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

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.