and subsequent dynamics.
Last but not least, ESA is the only positive signal that is recorded in a TA experiment. It is due to the new electronic transitions, such as 1 → 2, that become possible from the excited state, because probe absorption can bring the system to other higher energy states [33].
Overall, a TA experiment is simultaneously sensitive to several electronic transitions accessible from the ground and excited state(s) of the system. Virtually any photoexcited system is expected to provide several observables that can be used to follow the dynamics, making the technique very versatile. For instance, suppose that, for a given system, the GSB is difficult to observe because it falls out of the probing window. Then, one can still resort to SE or ESA as observables to monitor the evolving system. While a singlet excited state will typically give rise to strong SE, a triplet state is not expected to, due to the very low radiative rate toward the ground state. However, it should still be detectable through an ESA transition toward some higher triplet state, which should remain strongly allowed. Overall, following the spectral position and the intensity of one or more of these signals allows to reconstruct in detail the undergoing relaxations of the system, provided that the time resolution is good enough to resolve all the dynamics of interest (usually <100 fs). The analysis of TA data provides a wealth of information on the relaxation dynamics of the photoexcited system, such as excited state population decay, internal conversion or intersystem crossing, charge and energy transfer, energy relaxation, solvation of the excited state, and more [3, 8, 29, 34].
To achieve femtosecond time resolution, it is necessary to have short pump and probe pulses (50–80 fs) which keep their duration along the setup (for example they should not traverse too much glass) and, moreover, it is necessary that the two pulses are synchronized down to the scale of a few femtoseconds. Synchronization on these timescales cannot be achieved by the use of electronics. The only way to achieve such a precision is to use all‐optical strategies. In fact, a transient absorption setup typically exploits a delay stage in the optical path of one of the beams, which allows to change the relative delay between two pulses increasing or decreasing the path of one of them. It is easy to calculate that an increase in the path of 3 mm corresponds to a delay of 10 ps. In a standard setup, both beams derive from a single laser, the original beam being split in two portions which are used to generate separately the pump and the probe. In general, both pump and probe derive from the same laser source because it would be harder to synchronize with femtosecond accuracy two beams originating from two different lasers. The next section describes in more detail the main technical characteristics of a typical TA setup.
3.3.2 Typical Experimental Setups
A typical TA experimental setup involves the use of a laser that generates femtosecond pulses. Although the duration and the spectral characteristics of the pulses depend on the specific type of laser medium, many modern TA setups are based on amplified Ti:sapphire lasers, which typically produce pulses peaked at 800 nm with durations in the range 30–200 fs.
In the simplest configuration, the output of the laser is immediately split into two parts, which are used to generate the pump and the probe, respectively. The scheme of a typical setup is reported in Figure 3.4.
On the pump arm, the 800 nm beam passes through a series of optical elements used to control the characteristics of the beam, such as manipulating the spatial mode or the polarization, or altering the wavelength. For example, in Figure 3.4 the 800 nm beam is frequency‐doubled (type I phase matching) by a β‐BBO crystal in order to create a 400 nm beam (10–20% efficiency is easily achieved) meant to excite the sample. Alternatively, the fundamental Ti:sapphire beam could be sent to a NOPA, in order to fully tune the pump wavelength. Then, the beam is chopped, variably delayed, and focused on the sample. Pump spot on the sample should have a Gaussian spatial profile, with typical spot sizes of 50–200 μm. Importantly, the TA signal should be linear with the intensity of the pump, which means that the photoexcited transition is not saturated and that only a small percentage (typically 10% or less) of the system is excited. Besides, using excessive pump power may give rise to other problems, such as multi‐photon excitation contributions, white light generation in the sample, and so on. For all these reasons, typical pump energies per pulse in TA are usually limited to ten to hundred nJ pulse−1.
Figure 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
