Polarizability calculation of vibrating nanoparticles for intensity of low frequency Raman scattering

A new numerical method is introduced for calculating the polarizability of an arbitrary dielectric object with position dependent complex permittivity. Three separate numerical approaches are provided to calculate the dipole moment of a nanoparticle embedded in a dielectric matrix in the presence of an applied electric field. Numerical tests confirm the accuracy of this method when applied to several cases for which an exact solution is available. This method is especially well suited for the calculation of absolute Raman scattering intensities due to acoustic phonons in metallic and dielectric nanoparticles embedded in transparent matrices.