Bound states in the continuum in a quantum-mechanical waveguide with a subwavelength resonator

It has been shown that a bound state in the continuum of a symmetric quantum-mechanical waveguide with a resonator can be formed at an arbitrarily short length of the resonator. This effect is due to multimodal interference; therefore, it cannot be explained in the simplest two-mode approximation in the Friedrich–Wintgen model and requires the inclusion of at least three modes. The results obtained within the analytical model have been confirmed by the numerical simulation of the stubbed waveguide the attractive potential of the impurity in the resonator.