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 leads to describe the signal as follows:
(3.17)
where τ i and DAS i are the characteristic times and the relative amplitudes, and IRF is the instrumental response function that is supposed to be a Gaussian function with a width (≈FWHM/2.35) K b and peaking t 0 = 0, and ⊗ is the convolution operator. Once DAS i and related timescales τ i are identified, specific knowledge of the system needs to be used to attribute to each of these processes a definite meaning, finally leading to an exhaustive model of the sequence of relaxation events initiated by photoexcitation.
3.4 Ultrafast Fluorescence Spectroscopies
Another group of powerful ultrafast spectroscopic techniques are the fluorescence‐based techniques, such as fluorescence upconversion (FLUC) and Kerr gating‐based time‐resolved fluorescence. Both of them are time‐resolved electronic spectroscopic techniques capable of selectively detecting the (spontaneous) emission, typically with 50–200 fs time resolution, without any GSB or ESA contaminations. Because these methods are only sensitive to excited state dynamics, the signals they produce are much easier to interpret than TA; at the same time, some information remains hidden, such as ground state dynamics, or the population of non‐emissive states. For example, only fluorescent (singlet) excited states are usually measurable with these methods. In contrast, most (but not all) triplet excited states remain “dark” because their phosphorescence has too low a radiative rate to provide a detectable signal.
Both FLUC and Kerr gating experiments require the use of two pulses (called excitation and gate) and the possibility of changing the time delay between them. The excitation pulse directly interacts with the sample, initiating the fluorescence emission. Then, the gate pulse controls the temporal window in which the emitted fluorescence is sampled with femtosecond time resolution. In both cases, varying the delay between excitation and gate allows to follow the dynamics of the fluorescence. However, the two techniques achieve time resolution through the use of two different nonlinear optical effects. A FLUC experiment exploits SFG between the gate beam and the fluorescence, in order to sample the fluorescence signal within a time window defined by the cross‐correlation between the excitation and the gate. The Kerr‐gated ultrafast fluorescence is founded instead on the optical Kerr effect, i.e. on the modifications of refractive index of a medium induced by the exposure to a femtosecond pulse. A Kerr medium is used as an optical shutter activated by the gate beam, to select a temporal “slice” of the fluorescence signal to be measured. Details on the technical aspects of the two spectroscopies are given in the next subsections.
3.4.1 FLUC: The Experimental Method
A typical FLUC experiment involves the excitation of a sample by the pump beam and the collection of the largest possible fraction of the isotropically emitted fluorescence [2–4,41–44]. This is achieved by
