Mie and potential scattering by a refractive 1/r inhomogeneity: Electromagnetic scattering by an infinite Coulomb-like scatterer

•Electromagnetic scattering by a special type of radial refractive index profile is analyzed.•The Lorenz-Mie theory and the scalar/vectorial Born approximation are employed.•Similarities and differences to particle (Rutherford) scattering are found.•Shaped beams resemble wave packets and resolve cross-section divergences.•Photothermal microscopy measures an experimental realization.

The weak electromagnetic scattering of a special type of gradient index scatterer resembles the situation of charged particle scattering off an electrostatic Coulomb potential. Accordingly, plane-wave scattering for a radially symmetric decaying perturbation of the refractive index n(r)=n0−ν/k0r is studied. The experimental realization of this specific scattering is found in photothermal single particle microscopy. Vectorial scattering in Lorenz-Mie theory recovers the properties in the Born approximation of the corresponding potential scattering scenario. Shaped beams within the generalized Lorenz-Mie theory are found to resolve known pathologic properties of the problematic 1/r potential.