Raman transitions

Now we turn to vibrational Raman spectroscopy, in which the incident photon leaves some of its energy in the vibrational modes of the molecule it strikes or collects additional energy from a vibration that has already been excited. The gross selection rule for vibrational Raman transitions is that the molecular polarizability must change as the molecule vibrates. The polarizability plays a role in vibrational Raman spectroscopy because the molecule must be squeezed and stretched by the incident radiation in order that a vibrational excitation may occur during the photon-molecule collision. Both homonuclear and heteronuclear diatomic molecules swell and contract during a vibration, and the control of the nuclei over the electrons, and hence the molecular polarizability, changes too. Both types of diatomic molecule are therefore vibrationally Raman active. It follows that the information available from vibrational Raman spectra adds to that from infrared spectroscopy. 

The specific selection rule for vibrational Raman transitions is the Scune as for infrared transitions Av = +1). The photons that are scattered with a lower wavenumber than that of the incident Hght, the Stokes hnes, cffe those for which Ai =+1. The anti-Stokes lines (for which Ai = —1) cffe less intense them the Stokes lines because very few molecules are in m excited vibrationed state initially. 

---

Consider Raman transitions between thennalized molecular eigenstate g (ground) and molecular eigenstate/ (final). The quantum mechanical expression for responding to colours and j is the famous (thennalized) Kramers-Heisenbergequation [29]... 

The unique feature in spontaneous Raman spectroscopy (SR) is that field 2 is not an incident field but (at room temperature and at optical frequencies) it is resonantly drawn into action from the zero-point field of the ubiquitous blackbody (bb) radiation. Its active frequency is spontaneously selected (from the infinite colours available in the blackbody) by the resonance with the Raman transition at co - 0I2 r material. The effective bb field mtensity may be obtained from its energy density per unit circular frequency, the... 

Plenary 5. Manuel Cardona, e-mail address cardona .cardix.mpi-stuttgart.de (RS). Studies of high superconductors. These offer all possible Raman transitions—phonons, magnons, free carrier excitations, pair... 

Plenary 6. Shu-Lin Zhang et al, e-mail address slzhang pku.edu.cn (RS). Studies of phonon modes of nanoscale one-dimensional materials. Confinement and defect induced Raman transitions. 

In most CARS experiments, is held fixed, usually at 532 mn, the second hamionic of a Nd YAG laser output, while V2 is scaimed. The intensity of the output field at is enlianced whenever the difference - V2 equals the energy difference between two molecular levels coimected by a Raman transition. Unlike the... 

By analogy with Equation (6.6) the vibrational Raman transition moment is given by... 

Intensities of Raman transitions are proportional to R and therefore, from Equation (6.13), to (da/dx)g. Since a is a tensor property we cannot illustrate easily its variation with x instead we use the mean polarizability a, where... 

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... 

The rotational selection rule for vibration-rotation Raman transitions in diatomic molecules is... 

The similarity between a two-photon absorption and a Raman scattering process is even closer. Figure 9.27(a) shows that a Raman transition between states 1 and 2 is really a two-photon process. The first photon is absorbed at a wavenumber to take the molecule from state 1 to the virtual state V and the second photon is emitted at a wavenumber Vj,. 

Because Raman scattering is also a two-photon process the selection rules for two-photon absorption are the same as for vibrational Raman transitions. For example, for a two-photon electronic transition to be allowed between a lower state j/" and an upper state... 

Then Equation (9.20) is seen to be analogous to Equations (6.64) and (6.65) for vibrational Raman transitions. 

Although it is less often done, I have used an analogous symbolism for pure vibrational transitions for the sake of consistency. Here N refers to a vibrational (infrared or Raman) transition from a lower state with vibrational quantum number v" to an upper state v in the vibration numbered N. 

Keywords atom interferometry, laser cooling, Raman transition... 

We present here a summary of recent work with light-pulse interferometer based inertial sensors. We first outline the general principles of operation of light-pulse interferometers. This atomic interferometer (Borde et al., 1992 Borde et al., 1989) uses two-photon velocity selective Raman transitions (Kasevich et al., 1991), to manipulate atoms while keeping them in long-lived ground states. 

The fourth-order coherent Raman spectrum of a liquid surface was observed by Fujiyoshi et al. [28]. The same authors later reported a spectrum with an improved signal-to-noise ratio and different angle of incidence [27]. A water solution of oxazine 170 dye was placed in air and irradiated with light pulses. The SH generation at the oxazine solution was extensively studied by Steinhurst and Owrutsky [24]. The pump and probe wavelength was tuned at 630 nm to be resonant with the one-photon electronic transition of the dye. The probability of the Raman transition to generate the vibrational coherence is enhanced by the resonance. The efficiency of SH generation is also enhanced. 

Ifourth(fd, 2 Q) was multiplied with a window function and then converted to a frequency-domain spectrum via Fourier transformation. The window function determined the wavenumber resolution of the transformed spectrum. Figure 6.3c presents the spectrum transformed with a resolution of 6cm as the fwhm. Negative, symmetrically shaped bands are present at 534, 558, 594, 620, and 683 cm in the real part, together with dispersive shaped bands in the imaginary part at the corresponding wavenumbers. The band shapes indicate the phase of the fourth-order field c() to be n. Cosine-like coherence was generated in the five vibrational modes by an impulsive stimulated Raman transition resonant to an electronic excitation. 

The wavenumbers of the observed bands are identical with those of the spontaneous Raman spectrum of the solution and oxazine solid [27]. The impulsive stimulated Raman transition may initiate coherent vibrations in the electronic excited state. However, there was no sign of the excited-state vibrations superimposed on the ground-state bands in the spectrum of Figure 6.3. 

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.

The intensity of a Raman transition from the initial vibrational level i of the ground electronic state g to the final vibrational level j of the g state is given by equation 1 ... 

The selection rule for rotational Raman transitions are AJ = 2. This result relates to the involvement of two photons, each with angular momentum h, in the scattering process. Also allowed is A J = 0, but since such a transition implies zero change in energy it represents Raleigh scattering only. 

In addition to energy eigenvalues it is of interest to calculate intensities of infrared and Raman transitions. Although a complete treatment of these quantities requires the solution of the full rotation-vibration problem in three dimensions (to be described), it is of interest to discuss transitions between the quantum states characterized by N, m >. As mentioned, the transition operator must be a function of the operators of the algebra (here Fx, Fy, F7). Since we want to go from one state to another, it is convenient to introduce the shift operators F+, F [Eq. (2.26)]. The action of these operators on the basis IN, m > is determined, using the commutation relations (2.27), to be... 

As in the previous case of infrared transitions, one wants to calculate the line strengths S(v,J —> v, J ) defined in Eq. (2.127). For Raman transitions there are two contributions, as discussed in Chapter 1. The so-called trace scattering is induced by the monopole operator... 

Detailed theoretical and experimental investigations 328-330) of such coupling effects show that they are not caused entirely by these hole-burning effects, but that double quantum Raman transitions occur and that the interaction between both light fields and the molecule via the common level leads to a dynamic Stark splitting of the probe line 33D. 

Another explanation for their resonance Raman results could be a change in the zwitterionic nature of the merocyanine isomers in the different solvents which may result in changes in the Raman transition probabilities, or the spectral changes could be due to solvent shifts of the absorption spectrum, resulting in a change in the relative contribution of the different vibrational modes to each resonance Raman spectrum. We note that in the same article, the authors report the transient absorption spectra of the merocyanine forms, which clearly show that the BIPS spectrum in cyclohexane has more discrete vibrational modes than are observed in the polar solvents, which show more spectral broadening. Al-... 

---