Jumping and\nMerging of Bound States in the Continuum\non Degenerate Bands

This study delves into the complex behavior of bound\nstates in\nthe continuum (BICs) on degenerate bands, focusing on the interactions\nand transitions among high-order symmetry-protected BICs, Friedrich–Wintgen\nBICs (FW BICs), and accidental BICs. We provide a visualization for\nunderstanding the mechanisms by which careful manipulation of the\nphotonic crystal slab (PhCS) period can facilitate the topological\nbehavior of BICs on a band as well as the reversal of their topological\ncharges. Our results reveal that the accidental BICs move close to\nthe Dirac points and jump to another band, reversing their own topological\ncharges after the jump. As the FW BICs approach the symmetry-protected\nBICs with the topological charge of −2, the six Dirac points\nconverge toward the Γ point simultaneously, causing a jumping\nof the high-order Γ-point BICs to a different band. The breaking\nof the C<sub>6</sub><sup>z</sup> rotation symmetry prompts accidental\nBICs to jump to the focused band and merge with two FW BICs and a\nsplit BIC. Our research underscores the universal characteristic of\nBIC jumping at degenerate points, providing a deeper insight into\nthe topological properties of photonic systems and their practical\nimplications for the design of optical devices.