Bound states in the continuum in asymmetrical quantum-mechanical and electromagnetic waveguides

We study transport properties and the formation of bound states in the continuum (BIC) in asymmetric quantum mechanical and electromagnetic waveguides. An analytical model for an arbitrary asymmetric two-terminal quantum mechanical waveguide is proposed, and conditions of BIC formation are formulated. We show that the Friedrich-Wintgen mechanism of BIC formation in a system coupled to two continua takes place regardless of the symmetry of the system as long as the proportionate coupling condition is fulfilled. This result is illustrated by numerical simulation of two-dimensional quantum billiard and optical waveguide with a cavity. Due to the universal wave nature of BIC, the proposed BIC formation mechanism allows one to obtain BICs in the broader class of quantum mechanical, electromagnetic, acoustic, and other types of structures.