Brillouin and Raman scattering from the acoustic vibrations of spherical particles with a size comparable to the wavelength of the light

The inelastic light scattering of the acoustic vibration of spherical nanoparticles has been studied within a continuum approximation, extending the previous models, valid for small particles, to the case of particle sizes comparable with the wavelength of the light. A mechanism appears, i.e. the polarizability modulation related to density changes, which is typical of Brillouin scattering and is negligible for small particles. Furthermore, the contribution of the polarizability modulation induced by the relative displacements of atoms, which produces the Raman scattering in small particles, strongly changes. Spheroidal modes other than the l=0 and l=2 ones, the only Raman active in small particles, contribute to both scattering mechanisms. As the size increases, higher l modes with higher n, the index that labels the radial wave vector, become important. In relatively large particles, the active n, l ,m spheroidal modes are those with frequency close to that of the Brillouin active vibrations in the bulk material, i.e.,omega nl propto qvL, where q is the exchanged wave vector of the light and vL is the longitudinal sound velocity. Also torsional modes become active and produce depolarized light scattering with properties similar to those of transverse acoustic phonons.