Spectroscopy for Materials Characterization. Группа авторов
3.4 Scheme of a typical pump–probe setup.
On the second arm in Figure 3.4, supercontinuum generation is used to generate the probe pulse, a very common configuration in TA. The white light can be easily generated focusing a small portion of the 800 nm beam in a suitable material (sapphire crystal, water cuvette, etc.), generating a broadband pulse extending from 400 to 700 nm. The intensity of the 800 nm beam can be controlled and it is usually fixed at the value ∼1 μJ, which creates a single stable filament in the media. The spectral profile of the white light can be controlled by changing the media and by various filters, which are also used to get rid of the intense residual light at the fundamental wavelength. After generation and filtering of the white light probe, the latter can be split into two (not shown in Figure 3.4) by a beam splitter, creating a second, reference probe beam, which does not pass through the excited part of the sample and can be used to correct any artifacts coming from probe intensity and spectral fluctuations. Because of the highly nonlinear nature of white light generation, which is intrinsically very noisy, its fluctuations can be very strong, making the probe reference beam very useful for noise reduction.
After generation, the white light beam needs to be collimated and then focused on the sample. Probe spot on the sample should be Gaussian, of identical or slightly smaller size than the pump spot. In the latter case, the system is less sensitive to possible misalignments in the pump/probe overlap. Several variants of this approach are possible. For example, one can double the 800 nm before generating the white light. The supercontinuum generated from 400 nm then extends deeper to the UV, allowing to probe in the ∼300–600 nm spectral region. Another variant involves the use of two NOPAs, one used to produce the tunable pump pulse, and the other to produce a relatively broadband, and tunable probe [28].
As anticipated, the pump path is controlled by a motorized delay stage allowing a precise electronical control of pump–probe delay with precision of few femtoseconds. The probe and the pump are directed in such a way to overlap within the sample. Therefore, the absorption spectrum measured by the probe is collected from the region which has been previously photoexcited by the pump. If the sample is a liquid, it is generally made to continuously flow in a thin flow cell, or in a liquid jet, which strongly reduces photodamage. The flow speed should be regulated in order that every pump pulse hits a fresh portion of the sample. If the sample is a solid, it is usually moved by a motor stage in order to limit the excitation damage. The thickness of the sample is kept as low as possible (ideally, a few hundred μm) to reduce GVD and GVM effects which would tend to degrade time resolution.
After the sample, the probe beam is finally dispersed through a monochromator and sent to the detector, which measures its spectrum. Typically, the pump pulse is chopped, so that the detector alternates measures of I p and I u, allowing for a direct estimation of the TA signal according to Eq. (3.15). In case a reference probe beam is added, two independent detectors are used, in order to use the reference beam to correct the TA signal for probe fluctuations.
A full TA experiment consists in a temporal scan in which the delay between the two pulses is changed. The pump and probe pulses spatially overlap within the sample volume for the entire duration of the scan; in the time domain, the “zero time” of the experiment is identified when the pulses also overlap in time. Typically, time zero is found from the observation of the, so‐called, cross‐phase modulation (CPM) [35]. This is a signal related to the interaction of the probe with the variation of the refractive index induced by the pump inside the medium. It is responsible for a strong distortion of the data when the two pulses temporally overlap in the sample, so that it can be used to easily locate time zero. Once time zero is found, the TA scan is designed to cover from t < 0 to maximum delays of several hundreds of picoseconds, or even a few nanoseconds, in order to fully reconstruct the kinetics initiated by photoexcitation.
The ultimate time resolution of a TA experiment is controlled by the time duration of the two pulses. It is easily 100 fs or less, and can be as short as <10 fs in extreme cases [36, 37]. If the pulses are transform‐limited (ΔωΔt = 0.5), the time resolution is simply given by the cross‐correlation between the two pulse intensity profiles. Therefore, the duration of the pump pulse should be made as short as possible to optimize time resolution, minimizing GVD effects. The requirements, however, are less severe for the probe pulse. In fact, the time resolution does not change even if the probe pulse is chirped by GVD. Although GVD temporally broadens the probe pulse, this only implies a different temporal overlap between the pump and every wavelength of the probe. This effect needs to be compensated during data analysis (see next section), but does not degrade time resolution, because the TA measurement is carried out separately on each spectral component of the probe, dispersed on a multichannel detector after interacting with the sample. Thus, even if the probe is chirped, the time resolution is identical to that which would be obtained by transform‐limited pulses of the same total spectral width of the probe pulse [38]. In practice, probe pulses are often obtained by supercontinuum generation, yielding a very large bandwidth, hence a very short transform‐limited duration. In this situation, the factor ultimately controlling the temporal resolution is the duration of the pump pulse only, which should be kept as short as possible.
3.3.3 Data Analysis and Interpretation
Before data analysis, TA data need to be corrected for the effects of GVD and CPM. Because of GVD‐induced chirp, the probe pulse can be broadened to durations as long as ≈1 ps, and the time t 0(λ) of the interaction with the pump depends on wavelength. This causes an uncertainty on the definition of zero time, which is a crucial point in time‐resolved measurements. One way to measure t 0(λ) is conducting a TA experiment in a reference sample (e.g. the pure solvent) where only the CPM signal is observed. Its narrow temporal width can be then used to estimate the time resolution of the setup, and the time at which CPM is observed for any λ yields the GVD correction curve t 0(λ). Once this is known, kinetic traces from the sample data set are temporally shifted [33], so as to eliminate the wavelength dependence of the zero time, eliminating GVD effects. As for CPM, it is usually very difficult to compensate for its effects on the data. Therefore, after GVD corrections, the spectra collected in the temporal window around time zero where CPM is observed are typically removed from the data. As a consequence, the first useful spectrum is collected after a certain minimum delay from time zero, of the order of the time resolution of the experiment.
After GVD and CPM corrections, the following step is the extraction of the dynamics and the definition of the characteristic timescales of the sample dynamics. Whichever is the chosen data analysis method, its aim is to disentangle the various temporal dynamics contained within the signal and associate them with well‐defined spectral features. There are several approaches to do this. At the qualitative level, directly inspecting the TA spectra at various time delays and comparing the kinetic traces at different wavelengths is often the first step to have an idea on what processes are observed, and their approximate timescales. In this respect, one should keep in mind that TA spectra can be generally read using the same rational approach that is used to read traditional steady state optical data, where intensity variations are usually due to depopulation, and spectral shifts are due to energy relaxations.
After a qualitative analysis of TA data, more sophisticated approaches are usually applied. One of them is singular value decomposition (SVD) followed by a global analysis (GA) [39]. SVD is a mathematical method by which data are decomposed to a minimum number of relevant kinetics and spectra, and at the same time, white noise is removed from the data. GA is combined with SVD in order to find time constants which can describe the entire data, providing a global model simultaneously fitting the kinetics at all wavelengths. From the SVD and the global analysis, decay associated spectra (DAS) are extracted, which describe relevant changes of TA signal for each time constant found during GA [40]. Assuming a physical model that includes only incoherent relaxations (not oscillations or phase variations), the GA typically