Stokes component

Field enhancement factors observed in Raman scattering from molecules adsorbed on nanosurfaces are even larger. The intensity of Stokes component in Raman scattering is proportional to the square of dipole momentum on that frequency [61] ... 

Stokes (o)q+(0 ) scattering processes. The partial derivative factor, (3aij/9Qk)e evaluated at the equilibrium position of the normal coordinate comprises a necessary condition for Raman activity of the normal mode Q. Raman effects occur only for those normal modes that cause the molecule to undergo a net change in polarizability during the course of the vibration. While equation (7) implies that both Stokes and anti-Stokes components should appear with equal intensity, a quantum mechanical derivation shows that the Stokes/ anti-Stokes intensity ratio is proporti onal to the Boltzmann factor (7), and can be used to determine the molecular temperature of a collection of molecules. The statistical derivation is based upon the thermal population of ground and excited molecular vibrational states according to a Boltzmann distribution. 

Since an oscillating dipole moment is a source of new waves generated at each molecule, (8.5) shows that an elastically scattered wave at the frequency co is produced (Rayleigh scattering) as are inelastically scattered components with the frequencies co — con Stokes waves) and superelastically scattered waves with the frequencies o) + con (anti-Stokes components). The microscopic contributions from each molecule add up to macroscopic waves... 

Thus a Stokes and an anti-Stokes component are obtained, shifted by a frequency from the Rayleigh line. At normal temperatures, most of the molecules are in the lowest state v = 0) and few are in the t = 1 state. The intensity of the Stokes line, corresponding to the transition 0 1, is... 

The simple theory given above shows the origin of the Brillouin doublet which is the Stokes and anti-Stokes components of the scattered light each shifted from the frequency of the incident light by an amount given by Eq. (81). However what is observed experimentally is a triplet -three distinct bands. One of these is centered about the laser line itself and is called the Rayliegh line while the others constitute the Brillouin doublet. A schematic spectrum of the Rayliegh line and the Brillouin doublet is shown in Fig. 7. 

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