Raman anti-Stokes process

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 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). 

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 ... 

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 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. 

Fiq. 2. The quantum mechanical view of Raman scattering, (a) Stokes scattering process (b) anti-Stokes scattering process (8). 

The present study demonstrates that the analytic calculation of hyperpolarizability dispersion coefficients provides an efficient alternative to the pointwise calculation of dispersion curves. The dispersion coefficients provide additional insight into non-linear optical properties and are transferable between the various optical processes, also to processes not investigated here as for example the ac-Kerr effect or coherent anti-Stokes Raman scattering (CARS), which depend on two independent laser frequencies and would be expensive to study with calculations ex-plictly frequency-dependent calculations. 

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.

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... 

Marks, D. L., Vinegoni, C., Bredfeldt, J. S., and Boppart, S. A. 2004. Interferometric differentiation between resonant coherent anti-Stokes Raman scattering and nonresonant four-wave-mixing processes. AppZ. Phys. Lett. 85(23) 5787-89. 

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