Brillouin Study of the Quantization of Acoustic Modes in Nanospheres

The vibrational modes in three-dimensional ordered arrays of unembedded ${\mathrm{S}\mathrm{i}\mathrm{O}}_2$ nanospheres have been studied by Brillouin light scattering. Multiple distinct Brillouin peaks are observed whose frequencies are found to be inversely proportional to the diameter ($\approx 200–340\mathrm{n}\mathrm{m}$) of the nanospheres, in agreement with Lamb’s theory. This is the first Brillouin observation of acoustic mode quantization in a nanoparticle arising from spatial confinement. The distinct spectral peaks measured afford an unambiguous assignment of seven surface and inner acoustic modes. Interestingly, the relative intensities and polarization dependence of the Brillouin spectrum do not agree with the predictions made for Raman scattering.