Time Measurement on a Femtosecond Scale
The advances in the generation of ultrashort laser pulses in the past decade have allowed to realize the long standing dream of probing ultrafast dynamic electronic processes directly in the time domain. The direct measurement of the temporal evolution of particle plasmon oscillations with fs time-resolution has become possible.
We use a Kerr-lens-mode locked mirror-dispersion-controlled Ti:Sapphire laser to obtain fs time-resolution . This laser system relies on multilayer chirped dielectric mirrors for intercavity group-delay-dispersion control [3,4]. The construction kit, consisting of a mirror set and the Ti:Sapphire crystal, was purchased from FEMTO (Vienna, Austria) and installed within the scope of a diploma work . The laser delivers nearly transform limited 15 fs pulses with a high quality outperforming many existing commercial laser system.
Interferometric AutocorrelationAs the standard method for a time measurement on the fs time scale we use interferometric autocorrelation .
Figure 1: Set-up for interferometric fs autocorrelation measurement
Fig.1 shows the interferometric autocorrelation measurement set-up applied in our fs time resolution experiments. The optical pulses from the fs laser are split into two pulses of identical power by a symmetric beam splitter. The pulses are delayed with respect to each other in the two arms of a Michelson interferometer by a variable pulse delay time t'. At the output of the Michelson interferometer the pulses are combined again and sent collinearly through an optically nonlinear material. Both pulses are irradiated collinearly onto the sample, as in the fs regime any finite angle between them is accompanied by a geometrically induced timing error across the beam cross section. Selective detection of the second or third harmonic intensity is accomplished by a photomultiplier after passing the light through appropriate optical filtes.
By measuring the second or third harmonic intensity versus the pulse delay time we obtain the second order autocorrelation function (ACF) G2(t') or third order ACF G3(t')
respectively. Tresp corresponds to the detectors response time. At zero time delay (t'=0) the signal is maximum. For a delay increment of one-half light period, the two light fields add with opposite phase resulting in a near-zero signal. So the interference fringes provide a direct and accurate self-calibration of the measurement. For delay times t' of more than the total pulse length the two pulses are no longer overlapping and the ACF shows a constant background signal: we find a peak to background ratio of 8:1 for the second order ACF and a peak to background ratio of 32:1 for the third order ACF. The difference is caused by the fact that in the first case the fourth power and in the latter case the sixth power of the respective electric fields is involved.
In general, the ACF contains information on the pulse length and the temporal dynamics of the harmonic generation process involved. Therefore E(t*) in Eq.1 and Eq.2 corresponds to the optical field which is responsible for the higher harmonic generation in the nonlinear material.
Temporal evolution of the laser pulse field
BBO-crystal serves as a nonlinear optical medium with an instantaneous response to the incoming laser pulse field. Thus the ACF contains only information on the incoming fs laser pulse field. In this case E(t*) = Epulse(t*) is valid.
Figure 2: (a) solid line: measured 3rd order ACF of the laser pulse (maximum normalized to 32), filled circles: envelope of the calculated ACF (the dashed line serves as a guide to the eye) (b) spectrum of the fs laser pulse train, (c) a fourier transformed laser pulse spectrum (which is found to be equivalent to the temporal shape of the laser pulse) serves as the driving laser pulse field in the model calculations
Fig.2a shows the measured 3 rd order ACF  of the laser pulse (solid line in Fig.2) using a 25 micron thick BBO-crystal as THG-medium. The temporal shape of the laser pulse is found by fitting the experimentally obtained ACF by a calculated one varying the time function Epulse(t) . The best fit was found by using the fourier transformed spectrum of the laser pulse for Epulse(t) (transform limited case), see Fig.2b and Fig.2c for the laser pulse spectrum and the fourier transformed spectrum, respectively. The numerical result is compared to the measured ACF of the laser pulse in Fig.2a, where for the clarity of presentation only the upper envelope of the calculated ACF is marked by the filled circles. We find an excellent agreement with the experimental data.
Temporal evolution of the particle plasmon oscillationThe set-up used for the laser pulse duration measurements (see. Fig.1) is also used for plasmon decay time measurements. By replacing the BBO crystal in the autocorrelator by a metal nanoparticle sample a broadening of the generated ACF in comparison to the BBO-ACF is observed. Work relying on this technique was reported in [8,9,10,11,12,13,7].
Due to the finite lifetime of the particle plasmon oscillation a metal nanoparticle serves as a nonlinear medium with a non-instantaneous response to the incoming laser pulse field. In this case the ACF reflects the convolution of the temporal shape of the laser pulse and the exponential temporal decay of the plasmon oscillation. The field responsible for higher harmonic generation corresponds to the driven plasmon oscillation field E(t*) = Eplasmon(t*) in the nanoparticle.
Therefore the broadening of the ACF yields direct information on the duration of the plasmon oscillation. The most plausible and straightforward method for evaluating the plasmon decay is to compare experimentally determined ACF's with simulated ACF's. Thereby we find back the temporal evolution of the plasmon field by fitting the experimentally determined ACF with calculated ACF's using the plasmon decay time as the only fit parameter.
For the applicability of this plasmon decay time measurement method some preconditions have to be fulfilled:
- The system under investigation must have a measurable optical nonlinearity. For SHG this is fullfilled by using specific non-centrosymmetric SHG optimized samples [9,12]. In contrast, THG is dipole-allowed and therefore an universal optical property found for all materials.
- The optical nonlinearity must originate directly from the process of interest, which in our case is the plasmon oscillation. In this case the optical nonlinearity serves as a noninvasive sensor of the temporal behaviour of the laser pulse driven plasmon fields.
- The optical nonlinearity must not change during the measurement time. Thus the photon flux within the exciting beams must be kept below a certain limit in order not to change the electron temperature in the metal nanoparticles and therefore the optical constants, which would lead to an excitation intensity dependent broadening of the ACF.
- By using nanoparticle ensembles, as typically used for experiments, inhomogeneous absorption band broadening due to nonuniform particle shapes within an investigated ensemble must be taken into consideration. This can be done by using a suitable decay time evaluation process, involving the measured inhomogeneous absorption band in the calculation procedure .
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