Uncovering the origin of bound state in the continuum

TL;DR

This paper investigates the origin of bound states in the continuum (BICs) using a two-band model, revealing how tuning inter-band coupling can convert quasi-BICs into exact BICs without relying on symmetry or topological constraints.

Contribution

It introduces a general theory for BICs that applies to multiband systems and provides a new framework for their design across various physical fields.

Findings

Quasi-BICs arise from bound states coupled to a continuum.

Tuning inter-band coupling converts quasi-BICs into exact BICs.

The theory applies to photonics, acoustics, and ultracold atoms.

Abstract

Bound state in the continuum (BIC) and quasi-BIC represent a remarkable class of wave functions that disobey conventional intuition by exhibiting spatially localized modes embedded in the continuum spectrum. In recent years, these states have found important applications in interdisciplinary systems as a non-radiating mode with ultra-long lifetime. In these applications, a key question is how to convert a quasi-BIC into an exact BIC, and what the general criterion is for this transition. In this work, we uncover its origin using two steps in a two-band model with an arbitrary confining potential. Firstly, we demonstrate that a bound state coupled to a continuum band can yield quasi-BIC. Then, we show that tuning the coupling between the bands can convert the quasi-BIC into an exact BIC. In our theory, the real and complex poles of the spectra have a clear physical meaning for the quasi- and exact BICs, and we give the general criterion for exact BICs. Unlike previous proposals, our theory requires neither symmetry protection nor topological constraints and can be extended to a multiband model, providing a new framework for realizing BICs and offering new insights for their design in different fields, including photonics, acoustics, ultracold atoms and Bose-Einstein condensate with and without many-body interactions.