Raman scattering from small spherical particles

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Abstract
Raman coupling coefficients are calculated for the acoustic vibrations of a small dielectric sphere. The mean components of the strain tensor are calculated for the symmetric and quadrupolar Raman-active vibrational modes, within a continuum approximation which considers a vibrating homogeneous sphere. The Raman coupling coefficient depends on the crystalline structure and on the microscopic scattering mechanism. For cubic Bravais lattices and for a dipole-induced dipole scattering mechanism, the coupling coefficient of the symmetric vibrations vanishes. The Raman intensity of the inner modes is found to be small with respect to that of surface modes. The scaling law, which gives the Raman coupling coefficient as a function of the particle size, has been derived. The coupling of the sphere with a surrounding elastic medium has been considered and found to cause shift and broadening of the lines. This effect can alter significantly the estimated mean value and distribution of particle sizes.