Generalized Fano resonance theory based on Fabry-Perot cavity

Fano resonance is a pervasive phenomenon observed across many systems, which has traditionally been interpreted through the coupled harmonic oscillator model. However, the traditional model is limited, especially for different line shapes. In this study, we offer a generalized model by incorporating an imaginary coupling coefficient. This approach fundamentally differs from existing theories by identifying two unique Fano line shapes in the electric field of metallic Fabry-Perot cavity. The model connects the imaginary coupling coefficient with phase distribution of the coupling mode, thus revealing the relationship between Fano line shapes and the trend of phase shifts. This provides a new way for understanding and manipulating Fano resonance. The Fano resonance generation has been validated experimentally through reflection spectra. Our investigation offers a new perspective for understanding of Fano resonance via the coupled harmonic oscillator model and paves a way for the development of dynamically tunable Fano resonance devices.