Raman Stokes process

Figure 3.16. A few interactions contributing to the Raman-Stokes process (with creation of one phonon). The propagators are labeled with the notation of the text. The process a is of the first order b could be included by renormalization of the created exciton c would require the renormalization of the interaction (or the vertex).

The third common level is often invoked in simplified interpretations of the quantum mechanical theory. In this simplified interpretation, the Raman spectrum is seen as a photon absorption-photon emission process. A molecule in a lower level k absorbs a photon of incident radiation and undergoes a transition to the third common level r. The molecules in r return instantaneously to a lower level n emitting light of frequency differing from the laser frequency by —>< . This is the frequency for the Stokes process. The frequency for the anti-Stokes process would be + < . As the population of an upper level n is less than level k the intensity of the Stokes lines would be expected to be greater than the intensity of the anti-Stokes lines. This approach is inconsistent with the quantum mechanical treatment in which the third common level is introduced as a mathematical expedient and is not involved directly in the scattering process (9). 

According to classical theory, in Eq. (16.16), the first term represents an oscillating dipole that radiates light of frequency v0, that is, Rayleigh scattering. The second term is associated with the Raman scattering of frequency v0 - vm (Stokes process) and v0 + vm (anti-Stokes process). If (daldq)0 is zero, the vibration is not Raman active (Ferraro and Nakamoto, 1994). 

From Eq. (3.6-4) we immediately recognize that in stimulated Raman scattering processes where only one input laser field with frequency is employed, a coherent Stokes wave is generated for those Raman modes which have the highest ratio between differential Raman cross section and linewidth F. The latter corresponds to the dephasing time T2 of the physical system, F = l/Tj, and reflects the damping of the system. 

Fig. 11.1 Schematics of vibrational Raman process. Stokes process gives scattered lights that are lower in energy than the incident light, and anti-Stokes process gives scattered lights that are higher in energy than the incident light...

Here the and -f signs correspond to those Raman processes in which an elementary excitation is created or annihilated (Stokes and anti-Stokes processes, respectively). In crystalline solids, the quasi-momentum conservation gives the following relation between the wave vectors k, of the incident light, kj of the scattered light, and q of the elementary excitation ... 

This quantity plays an important role in other multi-photon processes, such as two-photon absorption, second harmonic generation and hyper-Raman scattering as three-photon processes, and coherent anti-Stokes Raman scattering (CARS), a four-photon process (Table 1.5). The two-photon absorption can be treated theoretically from Eq. (1.115) in the same way as the Raman scattering process discussed above. Thus, the transition rate for two-photon absorption is given by Eq. (1.161). 

The vibrational selection rules are the same for Raman spectroscopy as for infrared spectroscopy. In the Stokes process, the intense, monochromatic radiation t es a molecule from the v = 0 state to a virtual state, VO, from which it falls back to the v = 1 state. Similarly, in the anti-Stokes process, the virtual state VI is involved in the overall transfer of the molecule from the v = 1 to the v = 0 state. The Stokes and anti-Stokes transitions lie on the low and high wavenumber sides, respectively, of the exciting radiation. The intensity of the anti-Stokes line, relative to the Stokes transition is very low because of the lower population of the v = 1 state, compared to that of the v = 0 state. Consequently, Raman spectroscopy uses only the Stokes transitions. 

The reason for this rivalry is that the spontaneous Raman scattering is a weak effect and thus it is essential to optimise the experimental set-up. The crucial factor is that the efficiency of the Raman scattering process has one of the highest power dependencies on frequency of any optical effect. This efficiency is proportional to frequency to the fourth power and the intensity of a Stokes Raman band of a shift frequency is governed by... 

The regular pulse train of a mode-locked laser with the pulse-repetition frequency / corresponds in the frequency domain to a spectrum consisting of the carrier frequency vq = col2n and sidebands vq . q f q e N) (Sect. 6.1.4). If a molecular sample with a level scheme depicted in Fig. 7.13b and a sublevel splitting An = 2qf in the lower state is irradiated by such a pulse train, where the frequency vq is chosen as vo = (vi + v2 /2, the two frequencies vi,2 = vo qf are absorbed on the two molecular transitions vi, V2. This may be regarded as the superposition of two Raman processes ([1) 2) -> 3) Stokes process) and ( 3) 2) 1) anti-Stokes process), where the population of the two sublevels 1) and 13) oscillates periodically with the frequency Av = AE/h. The level splitting AE can be obtained much more accurately from this oscillation frequency than from the difference of the two optical frequencies vi, V2. 

In a pure crystal, i.e., one exhibiting translational invariance, kinematical constraints imposed by wavevector conservation dictate one of the most important constraints on the Stokes Raman scattering process, namely,... 

In principle, such a coherent Raman mixing process can provide additional Raman gain to the sequentially pumped multi-order Stokes process through... 

The anti-Stokes/Stokes electric field produced by the CARS/CSRS (Coherent Stokes Raman Scattering) process at the focus is given by ... 

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