First principles derivation of a Rayleigh Gans Debye model for scattering from anisotropic inhomogeneities

Abstract: Scattering problems are important in describing light propagation in wide ranging media such as the atmosphere, colloidal solutions, metamaterials, glass ceramic composites, transparent polycrystalline ceramics, and surfaces. The Rayleigh Gans Debye (RGD) approximation has enjoyed great success in describing a wide range of scattering phenomena. We derive a generalized RGD formulation from the perturbation of Maxwell equations. In contrast to most treatments of RGD scattering, our formulation can model any soft scattering phenomena in linear media, including scattering by stochastic process, lossy media, and by anisotropic inhomogeneities occurring at multiple length scales. Our first-principles derivation makes explicit underlying assumptions and provides jumping off points for more general treatments. The derivation also facilitates a deeper understanding of soft scattering. It is demonstrated that sources of scattering are not interfaces as is often presumed, but excess accelerating charges emitting uncompensated radiation. Approximations to the equations are also presented and discussed. For example, the scattering coefficient in the large size RGD limit is shown to be proportional to the correlation length and the variance of a projected phase shift.