AI 中文总结
研究开放光学腔中准正常模式，用从引力物理转移来的双曲面方法结合伪谱分析，开发几何 - 光谱框架，能计算光学QNMs并研究其光谱稳定性，还将相关技术扩展到色散电磁学，为研究光学系统稳定性和灵敏度提供基础。
AI 中文摘要
我们为紧致支撑的开放光学腔中准正常模式（QNMs）的计算和稳定性分析开发了一个几何 - 光谱框架。从引力物理转移到电磁学的双曲面方法，将出射边界条件直接纳入光学共振问题的公式中。色散和吸收介质通过辅助场公式用洛伦兹模型介电常数描述，使用切比雪夫光谱方法解决由此产生的非厄米特光谱问题。然后按照[2]将分析扩展到光学设置，用于研究光学共振在微扰下的稳定性。伪谱提供了关于共振灵敏度的信息，而这些信息仅靠QNM光谱是无法获得的。通过比较不同标量积选择所获得的稳定性特性，特别关注用于定义伪谱的范数的作用。结果表明，光谱稳定性的评估与测量微扰的函数设置密切相关。因此，将双曲面公式与伪谱分析相结合，使得计算光学QNMs并研究其光谱稳定性成为可能。该方法将为引力物理中的共振问题开发的技术扩展到色散电磁学，并为研究开放光学系统中的稳定性和灵敏度提供了基础。
英文摘要
We develop a geometric--spectral framework for the computation and stability analysis of quasi-normal modes (QNMs) in open optical cavities of compact support. The hyperboloidal approach, transferred from gravitational physics to electromagnetism [1], incorporates outgoing boundary conditions directly into the formulation of the optical resonance problem. Dispersive and absorbing media are described by a Lorentz-model permittivity through an auxiliary-field formulation, and the resulting non-Hermitian spectral problem is solved using Chebyshev spectral discretization.Pseudospectrum analysis is then extended to the optical setting following [2] and used to study the stability of optical resonances under perturbations. The pseudospectrum provides information on the sensitivity of the resonances that is not contained in the QNM spectrum alone. Particular attention is given to the role of the norm used to define the pseudospectrum, by comparing the stability properties obtained with different choices of scalar product. The results show that the assessment of spectral stability is closely related to the functional setting in which perturbations are measured. Combining the hyperboloidal formulation with pseudospectrum analysis therefore makes it possible to compute optical QNMs while also studying their spectral stability. The approach extends techniques developed for resonance problems in gravitational physics to dispersive electromagnetism and provides a basis for studying stability and sensitivity in open optical systems.
