We consider Bloch bound states in the radiation continuum in periodic arrays of dielectric spheres. It is demonstrated that the bound states are associated with phase singularities of the quasimode coupling strength. That makes the bound states topologically protected and, therefore, robust against any variation of parameters preserving the periodicity and rotational symmetry about the array axis. It is shown that under variation of parameters the bound states can only be destroyed by either annihilation of the topological charge or by migration to the sector of the parametric space where the second radiation channel is open.

Bound states in the continuum in open acoustic resonators 1We consider bound states in the continuum (BSC) or embedded trapped modes in twoand three-dimensional acoustic axisymmetric duct-cavity structures. We demonstrate numerically that under variation of the length of the cavity multiple BSCs occur due to the Friedrich-Wintgen two-mode full destructive interference mechanism. The BSCs are detected by tracing the resonant widths to the points of the collapse of Fano resonances where one of the two resonant modes acquires infinite life-time. It is shown that the approach of the acoustic coupled mode theory cast in the truncated form of a two-mode approximation allows us to analytically predict the BSC frequencies and shape functions to a good accuracy in both two and three dimensions.

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We develop the effective non-Hermitian Hamiltonian approach for open systems with Neumann boundary conditions. The approach can be used for calculating the scattering matrix and the scattering function in open resonatorwaveguide systems. In higher than one dimensions the method represents acoustic coupled mode theory in which the scattering solution within an open resonator is found in the form of expansion over the eigenmodes of the closed resonator decoupled from the waveguides. The problem of finding the transmission spectra is reduced to solving a set of linear equations with a non-Hermitian matrix whose anti-Hermitian term accounts for coupling between the resonator eigenmodes and the scattering channels of the waveguides. Numerical applications to acoustic two-, and three-dimensional resonator-waveguide problems are considered.