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       Alice Sciortino and Fabrizio Messina

       Department of Physics and Chemistry – Emilio Segrè, University of Palermo, Palermo, Italy

      Traditional steady state spectroscopies, addressed in Chapter 1 of this book, are essential tools to characterize a physicochemical system through the extensive mapping of its energy landscape and transitions. However, these classical methods cannot capture the dynamical aspects driving the response of the system after an initial perturbation. These aspects can only be addressed by time‐resolved spectroscopic techniques, which are methods capable of following in time the evolution of a physicochemical system, after it has been initially brought out of equilibrium by a defined stimulus, such as photon absorption. Indeed, a thorough understanding of these dynamics, as they unravel in time, is often crucial to fully elucidate the behavior of a system of physical, chemical, or biological interest.

      Photoexcitation of any physical system triggers a complex sequence of phenomena occurring over many temporal orders of magnitude after initial photon absorption, and responsible for the ultimate outcome of the photocycle. The primary and most fundamental dynamics, however, usually occur on picosecond (1 ps = 10−12 s) or femtosecond (1 fs = 10−15 s) timescales for many well‐known processes of fundamental interest in photophysics and photochemistry [1]. In particular, it can be argued that femtoseconds are the “fundamental” timescale for any physicochemical process involving short‐range atomic rearrangements, such as chemical reactions or molecular relaxations, because the vibrational period of nuclei always fall in the femtosecond time range (∼10 fs for the OH vibration). Thereby, it is evident that very fast, or rather “ultrafast,” spectroscopic techniques are compulsory to investigate these types of phenomena.

      This chapter addresses a variety of experimental methods usually referred to as ultrafast or femtosecond spectroscopies. These techniques are capable of time resolutions reaching a few femtoseconds, which are essential to reconstruct in detail the course of events initiated by photoexcitation, achieving a comprehensive understanding of the photocycle of any physical system. Examples of typical phenomena which are addressed by femtosecond methods are molecular energy relaxations, such as internal conversion or intersystem crossing [2], solvation dynamics, electron and energy transfer events [3–5], fluorescence quenching [5], dynamics of charge carriers and excitons in semiconductors [6], and photochemical reactions [7]. For these reasons, femtosecond techniques are today well‐established and considered a fundamental tool in spectroscopy.

      The general idea behind most femtosecond spectroscopies is to use at least two, or more, light pulses with very short time durations to follow in real time the undergoing dynamics. One of the pulses, for example, is resonant to an electronic transition of the investigated system, and its absorption by the system causes an injection of energy and a quasi‐instantaneous redistribution of the electronic charge. Then, the successive dynamics are studied by taking spectroscopic snapshots of the excited systems at variable delays, by the use of a second light pulse. This can be done by using one of several possible spectroscopic observables, capable of retrieving different types of information,

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