Electromagnetic Quasinormal Modes: A Foundational Framework for Describing Fano Resonances of Extinction Spectra

ABSTRACT Fano resonances are interference signatures characterized by an asymmetry parameter and an intensity parameter . Traditionally, the Fano parameters are described phenomenologically through fits, limiting physical insight and practical applicability. Available analytical formulations of the Fano parameters are only applicable for extinction spectra and fail to capture realistic scenarios such as nanoresonators on substrates or arbitrary illumination. Here, we develop an ab initio Maxwellian framework based on quasinormal modes (QNMs) that provides a natural physically transparent interpretation of extinction spectra of arbitrarily shaped objects. We show that each individual QNM response inherently exhibits a Fano profile and derive general explicit analytical expressions for and . We further introduce an approximation that enables rapid evaluation of these quantities and allows ultrafast, yet accurate, reconstruction and optimization of extinction spectra using Fano parameters. Numerical and experimental validations confirm the high accuracy, computational efficiency, and ease of implementation of our approach across diverse electromagnetic systems, including photonic exceptional points and dispersive nanoresonators on substrates under arbitrary illumination. This framework provides a clear physical understanding and precise control of resonant line shapes, paving the way for advanced spectral design and optimization in nanophotonics.