Model of Coupled Oscillators for Fano Resonances

Abstract

The use of analogies in numerical simulations and experiments can be a powerful tool to extract useful information, understand and design optical and electromagnetic systems based on the Fano effect. The model of coupled oscillators has been used over decades to interpret the Fano interference effect in a variety of optical, plasmonic and microwave systems. Fano resonances can be modeled with systems of weakly or strongly coupled mechanical oscillators, providing insight into the dynamics of the radiative continuum and the localized resonance. The coupled oscillator model has been revisited and used extensively in optical and electromagnetic analogs of Fano resonances in the recent years, and has also been the subject of further elaborations bringing it quite far from its standard form: this includes an explicit distinction between non-radiative and radiative losses, the relationship between the driving force and the radiative damping of the bright oscillator, its extension to non-linear effects (such as second or third harmonic generation), and the inclusion of a phase in the coupling term. Further work which has been conducted to understand the interplay between the bright mode and the dark mode in Fano-resonant systems is discussed, in particular the effect of modes coupling and non-radiative losses on its spectral lineshape. For this purpose, the Fano formula and its generalization to lossy systems have been derived in the coupled oscillator system. Finally, an extended coupled oscillator model including radiative losses as a result of Abraham-Lorentz force on accelerated charges is discussed. It allows a model of hybridization taking into account radiative losses and radiative coupling. Both phenomena of superradiance and subradiance, as well as the interaction between hybridized modes can be predicted. The purpose of this Chapter is to review these different forms of coupled oscillator models for Fano-resonant optical and microwave systems, and provide theoretical and experimental examples of applications.