Nested formation mechanisms of Fano line shape in far-field response of coupled waveguide multilayer structure revealed by analyses of local electric fields

Abstract

Based on electromagnetic calculations, the formation mechanism of the Fano line shape in the attenuated total reflection (far-field) spectrum of a coupled waveguide multilayer structure is studied in detail by tracing back to the behaviors of local electric fields. The Fano line shape of absorptance [Formula: see text] directly related to the reflectance by [Formula: see text] is shown to be generated by a superposition of a Fano line shape exhibited by local absorption in one of the waveguide layers and a Lorentzian line shape exhibited by local absorption in another waveguide layer. It is also shown that the Fano line shape of the first waveguide layer is generated by a superposition of different Fano line shapes exhibited by local electric fields at different positions inside the waveguide layer. These results unveil the nested mechanisms of the Fano line shape formation hidden in the behaviors of local electric fields. The Fano resonance inside the first waveguide layer is thought to be an example of the multiple Fano resonance arising from the interaction between multiple continua with a discrete state.