Generalized Wigner-Smith analysis of resonance perturbations in arbitrary $Q$ non-Hermitian systems

TL;DR

This paper extends the generalized Wigner-Smith analysis to arbitrary Q-factor non-Hermitian systems, linking it with electromagnetic perturbation theory and demonstrating its application in designing nanoresonator sensors and analyzing scattering sensitivities.

Contribution

It introduces a unified framework connecting Wigner-Smith formalism with electromagnetic perturbation theory for open resonant systems of any Q factor.

Findings

Numerical examples validate the extended method.

Enhanced sensitivity of scattering zeros to perturbations.

Successful inverse design of nanoresonator sensors.

Abstract

Perturbing resonant systems causes shifts in their associated scattering poles in the complex plane. In a previous study [arXiv: 2408.11360], we demonstrated that these shifts can be calculated numerically by analyzing the residue of a generalized Wigner-Smith operator associated with the perturbation parameter. In this work, we extend this approach by connecting the Wigner-Smith formalism with results from standard electromagnetic perturbation theory applicable to open systems with resonances of arbitrary quality factors. We further demonstrate the utility of the method through several numerical examples, including the inverse design of a multi-layered nanoresonator sensor and an analysis of the enhanced sensitivity of scattering zeros to perturbations.