Mittag-Leffler expansion of the optical scattering matrix via rescaled scattering channels

The optical scattering matrix describes how light interacts with scatterers by relating incoming and outgoing waves via scattering channels. It can be expanded in terms of optical resonances through a pole expansion, providing an efficient and physically intuitive alternative to full-wave simulations. Common choices for scattering channels coming from Mie theory result in scattering matrices being exponentially divergent in the complex frequency plane, preventing a Mittag-Leffler expansion. We show that a Mittag-Leffler expansion becomes possible by rescaling scattering channels. However, this approach is not unique. Certain rescalings can introduce new artificial poles that do not originate from optical resonances.