Fitting decay time values of eumelanin suspensions, carried out in DMSO‐methanol mixture. The suspension was excited at 2.254 eV. Table adapted from [17].
Abstract
This chapter reports on one of the nonlinear spectral features, the inverse Raman scattering (IRS), observed upon the interaction of ultrafast‐pulsed lasers in a Raman‐active medium. Hereby, a comprehensive theoretical description of the IRS is exposed. Furthermore, the investigation carried out on synthetic eumelanin dispersions is addressed to show how the transient absorption measurements can be influenced by the IRS, if probing at energies close to Stokes and anti‐Stokes vibrational modes of the medium. A thorough analysis demonstrates that the IRS affects the sign of dynamics but not relaxation times. A specific kind of spectroscopy based on the IRS effect (ultrafast Raman loss spectroscopy) is eventually illustrated as valuable tool to characterize the structure of molecules and to investigate their dynamics during chemical reactions, even occurring at ultrafast timescales.
Keywords
- nonlinear Raman spectroscopy
- stimulated Raman scattering
- inverse Raman‐scattering
- femtosecond transient absorption spectroscopy
- stimulated Raman gain spectroscopy (SRGS)
- ultrafast Raman loss spectroscopy (URLS)
1. Introduction
Nowadays, the possibility to investigate optical nonlinearities offers great insights on material properties and the interaction between light and matter. After the interaction with a strong optical field, the response of the material will be no longer linearly dependent on its strength, instead nonlinear effects start playing major roles. Due to crystal structures and symmetries of media, the third order is the nonlinearity of the lowest order that can be observed in all media [1], and thus has become a valuable tool to investigate structural and dynamic aspects of matter. Among the third‐order nonlinear effects (e.g., third‐harmonic generation, optical Kerr effect), the four‐wave mixing (FWM) is the mostly explored since it generalizes all the third‐order nonlinearities. The FWM relies on the mixing of three input signals, which results in the generation of a fourth output field. When one of the input signals is resonant with the frequencies of the material, the FWM process can be enhanced and is called
In this chapter, we discuss one of the FWM processes which contributes to the stimulated Raman scattering, called inverse Raman scattering (IRS). The theory behind the IRS effect will be explained, resorting to Feynman dual‐time line (FDTL) diagrams [3], as well as its application as a spectroscopic tool. Furthermore, the connection held between the IRS and the femtosecond transient absorption (FTA) spectroscopy will be clarified, pointing out the important role the IRS effect plays on the temporal evolution of relaxation dynamics in FTA.
2. Inverse Raman scattering: theory
To describe the SRS and its origin, we begin by discussing the interaction of an optical field of frequency
The two processes hereby depicted reinforce one another: the modulation of the vibrational frequencies interacts with the incoming laser beam frequency, leading to a Stokes field which increases the amplitude of the vibrational oscillation, and eventually strengthens the Stokes frequencies. This condition of amplification is called vibrational coherence, and it can be probed by a third laser beam, determining the stimulated Raman scattering [4]. The mathematical expressions of energy conservation and phase matching are given below:
with
The probability of annihilation of a photon with frequency
where
Here,
As stated in Eq. (3), the absorption of a photon with frequency
Even if there are other nonlinear processes involved, due to the intensity of the laser field typically used, the treatment of the SRS can be narrowed down to three relevant equations in the classical description, reporting on the laser excitation frequency
Here,
assuming that the incoming field intensity is constant, that is,
where
It follows that the intensities at the anti‐Stokes frequencies are higher than the corresponding ones at the Stokes frequencies [7, 9, 10]. In the spontaneous Raman scattering, at room temperature the populations in the excited vibrational levels are negligible, as described by Boltzmann distribution, thus the anti‐Stokes peaks are weak. However, in the stimulated process (such as IRS) the Boltzmann distribution does not describe anymore the energy levels population, and a strong anti‐Stokes emission can be observed [11].
