NTU Scientists Unveil Novel Method for Analyzing Resonance Perturbations in Complex Non-Hermitian Systems
Asst Prof Matthew Foreman and his team from Nanyang Technological University (NTU) have achieved a significant milestone with the acceptance of their latest research paper, titled "Perturbing scattering resonances in non-Hermitian systems: a generalized Wigner-Smith operator formulation", by Newton, published by Cell Press. This work explores new theoretical frontiers in understanding resonance behaviors in non-Hermitian systems, an area with wide implications in photonics, quantum systems, and complex scattering environments. This marks a significant contribution to the scientific conversation around non-Hermitian physics, with NTU researchers pushing boundaries and shaping the future of applied electromagnetics.
The new formulation offers a robust way to calculate resonance shifts in the complex frequency plane induced by arbitrary system perturbations. Unlike prior methods that were often limited to high-quality factor resonances (Q ≫ 1), this new theory is valid for resonances of arbitrary quality factors. Derived from fundamental complex analytic arguments, it provides new insights into the resonant properties of non-Hermitian systems across a broad range of physical scenarios. The researchers demonstrated that for high-Q resonances, their results align with established traditional perturbation formulas. The method has been numerically validated through applications to complex photonic networks and a multi-layered nanoresonator sensor.
Key Contributions and Potential Impact:
• Comprehensive Resonance Analysis: The generalized WS operators provide a versatile tool for analyzing a wide spectrum of resonant systems, offering fresh insights into non-Hermitian system behavior.
• Enhanced Sensing Technologies: The method can track shifts in both scattering poles and zeros. It has been shown that scattering zeros exhibit significantly enhanced sensitivity to perturbations compared to poles, opening new avenues for highly sensitive sensor development, such as in the inverse design of multi-layered nanoresonator sensors for detecting ambient refractive index variations.
• Optimized Lasing and Absorption: The theory can predict optimal pump profiles for single-mode lasing without explicitly calculating the mode distribution, simply by considering generalized WS operators associated with gain coefficients. Similarly, it can guide the selective introduction of loss to achieve coherent perfect absorption of desired modes.
• Broad Applicability: This generalized WS operator framework is applicable to diverse fields of resonant physics, including optics, particle physics, acoustic engineering, and cosmology, serving as a valuable resource for the analysis and design of future resonance-based systems and technologies.
This research was led by Niall Byrnes and Matthew R. Foreman from NTU's School of Electrical and Electronic Engineering.
Acknowledgements. N.B. was supported by Singapore Ministry of Education Academic Research Fund (Tier 1) Grant RG66/23 . M.R.F. was supported by funding from the Institute for Digital Molecular Analytics and Science (IDMxS) under the Singapore Ministry of Education Research Centres of Excellence scheme and by Nanyang Technological University Grant SUG:022824-00001.
