Analytical and numerical study of Friedrich–Wintgen bound states in the continuum in a compact acoustic cavity

Bound states in the continuum (BICs) within open acoustic cavities provide a promising way for achieving high-quality factor resonances which can be exploited in numerous acoustic devices. One particularly intriguing mechanism for the formation of BICs is the Friedrich–Wintgen (FW) mechanism, in which a BIC emerges due to destructive interference between two resonant modes that coexist within the same cavity. Here, we investigate FW-BICs in a simple acoustic T-shaped cavity based on slender tubes. The T-shaped cavity consists of two horizontal arms of lengths d2 and d3 coupled to a vertical stub of length d1. The whole cavity is inserted between two semi-infinite waveguides. We show that the FW-BICs can be obtained when the two horizontal guides d2 and d3 are taken commensurate. These BICs are independent of d1 and the two semi-infinite waveguides. We demonstrate that the FW-BIC appears as the result of the interaction of two eigenmodes of the isolated cavity, the width of one mode vanishes giving rise to a FW-BIC, while the width of the other mode becomes maximal. By breaking the BIC condition, the latter turns into quasi-BICs in the shape of acoustic induced transparency or acoustic induced reflection resonances. The quasi-BICs are characterized by narrow width and high-quality factors which makes them suitable for filtering and sensing applications as well as tuning the far-field radiation of a source inside the cavity. The analytical results are obtained by means of the Green's function method and confirmed by finite element simulation in comsol.