Total reflection of two guided waves for embedded trapped modes

To investigate the mechanism of wave trapping, acoustic embedded trapped modes associated with two-resonant-mode interference in two-dimensional duct–cavity structures are calculated by the feedback-loop closure principle, which allows us to analyze the traveling modes that construct the trapped modes. The exact two coexisting resonant modes that underpin an embedded trapped mode in a cavity open to two semi-infinite ducts are numerically demonstrated. At the interface between the cavity segment and a duct, total reflection can occur for a particular combination of two propagative guided waves in the cavity. With a particular cavity length and a particular frequency, total reflection also happens for the two reflected waves at the opposite end of the cavity. In this way, the two coexisting standing waves underpin a trapped mode. It is found that the two standing waves are not two closed-cavity modes. Thus, this work presents a new understanding of such embedded trapped modes as a product of total reflection of two guided waves at the interface between two waveguides, rather than interference between two eigenmodes of a closed cavity. Such total reflection of multiple guide modes is a result of mutual cancellation in transmission to the propagative channel(s) of the ducts. Thus, trapped modes involving more than two standing waves may occur at higher frequencies where more traveling modes in the ducts are propagative. For quasi-trapped modes, the Fano scattering phenomenon owing to the effects of two acoustic channels is also shown.