3. Inverse Raman scattering: spectroscopy
The IRS effect can be described by the Feynman dual‐time line (FDTL) diagrams in the Liouville space with the ket and bra evolution (Figure 2) [12]. Using the FDTL diagrams and the related energy level diagrams, it is possible to illustrate the temporal evolution of the density matrix in the four‐wave mixing process, which the IRS is based on. The temporal evolution goes from
In the energy diagrams,
According to Lee's papers [3, 14], it is possible to extrapolate the mathematical expression of the third‐order polarization from the FDTL diagrams. The time‐dependent third‐order polarization in the IRS effect in the probe direction (i.e., wave vector
Here, the four‐time correlation function
where
Once defined the third‐order polarization for both effects IRS (I) and IRS (II), it is possible to show the variation in intensity of the stimulated Raman signal as function of the frequencies, to be given by
where
The aforementioned variation in intensity
4. Inverse Raman scattering: experiments
4.1. Experimental setup
To carry out FTA measurements, a noncollinear geometry in the pump‐probe setup is used. A diode‐pumped Ti:Sapphire femtosecond oscillator generates a ∼100 fs pulse at a repetition rate of 78 MHz. The so‐generated pulses are stretched and amplified by a regenerative Ti:Sapphire amplifier, pumped by a Q‐switched Nd3+:YLF laser at 1‐KHz repetition rate, and eventually compressed, leading to 4 mJ, ∼100 fs pulses at 798 nm. A beam splitter sends 90% of the outcoming pulse to an optical parametric amplifier to provide tunability over a broad spectral range (290–2600 nm). This tuneable laser pulse is sent through a depolarizer, an optical chopper, and finally focused on the sample in 1 mm spot, yielding an excitation density of 5 × 1014 photon pulse−1 cm−2. The remaining 10% of the radiation is delayed in time by an optical delay line and focused on a CaF2 crystal to generate a white‐light continuum radiation, spanning between 450 and 800 nm. The WLC radiation is used as probe beam spatially overlapped to the pump pulse on the sample. The light transmitted by the sample is coupled into an optical fiber and sent to a charge‐coupled device (CCD) spectrometer. The temporal resolution (∼200 fs) is determined by the cross‐correlation between the width of pump and probe pulses overlapping on the sample. The chromatic aberrations are removed by chirp correction software.
4.2. The IRS related to FTA experiments
So far, the nature of the IRS has been described. In this section, the IRS will be treated in relation with femtosecond transient absorption (FTA) experiments. In an FTA experiment, the intensity transmitted by an unexcited medium is given by
where
By expressing the transient absorption signal as function of the detected difference in intensity, Eq. (19) can be obtained
and, thus, it is possible to directly relate the IRS effect to the FTA measurements. At Stokes frequencies, the probe‐beam field experiences gain in intensity as already described above. Hence, the argument of the logarithm in Eq. (19) is larger than 1 and the transient absorption
Due to the different amount of photons detected in the femtosecond transient absorption experiments caused by the inverse Raman‐scattering effect, it is crucial to recognize the presence of such coherent artifact to avoid misinterpretation in the analysis of the FTA spectra. Hereafter, the relaxation dynamics of a dispersion of eumelanin suspended in a DMSO‐methanol mixture (1:20 ratio) is investigated by means of FTA. This sample was chosen to demonstrate the influence of the IRS, whose signal arises from the solvent used, in the temporal relaxation of the eumelanin pigments.
4.3. Decoupling IRS features from FTA dynamics
To investigate the influence of the IRS on the transient absorption dynamics, suitable probing energies have to be chosen accurately. To this end, the temporal evolutions of the Raman features have been analyzed. From Figure 6, it is clear that probing the sample dynamics at
The dynamics in the aforementioned regions is shown in Figure 7 for the eumelanin suspension in DMSO‐methanol mixture [17]. The temporal relaxation of these pigments is well reported [18], and is consistent with the data herein shown. At the same time, it is possible to appreciate a change in the sign of the differential absorption at very short time delays (first hundreds of femtoseconds) upon the probed energy, disclosing the influence of the IRS. When the probe‐beam frequency is lower than the one at which the Stokes features appears, an IRS‐free FTA dynamics is observed. In fact, as presented in Figure 7a (
The second contribution occurs only in the first hundreds of femtoseconds instead. This is due to the fact that the vibrational coherence needed to achieve the inverse Raman scattering persists as long as pump and probe pulses are temporally overlapped. Since the frequency of the probe pulse resonates with one of the Stokes features, a reinforcement of the vibrational modes of the solvent follows. Due to the resonance at the Stokes frequency, a gain in the intensity of the probe beam is achieved and the IRS appears as an emission of photons as described by the theoretical model presented by Rai et al. [4]. An increase in transmitted intensity is registered as a negative
In Figure 7c, the FTA dynamics of the eumelanin probed at frequencies between the incoming pump beam and the anti‐Stokes features is presented. If
The decay time obtained from the fit of the eumelanin dynamics is reported in Table 1 for the DMSO‐methanol suspension. It is worth noting that regardless of the frequency of the probe pulse, the decay times of the samples are comparable. In fact, the IRS does not affect the relaxation dynamics of the pigment. However, the IRS influences the sign and the amplitude of the FTA measurements.
