Multimode resonances, intermode bound states, and bound states in the continuum in waveguides

We study analytically and numerically the formation of bound states in the continuum (BICs) in quantummechanical and optical spatially symmetric multimode waveguide systems. The widely used Friedrich-Wintgen model predicts a BIC for two (nearly) degenerate eigenstates of the resonator. However, numerical calculations typically show that BICs may appear away from the degeneracy point (or avoided crossing region) in the energy-parameter space. From the two-mode point of view based on the Friedrich-Wintgen model, such BICs can be considered as accidental. In this paper, we go beyond the two-mode approximation and, appealing to the notion of intermode bound states, provide an illustrative procedure for deriving conditions for BIC formation within an arbitrary finite-mode approximation. In particular, we show that a three-mode approximation allows the description of a continuous transition of a BIC between different pairs of modes, which can be associated with it within the two-mode model. Also, a manifestation of exceptional points as (anti)resonance coalescence is discussed. Analytical conclusions are verified by the results of numerical simulations of two-dimensional quantum-mechanical and optical stubbed waveguides with confining impurities in the stub. Moreover, numerical simulations confirm the existence of BICs in optical subwavelength resonators, which were earlier predicted in quantum-mechanical waveguides.