General theory of elastic light scattering

A general theory of elastic light scattering is presented. The incoming and scattered light are described by the coherency matrix, which is written in spherical tensor form. The coherency matrix has three tensorial components in our representation: a scalar (the intensity), an axial vector (the ellipticity), and a second rank tensor (directly related to the inclination of the optical axes). It is shown that using Racah algebra, the components of the coherency matrix for the incident and scattered light can be related by rather compact formulas, involving Wigner's 9-J symbols. The simplicity of the treatment allows us to include any higher multipole effects in the scattering, like the magnetic dipole and electric quadrupole contributions. For the pure electric dipole scattering, our theory gives a unique interpretation of the scattering in terms of moments of the molecular correlation function. Only two moments can be observed when the correlations are short compared to the wavelength of the light, while, for long ranged correlations, it would be possible in principle to discriminate between the various contributions by analyzing the angular dependence of the scattered light. A short survey of the real systems in which this might be the case is given.