Evolution of degenerate pairs of bound states in the continuum with broken symmetry

Bound states in the continuum (BICs) with exceptionally high quality factors (Q factors) have become focal points in photonic device research, finding applications in nonlinear enhancement, laser generation, sensing, and beyond.In this study, we systematically investigate the intricate relationship between the in-plane symmetry groups of photonic crystals and symmetryprotected BICs (SP-BICs) using a rigorous group theory approach.By modifying the spatial distribution of refractive indices to perturb the C2 and C3 symmetries within a C6v photonic crystal slab, we introduce a novel method to enable precise tuning of BIC resonances, including the BIC frequency, Q factor, and polarization state.The proposed group theory approach and tuning mechanism establish a pioneering pathway for the design and tunability of BICs, opening avenues for the development of advanced photonic devices with tailored functionalities such as tunable lasers and optical sensors with enhanced performance.