Resonance structure in weakly absorbing spheres

The well-known resonance structure in the scattering amplitudes for dielectric spheres (Mie scattering) is known to arise from poles in the complex size parameter plane, with the sharpest resonances being due to poles that are close to the real axis. It is also well known that these resonances are damped by the presence of an absorption component in the refractive index. In this paper we show that for small absorption components, the poles move away from the real axis linearly. This result may then be used to study changes in the height, width, and area under the resonances. Perhaps the most interesting result concerns the area, which remains constant over a large range of k.