  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.
