Generalized Wigner-Smith theory for perturbations at exceptional and diabolic point degeneracies

TL;DR

This paper introduces a residue-based perturbation theory using generalized Wigner-Smith operators to accurately predict resonance splitting at diabolic and exceptional points, validated through models and electromagnetic simulations.

Contribution

It presents a novel theoretical framework for quantifying spectral degeneracy perturbations solely from scattering data, applicable to non-Hermitian wave phenomena.

Findings

Excellent agreement between theory and simulations

Accurate prediction of resonance splitting from scattering data

Framework enables precision tuning and inverse design

Abstract

Spectral degeneracies, including diabolic (DP) and exceptional (EP) points, exhibit unique sensitivity to external perturbations, enabling powerful control and engineering of wave phenomena. We present a residue-based perturbation theory that quantifies complex resonance splitting of DP and EP type spectral degeneracies using generalized Wigner-Smith operators. We validate our theory using both analytic Hamiltonian models and numerical electromagnetic simulations, demonstrating excellent agreement across a range of cases. Our approach accurately predicts degenerate resonance splitting using only scattering data, offering a powerful framework for precision tuning, inverse design, and practical exploitation of non-Hermitian phenomena.