Generalized Wigner-Smith theory for perturbations at exceptional and diabolic point degeneracies
arXiv:2508.05039 · doi:10.1364/OL.575813
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.
2 figures
References in corpus (22)
- Non-Hermitian Physics
- On-chip Single Nanoparticle Detection and Sizing by Mode Splitting in an Ultra-high-Q Microresonator
- Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering for systems with broken time reversal invariance
- Enhanced sensitivity operation of an optical gyroscope near an exceptional point
- Observation of coherent perfect absorption at an exceptional point
- Perfectly absorbing exceptional points and chiral absorbers
- Focusing inside Disordered Media with the Generalized Wigner-Smith Operator
- Learning and avoiding disorder in multimode fibers
- Maximum information states for coherent scattering measurements
- Optimal Wave Fields for Micro-manipulation in Complex Scattering Environments
- Exceptional-point Sensors Offer No Fundamental Signal-to-Noise Ratio Enhancement
- Stationary Charge Radiation in Anisotropic Photonic Time Crystals
- Optimizing light storage in scattering media with the dwell-time operator
- Coherent wave control in complex media with arbitrary wavefronts
- Petermann factors and phase rigidities near exceptional points
- Non-resonant Density of States Enhancement at Low Energies for Three or Four Neutrons
- Optimal Cooling of Multiple Levitated Particles through Far-Field Wavefront-Shaping
- Photon-efficient optical tweezers via wavefront shaping
- Wigner-Smith time-delay matrix in chaotic cavities with non-ideal contacts
- Wigner-Smith Time Delay Matrix for Electromagnetics: Theory and Phenomenology
- Generalized Wigner-Smith analysis of resonance perturbations in arbitrary non-Hermitian systems
- Perturbing scattering resonances in non-Hermitian systems: a generalized Wigner-Smith operator formulation