Bound states in the continuum and Fano resonances in subwavelength resonator arrays

TL;DR

This paper demonstrates the existence of bound states in the continuum in subwavelength resonator arrays and analyzes how slight symmetry breaking leads to Fano resonances with asymmetric scattering behavior.

Contribution

It provides a rigorous proof of BICs in such systems and explicitly characterizes Fano resonances through asymptotic analysis of the scattering matrix.

Findings

Existence of bound states in the continuum in subwavelength resonator arrays

Symmetry breaking enables excitation of BICs and induces Fano resonances

Explicit computation of the scattering matrix reveals asymmetric transmission features

Abstract

When wave scattering systems are subject to certain symmetries, resonant states may decouple from the far-field continuum; they remain localized to the structure and cannot be excited by incident waves from the far field. In this work, we use layer-potential techniques to prove the existence of such states, known as bound states in the continuum, in systems of subwavelength resonators. When the symmetry is slightly broken, this resonant state can be excited from the far field. Remarkably, this may create asymmetric (Fano-type) scattering behaviour where the transmission is fundamentally different for frequencies on either side of the resonant frequency. Using asymptotic analysis, we compute the scattering matrix of the system explicitly, thereby characterizing this Fano-type transmission anomaly.