Analysis of transition from Lorentz resonance to Fano resonance in plasmon and metamaterial systems

Fano resonance, viewed as a quantum interference between continuum and discrete states, demonstrates an asymmetric spectral line shape. Fano resonance is also observed in metamaterials and plasmonic nanostructures and could be explained by the coupling of two classical Lorentz oscillators. A unambiguous connection between Fano resonance and Lorentz resonance plays a vital role in the design and optimization of metamaterials and plasmonic materials for both mechanism understanding and applications. In this paper, a numerical method is employed to schematically investigate the parameters connection between Fano and Lorentz resonance. Both Fano resonant frequency and line-width are parabolic dependent with the coupling coefficient of the Lorentz oscillators. A distinct transition effect can be observed in the Fano parameters when the eigen-frequencies of Lorentz oscillators are tuned. Our results suggest that the controlling of Fano resonance can be done by designing of Lorentz resonance in metamaterials and plasmonic materials artificially, which sustains mimicking the quantum effect by classic systems.