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

TL;DR

This paper demonstrates that static modes with zero eigenfrequency are essential in quasinormal mode expansions for absorbing dielectric nanoresonators, significantly affecting scattering and resonance phenomena.

Contribution

It reveals the crucial role of static modes in modal theories for nanoresonators made of absorbing dielectrics, highlighting their impact on scattering and resonance analysis.

Findings

Static modes contribute significantly to off-resonance signals.

Excluding static modes leads to inaccurate internal fields and cross-sections.

Including static modes improves the accuracy of modal expansions.

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.