Stokes Raman transition

The mechanism for Stokes and anti-Stokes vibrational Raman transitions is analogous to that for rotational transitions, illustrated in Figure 5.16. As shown in Figure 6.3, intense monochromatic radiation may take the molecule from the u = 0 state to a virtual state Vq. Then it may return to u = 0 in a Rayleigh scattering process or to u = 1 in a Stokes Raman transition. Alternatively, it may go from the v = state to the virtual state Fj and return to V = (Rayleigh) or to u = 0 (Raman anti-Stokes). Flowever, in many molecules at normal... 

Fig. 2 Jablonski energy level diagram illustrating possible transitions, where solid lines represent absorption processes and dotted lines represent scattering processes. Key A, IR absorption B, near-IR absorption of an overtone C, Rayleigh scattering D, Stokes Raman transition and E, anti-Stokes Raman transition. S0 is the singlet ground state, S, the lowest singlet excited state, and v represents vibrational energy levels within each electronic state.

Here Uab is the Raman transition moment, fic is the infrared transition moment, g and V refer to ground and excited vibrational states, coir is the input infrared frequency, coq is the resonance frequency of the adsorbate, and T is a damping factor [8, 14—17]. Thus, the SFG intensity is related to the product of an (anti Stokes) Raman transition and an infrared transition. The SFG intensity is enhanced when the input infrared wavelength coincides with a vibrational mode of the adsorbate and the result of an SFG spectrum corresponds to the vibrational levels of the molecule. This situation is shown schematically in Fig. 5.1. From (5), non-zero SFG intensity will occur only for transitions that are both Raman and IR allowed. This situation occurs only for molecules lacking inversion symmetry [19]. 

Raman line intensities are proportional to the number density N of molecules in the initial state /c>, which is in turn proportional to the pertinent Boltzmann factor for that state at thermal equilibrium. Consequently, the relative intensities of a Stokes transition /c> - m> and the corresponding anti-Stokes transition m> -> /c> are 1 and exp — hoj kjkT), respectively. (The factor coicol varies little between the Stokes and anti-Stokes lines, because the Raman frequency shifts are ordinarily small compared to cui.) Hence the anti-Stokes Raman transitions (which require molecules in vibrationally excited initial states) are considerably less intense than their Stokes counterparts, particularly when the Raman shift (o k is large. In much of the current vibrational Raman literature, only the Stokes spectrum is reported (cf Fig. 10.1). 

Fig. 12.8 In coherent Raman spectroscopy, a beam of electromagnetic radiation with frequency Vp and wavevector kp, and a second beam with frequency Vj and wavevector are focused on the sample. Radiation emitted with frequency v = 2Vp — Vj and wavevector kf= 2kp — k, is collected. Stokes Raman transitions of the ground electronic state are stimulated when Vp — v, = v, where hv is a vibrational mode of the sample anti-Stokes transitions are stimulated when Vp — v = —v... 

Figure 12.8 shows a typical arrangement of the excitation and signal beams for coherent Raman scattering. Two incident beams are required. The sample interacts twice with a field with frequency Vp and wavevector kp from the pump beam and twice a field with wavevector and frequency Vj from the Stokes beam. If the two fields overlap temporally and spatially, they can induce anti-Stokes Raman transitions of a vibrational mode with frequency o when Vj — = o. Stimulated... 

As already introduced in section I of this chapter, in a CARS process (Figures 7.9a-c see also Figure 7.1c), a Raman transition between two vibrational energy levels of a molecule is coherently driven by two optical laser fields (frequencies co and co) and subsequently probed by interaction with a third field at frequency co, . This generates the anti-Stokes signal at the blue-shifted frequency cars = p- The... 

A CCD Raman spectrometer coupled with a 10-mW He-Ne laser has been used to eliminate fluorescence because the long-wavelength excitation by the He-Ne laser is not as likely to cause fluorescent transitions (71). Because of its directional property, coherent anti-Stokes Raman scattering (CARS) is also effective in avoiding fluorescence interference (see CARS in Section 3.9). 

Here, E is the strength of the applied electric field (laser beam), a the polarizability and / and y the first and second hyper-polarizabilities, respectively. In the case of conventional Raman spectroscopy with CW lasers (E, 104 V cm-1), the contributions of the / and y terms to P are insignificant since a fi y. Their contributions become significant, however, when the sample is irradiated with extremely strong laser pulses ( 109 V cm-1) created by Q-switched ruby or Nd-YAG lasers (10-100 MW peak power). These giant pulses lead to novel spectroscopic phenomena such as the hyper-Raman effect, stimulated Raman effect, inverse Raman effect, coherent anti-Stokes Raman scattering (CARS), and photoacoustic Raman spectroscopy (PARS). Figure 3-40 shows transition schemes involved in each type of nonlinear Raman spectroscopy. (See Refs. 104-110.)... 

Figure 1 Schematic representation of a time-resolved coherent Raman experiment, (a) The excitation of the vibrational level is accomplished by a two-photon process the laser (L) and Stokes (S) photons are represented by vertical arrows. The wave vectors of the two pump fields determine the wave vector of the coherent excitation, kv. (b) At a later time the coherent probing process involving again two photons takes place the probe pulse and the anti-Stokes scattering are denoted by subscripts P and A, respectively. The scattering signal emitted under phase-matching conditions is a measure of the coherent excitation at the probing time, (c) Four-photon interaction scheme for the generation of coherent anti-Stokes Raman scattering of the vibrational transition.

A tunable mid-IR pulse at frequency >ir pumps vibrational excitations in a polyatomic liquid (all work discussed here is at ambient temperature 295 K). A time-delayed visible probe pulse at frequency >l generates incoherent anti-Stokes Raman scattering. For an instantaneous pump pulse arriving at time t = 0, the change in the anti-Stokes intensity of transition i, with frequency o) the anti-Stokes transient, is (44)... 

Raman Selection Rules. For polyatomic molecules a number of Stokes Raman bands are observed, each corresponding to an allowed transition between two vibrational energy levels of the molecule. (An allowed transition is one for which the intensity is not uniquely zero owing to symmetry.) As in the case of infrared spectroscopy (see Exp. 38), only the fundamental transitions (corresponding to frequencies v, V2, v, ...) are usually intense enough to be observed, although weak overtone and combination Raman bands are sometimes detected. For molecules with appreciable symmetry, some fundamental transitions may be absent in the Raman and/or infrared spectra. The essential requirement is that the transition moment F (whose square determines the intensity) be nonzero i.e.. 

Periodic oscillations in this dipole can act as a source term in the generation of new optical frequencies. Here a is the linear polarizability discussed in Exps. 29 and 35 on dipole moments and Raman spectra, while fi and x are the second- and third-order dielectric susceptibilities, respectively. The quantity fi is also called the hyperpolarizability and is the material property responsible for second-harmonic generation. Note that, since E cos cot, the S term can be expressed as -j(l + cos 2 wt). The next higher nonlinear term x is especially important in generating sum and difference frequencies when more than one laser frequency is incident on the sample. In the case of coherent anti-Stokes Raman scattering (CARS), X gives useful information about vibrational and rotational transitions in molecules. 

J, R, Andrews, R. M. Hochstrasser, and H. P. Trommsdorff. Vibrational transitions in excited states of molecules using coherent Stokes Raman spectroscopy application to ferrocytochrome-c. Chem. Phys., 62 87-101 (1981),... 

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