Relation between Raman backscattering from droplets and bulk water: Effect of refractive index dispersion

A theoretical framework is presented that permits investigations of the relation between inelastic backscattering from microparticles and bulk samples of Raman-active materials. It is based on the Lorentz reciprocity theorem and no fundamental restrictions concerning the microparticle shape apply. The approach provides a simple and intuitive explanation for the enhancement of the differential backscattering cross-section in particles in comparison to bulk. The enhancement factor for scattering of water droplets in the diameter range from 0 to 60\,\textmu m (vitally important for the \emph{a priori} measurement of liquid water content of warm clouds with spectroscopic Raman lidars) is about a factor of 1.2-1.6 larger (depending on the size of the sphere) than an earlier study has shown. The numerical calculations are extended to 1000\,\textmu m and demonstrate that dispersion of the refractive index of water becomes an important factor for spheres larger than 100 \textmu m. The physics of the oscillatory phenomena predicted by the simulations is explained.