Spectroscopy for Materials Characterization. Группа авторов

      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 large solid‐angle collection optics, such as a parabolic mirror with short focal length and large diameter. The fluorescence is then collimated and refocused on a nonlinear crystal such as a BBO or KDP, by a pair of parabolic mirrors arranged in a telescope. In the BBO, the fluorescence spatially overlaps with the second beam, the gate, so that sum frequency generation occurs and a frequency upconverted pulse is generated and sent to detection. Because SFG occurs only within the temporal duration of the gate, SFG involves only a defined femtosecond temporal “slice” of the emission, even if the latter is nanosecond‐lived. By measuring the intensity of the upconverted pulse as a function of excitation–gate delay, the entire emission kinetics can then be reconstructed.

      3.4.2 FLUC: Typical Experimental Setups

A possible implementation of these concepts is reported in the bottom of Figure 3.5. Here, the gate wavelength is set at 800 nm, and the fluorescence is in the visible range, yielding an upconverted pulse in the near‐UV, as can be obtained from the SFG equation: ω _PL + ω _gate = ω _up. Some technical upgrades allow to detect a fluorescence in the UV range (≈280 nm) [2, 42], which corresponds to generating and detecting the upconverted pulse in the deep‐UV (≈210 nm). While the excitation pulse intensity is limited by linearity requirements, the intensity of the gate beam cannot usually overcome 1 μJ per pulse because of practical reasons (e.g. BBO damage). Moreover, the thickness of the BBO is limited by time resolution requirements (e.g. limiting GVD in the SFG process), and the number of fluorescence photons participating in SFG process at any given delay is only a tiny portion of the total emission, because of the very short duration of the gate pulse (tens of femtoseconds vs. nanosecond lifetime). Thereby, the upconverted signal is in practice very weak, even as low as <1 upconverted photon per excitation pulse. FLUC thus requires great care in isolating this signal, which is achieved by a combination of spatial and spectral filtering methods, and finally directing to a highly sensitive detection system, such as a single photon counter or a highly sensitive CCD [2].

Figure 3.5 Scheme of a typical fluorescence upconversion setup.

      Recording the upconverted pulse as a function of the gate delay allows to reconstruct the kinetics of the emission at a given wavelength, at variable delays from photoexcitation, with femtosecond time resolution. In particular, the temporal resolution of these experiments is ultimately determined, once detrimental effects are eliminated (e.g. GVM in the BBO), by the cross‐correlation between the pump and the gate, which can be as low as a few tens of femtoseconds. Notably, efficient SFG can only occur if the phase matching condition (Δk = 0) is fulfilled, which only occurs at a precise orientation of the nonlinear crystal. Thus, the simplest approach to FLUC is acquiring single‐wavelength fluorescence kinetics, as a function of excitation–gate delay, for a given crystal orientation. Rotating the nonlinear crystal changes the phase matching condition and allows to upconvert different spectral portions of the emission band. Then, repeating the measurement with different crystal positions allows to reconstruct the dynamics of the entire fluorescence band as a function of wavelength and time [45].

      In Figure 3.5, the excitation beam is obtained by SHG of the fundamental Ti:sapphire beam, chopped, and finally focused on the sample by a parabolic mirror. After excitation of the sample, the spontaneous emission is collected and collimated by second parabolic mirror and, then, focused by a third parabolic mirror with the same diameter into the SFG crystal, where the delayed gate at 800 nm finally overlaps to the fluorescence spot. The setup uses a slightly noncollinear geometry to facilitate separation of the three beams after the nonlinear crystal, although the noncollinearity angle is kept very low in order to reduce GVM effects within the crystal, which would otherwise degrade time resolution. After the nonlinear crystal, the upconverted emission passes through a monochromator, and UV pass‐band filters, and is finally sent to a photomultiplier (PMT), the output of which is read by a lock‐in amplifier. In this configuration, the data are collected as single‐wavelength traces. The detected wavelength is determined by rotating the nonlinear crystal, thus, determining a certain phase matching angle. More sophisticated setups use broad wavelength detection, which is obtained by substituting the PMT with a CCD camera, and by performing a computer‐controlled rotation of the nonlinear crystal during data acquisition. By this method, the whole emitted spectrum can be acquired at any given delay [2, 42].

      Interestingly, because of the phase matching condition, the SFG process is automatically polarization sensitive, meaning that only the fluorescence component that has the same polarization of the gate (type I phase matching) is upconverted in the BBO and detected by the setup. Therefore, by adding a waveplate in the pump arm, as in a TA experiment, the