Читать книгу Spectroscopy for Materials Characterization - Группа авторов - Страница 60

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.