex dielectric function upon the electron occupation number.…”