Linear Rayleigh and Raman scattering to the second order: analytical results for light scattering by any scatterer of size k0d ≲ 1/10

We extend the usual multipolar theory of linear Rayleigh and Raman scattering to include the second-order correction. The new terms promise a wealth of information about the shape of a scatterer and yet are insensitive to the scatterer's chirality. Our extended theory might prove especially useful for analysing samples in which the scatterers have non-trivial shapes but no chiral preference overall, as the zeroth-order theory offers little information about shape and the first-order correction is often quenched for such samples. A basic estimate suggests that our extended theory can be applied to a scatterer as large as k₀d ∼ 1/10 with less than ∼ 0.1% error resulting from the neglect of the third- and higher-order corrections. Our results are entirely analytical.