A Finite-Difference Time-Domain approach for dispersive magnetic media

We extend the Finite-Difference Time-Domain method to treat dispersive magnetic media by incorporating magneto-optical effects through a frequency-dependent permittivity tensor. For benchmarking our method, we consider the light scattering on a magnetic sphere in the Mie regime. We first derive the analytical scattering expressions which predict a peak broadening in the scattering efficiency due to the atomic energy level splitting in the presence of a magnetic field, together with an additional rotated part in the scattered field profile due to the Faraday rotation. We show that our numerical method is able to capture the main scattering features and discuss its limitations and possible improvements in accuracy.