Solvent | Probe energy (eV) | ||
---|---|---|---|
DMSO‐methanol | 1.741 | 1.5 ± 0.2 | 10.1 ± 0.9 |
1.823 | 1.6 ± 0.3 | 16.9 ± 1.4 | |
2.460 | 1.5 ± 0.1 | 15.3 ± 1.2 |
4.4. Ultrafast Raman loss spectroscopy as diagnostic tool
The very need of high spatial and temporal resolution to investigate molecular reaction pathways has pushed toward the development of femtosecond stimulated Raman scattering. The aim is to be able to follow structural changes in molecules during a reaction occurring on short timescales, spanning from femtoseconds to picoseconds. The ability of femtosecond stimulated Raman spectroscopy lies in the high temporal resolution with which molecular vibrations can be collected, giving deep insights into reaction dynamics. Charge‐transfer processes have been intensely investigated by FSRS; for example, long‐debated studies on 4‐(dimethylamino)benzonitrile, due to the discrepancy between the structural simplicity of this push‐pull molecule and the complexity of the excited electronic levels, have been recently come to an end. In fact, the crucial role played by intramolecular and solvent reorganizations has been at the forefront of a systematic investigation, regarding three different dynamics on various timescales: the ππ* relaxation, the internal conversion, and the vibrational relaxation [21, 22]. By investigating the excited‐state proton transfer by FSRS, Fang et al. attributed to the skeletal motions the origin of the fluorescent form of a green fluorescent protein from
One of the specific methods enrolled by the femtosecond‐stimulated Raman spectroscopy relies on the IRS effect and is called femtosecond inverse Raman scattering (FIRS) [2], or ultrafast Raman loss spectroscopy (URLS) [4]. In URLS, the decrease in intensity of the probe beam, as described in Section 4.2, is completely described by the IRS effect and is used as fingerprint to follow in time the reaction pathways. Moreover, this spectroscopic tool shows some beneficial features missing in the general FSRS. The intensity of the Raman peaks at the anti‐Stokes frequencies results higher than what is measured at the Stokes frequencies (Raman gain), leading to a better signal‐to‐noise ratio [7, 9, 10]. Second, looking at the blue side of the pump pulse to identify the spectral features of the sample helps to reject the fluorescence signal, which appears on the red side [2]. Finally, the detector dynamic range has higher efficiencies on the anti‐Stokes than on the Stokes side, minimizing the noise levels and thus allowing for clearer imaging (FIRS microscopy) [28–32], for example, in tissues [33] and drug‐delivery processes [34–36].
In the previous paragraph, it was shown that investigating the temporal evolution of the
First, it is of crucial importance to identify the spectral features encountered in the FTA measurements, and ascribe them to specific vibrational modes. To this end, the Raman spectrum of the solvent mixture (DMSO‐methanol, 1:20 in ratio) was collected. As can be seen in Figure 8a, the Raman spectrum is dominated by three narrow peaks and a broad band. These features are recognized as follows: CO stretching and SO stretching in methanol and in DMSO, overlapping at 0.125 eV (peak I); CH2 bending in methanol at 0.177 eV (peak II); CH stretching in methanol at 0.352 and 0.365 eV (symmetric and antisymmetric vibrational mode), and in DMSO at 0.361 eV (peak III); OH stretching in methanol at 0.414 eV (peak IV) [39–41]. A direct correspondence of the Raman peaks shown in Figure 8a is found in the FTA measurements depicted in Figure 8b. In fact, the spectral evolution at ultrashort time delays shows specifically the same Raman features occurring symmetrically to the pump pulse at Stokes and anti‐Stokes frequencies.
Tuning the pump pulse to lower energies, the spectral features follow the energy shift, maintaining constant the energy difference between each of them and the pump pulse (spectra from red to blue in Figure 8b). Computing
Once identified the Raman vibrational modes, it is possible by URLS to investigate them specifically and, in particular, to address their spectral evolution in time. This can give insights on the transient structure of the molecules and on the dynamics of the specific vibrational modes. Here, we report on a very preliminary analysis ran in such direction on the aforementioned sample; in Figure 9 the C─H Raman vibrational mode located at 2.641 eV, upon pumping the sample at
This example should visually explain the potential and the strength of the URLS as spectroscopic tool. In fact, the results here collected, and the many more presented in literature [37, 38, 42], unambiguously demonstrate the ability of the technique to select specific bonds and study their dynamics upon photoexcitation, at ultrafast timescales. However, further investigations are required to relate the experimental observations to the ultimate structure of the solvent molecules.
5. Conclusions
In this chapter, the authors presented a complete description of the inverse Raman scattering effect, one of the four‐wave mixing processes contributing to the stimulated Raman scattering process. Feynman dual‐time line diagrams and energy level diagrams were used to explain the theory behind the IRS effect. Once addressed the nature of the IRS effect, its close relation with the transient absorption pump‐probe experiment was described, as well as the influence on the temporal evolution of the sample dynamics. To this end, the dynamics of eumelanin dispersions carried out at different exciting energies were shown, pointing out the crucial role of the IRS in the relaxation dynamics of the sample. Finally, the implementation of the IRS effect as diagnostic tool in determining the structures and interactions among molecules was presented. In fact, the high resolution achieved in the time and spectral domains showed by ultrafast loss Raman spectroscopy enables to follow specifically the electronic structure of molecules while undergoing chemical reactions, even on ultrafast timescales.
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