the infrared vibrational absorption. For example, transient absorption (TA) or pump/probe methods, discussed in Section 3.3, exploit a pump/probe approach, where the changes of visible or infrared absorption are detected and followed in time after excitation. Other methods rely on different observables, such as the spontaneous emission (ultrafast fluorescence, discussed in Section 3.4) or the Raman scattering (Section 3.5). From the technical point of view, femtosecond spectroscopies are characteristically nonlinear optical experiments, which make large use of a wide toolbox of laboratory techniques in nonlinear and laser optics, to manipulate, generate, detect, and control femtosecond‐pulsed light beams in various spectral regions, as described in Section 3.2.
The development of the field of femtosecond spectroscopy has been characterized by a progressive and dramatic improvement in what can be practically achieved. With time, a femtosecond time‐resolved version has been developed for almost any traditional spectroscopic technique, including, in recent times, photoemission spectroscopy [10], X‐ray scattering [11], X‐ray absorption [12], or optical microscopy methods [13]. The last frontier in the field is pushing even more the time resolution of these experiments, to the extent that the first attosecond (1 as = 10−18 s) experiments have been emerging in the last years [10, 14].
When these methods are properly combined, it is often possible to literally track in real time the flow of charge and energy through time and space after photoexcitation. The potential of these methods is testified by their applications on a wide variety of different systems and nanosystems, such as semiconductor NPs [8], molecules and macromolecules in solution [15], carbon nanomaterials [16], and many others, always providing very useful insight on their photoinduced behaviors. Besides reconstructing the photocycle, a further capability of femtosecond experiments is disentangling homogeneous and inhomogeneous broadenings of the spectral lines, via methods like TA hole burning [17] or four‐wave mixing [18], which do not have an equivalent in traditional spectroscopy.
The chapter is organized as follows. First, a general presentation of the characteristics of fs laser beams will be presented in Section 3.2, as needed to follow the rest of the chapter. Then, three well‐established ultrafast spectroscopic methods will be described: transient absorption (Section 3.3), femtosecond‐resolved fluorescence (Section 3.4), and femtosecond Raman (Section 3.5). In the final section (Section 3.6), four different case studies will be presented, to illustrate the utility of these techniques in selected real‐case scenarios.
3.2 Ultrafast Optical Pulses
3.2.1 General Properties
An ultrafast optical pulse is an electromagnetic pulse characterized by a very short duration (from few femtoseconds to few hundreds of femtoseconds) and a broad spectral distribution (10–100 nm FWHM) in the near‐infrared, visible, or UV spectral range. Generating ultrafast pulses relies on the use of a mode‐locked laser, which exploits the amplification of a large number of laser modes oscillating in‐phase within the laser cavity [19, 20]. The most widespread type of femtosecond mode‐locked laser in modern spectroscopy is the Ti:sapphire laser. A typical Ti:sapphire oscillator emits laser pulses with a central wavelength tunable around 800 nm, typical duration of 10–100 fs, energy of 1–100 nJ pulse−1, and repetition rate of ∼80 MHz. By using an external amplifier, these pulses can be then amplified up to μJ or mJ per pulse with a proportional reduction of the repetition rate. Because of the very short duration, these numbers imply intensities as high as tens of GW per cm2, which can easily be achieved even without focusing. These intense, amplified pulses are then available to feed a range of experiments in nonlinear optics and spectroscopy such as those described in this chapter. The details of mode‐locking will not be further discussed here, and the rest of this section will be devoted to describing some general properties of propagating femtosecond light pulses.
The time dependence of the oscillating electric field in an amplified ultrashort pulse is described by
3.2.1.1 Dispersion Effect: Group Velocity Dispersion
When dealing with optical pulses with femtosecond pulse durations, it is important to consider the effects of group velocity dispersion (GVD). The latter affects the duration of a light pulse which traverses any media, because of the frequency dependence of the refractive index n(ω). GVD is defined as:
(3.1)
where v g is the group velocity. The latter can be written as:
(3.2)
GVD is measured in fs2 mm−1 and, in a transparent region, is typically positive because of the characteristic dependence of n on frequency. During propagation, every spectral component of the pulse acquires a different delay, resulting in a temporal broadening of the pulse without any spectral changes [21]. To visualize the effect of GVD on a Gaussian pulse passing through a medium, a simulation is shown in Figure 3.1. From top to bottom, three pulses are shown, representing a transform‐limited Gaussian with FWHM = 5 fs centered at 550 nm, and the same pulse after passing through 1 or 2 mm SiO2, respectively. As evident from the figure, GVD substantially enlarges the pulse duration, increasing it to several hundreds of femtoseconds. The pulse duration Δt, that is the FWHM of the Gaussian intensity profile, broadens to Δt b given by:
(3.3)
