Quantum confinement of phonons

There is an analogous quantization effect of the phonon vibrations of multilayer structures (Santos, Hundhausen and Ley 

The condition for observation is that the phonon coherence length is larger than the layer thickness. Low frequency acoustic modes fulfill this condition because they are an in-phase motion of a large number of atoms and are not strongly influenced by the disorder-instead reflecting the average bulk elastic properties of the materials. 

The periodicity of the multilayer provides an additional scattering of the phonons and introduces an artificial Brillouin zone. This leads to a folding of the phonon dispersion curves at wave vectors n/L, where L is the multilayer spacing. 

The dispersion of acoustic modes in a uniform material is given by 

Raman backscattering occurs at twice the wave vector of the incident light, 2fcp = 4nn/Xp, where Xp is the wavelength of the light and n the 

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