with the additional term of the phonon wave. Some of the scattered phonons are forbidden by crystal
symmetry and in this case, there are no peaks captured by the Raman spectroscopy.
χ = χ 0 +
∂χ
∂X
Xcos(Ωt) (243)P = 0 χEcos(ωt) + 0
∂χ
∂XXcos(Ωt)Ecos(ωt) (244)In fig. 124 the stokes and anti-stokes peaks could be seen in the intensity-over-ωdiagram. An interest-
ing fact is, that the peaks of the stokes and anti-stokes process do not have exactly the same height.
This has to do with the probability that a phonon would be absorbed or emitted. Equations (245)
and (246) show the intensity of the peak in dependence of the numbernkof phonons in the statek.
Stokes:I(ω−Ω) ∝ nk+ 1 (245)
Anti-Stokes:I(ω+ Ω) ∝ nk (246)If the temperature gets smaller, the ratio between the intensity of the stokes and anti-stokes peaks
gets bigger and it is possible to calculate the probability that the state is occupied. The ratio of the
heights at different temperatures can be seen in fig. 125.
Figure 125: Different heights of stokes and anti-stokes peaks depending on the temperature