Perturbing scattering resonances in non-Hermitian systems: a generalized Wigner-Smith operator formulation

TL;DR

This paper introduces a new method using generalized Wigner-Smith operators to analyze how perturbations affect resonances in non-Hermitian systems, validated through photonic network applications.

Contribution

The paper presents a novel approach linking generalized Wigner-Smith operators to cavity perturbation theory for analyzing resonance shifts in non-Hermitian systems.

Findings

Effective calculation of resonance pole shifts in complex systems

Validation through application to photonic networks

Enhanced understanding of non-Hermitian resonance properties

Abstract

Resonances of open non-Hermitian systems are associated with the poles of the system scattering matrix. Perturbations of the system cause these poles to shift in the complex frequency plane. In this work, we introduce a novel method for calculating shifts in scattering matrix poles using generalized Wigner-Smith operators. We link our method to traditional cavity perturbation theory and validate its effectiveness through application to complex photonic networks. Our findings underscore the versatility of generalized Wigner-Smith operators for analyzing a broad spectrum of resonant systems and provides new insight into resonant properties of non-Hermitian systems.