Figure 123: Stokes and anti-stokes process of Raman spectroscopyThe equations for the conservation of energy and momentum are:
ω = ω′±Ω (241)
k = k′±K±G (242)In the equation of the momentum conservation an additional term appears, which is a reciprocal
lattice vectorG. Whenever a collision like this happens in a crystal, the crystal can give or absorb
momentum with the reciprocal lattice vector, which is discrete.
Now we think of the problem in terms of waves and not particles. We start with a susceptibility that
is constant over the time. The∆χin fig. 124 stands for any kind of wave which comes along the
crystal. For example, the wave belongs to a phonon, so the structure gets stretched locally and this
has influence on the susceptibility and it gets modulated by the frequency of the phonon wave.
Figure 124: Modulation of susceptibility and the effect to the spectrum of the scattered intensityMathematically this can be explained by an oscillating term in the formula ofχin eqn. (243). The
result is that the polarization doesn’t oscillate only with the frequency of the incoming light, but also