Global phase diagram of bound states in the continuum

Bound states in the continuum (BICs) in photonic-crystal slabs have been conventionally classified into three types: single-resonance parametric, symmetry-protected, and Friedrich-Wintgen BICs. Here, we show that the singleresonance parametric BICs come from the coupling between the guided resonance (GR) and Fabry-Perot (FP) modes, and the symmetry-protected BICs from the coupling between degenerate GR modes. Hence, the three types of BICs in photonic-crystal slabs can be classified by the three different Friedrich-Wintgen origins. Based on this universal classification, a global phase diagram of BICs can be obtained with each phase identified by the indices of the three different Friedrich-Wintgen-type BICs. When BICs are created or annihilated, a phase transition occurs and is experimentally observed, in which the FP modes play a significant role. Our work shows a clear physical picture on whether BICs exist and how sensitive they are to changes in the parameter space, and enables improvements in experiment design and applications.