Behavior of the Lorenz-Mie poles in the complex space of sphere parameters

We studied the position and motion of poles of Lorenz-Mie (LM) coefficients, responsible for LM resonances, in the space of complex parameters: the size, the refractive index of the sphere, and the refractive index of the host medium. We performed a comprehensive theoretical analysis and classified all resonances according to their asymptotic behavior and origin. In particular, we proved a few lemmas concerning the logarithmic derivatives of Riccati-Bessel functions and used them to prove the absence of LM poles in some areas of the complex plane (depending on the host medium). We also performed extensive numerical calculations of pole trajectories, which fully confirm all theoretical predictions and provide additional details in the intermediate range of size parameters.