Quasinormal modes expansions for nanoresonators made of absorbing dielectric materials: study of the role of static modes

Abstract: The interaction of light with photonic resonators is determined by the eigenmodes of the system. Modal theories based on quasinormal modes provide a natural tool to calculate and understand light scattering by nanoresonators. We show that, in the case of resonators made of absorbing dielectric materials, eigenmodes with zero eigenfrequency (static modes) play a key role in the modal formalism. The excitation of static modes builds a non-resonant contribution to the modal expansion of the scattered field. This non-resonant term plays a crucial physical role since it largely contributes to the off-resonance signal to which resonances are added in amplitude, possibly leading to interference phenomena and Fano resonances. By considering light scattering by a silicon nanosphere, we quantify the impact of static modes. This study shows that the importance of static modes is not just formal. Modal expansions without static modes reconstruct an incorrect internal field and incorrect extinction and absorption cross-sections. Static modes are of prime importance in an expansion truncated to only a few modes.