Splitting and merging of bound states in the continuum through defect engineering

Bound states in the continuum (BICs) are electromagnetic eigenstates that theoretically exhibit infinite quality factors. However, scattering losses induced by manufacturing defects inevitably affect the confinement performance of BICs. Studies have shown that combining multiple BICs can enhance their robustness against such defects. Currently, approaches to merging BICs at off-$\mathrm{\ensuremath{\Gamma}}$ points typically rely on altering the geometry of the central structure, which not only increases the complexity of device design but also potentially raises costs. Based on this, we propose a scheme that maintains the central structure while introducing specific defect holes to break the in-plane symmetry of the system, thereby inducing the splitting of the higher-order BIC and forming multiple off-$\mathrm{\ensuremath{\Gamma}}$ BICs. Subsequently, these split BICs, along with the accidental BICs, will merge at the off-$\mathrm{\ensuremath{\Gamma}}$ point as the structural parameters are varied. The proposed concept not only enhances optical confinement but also enables flexible control over the splitting direction of the higher-order BIC by manipulating the spatial positions of the defect apertures. More importantly, by rationally designing the positions of defects, we can construct merging BICs at arbitrary wave vectors through manipulations of split BICs and accidental BICs. Furthermore, even in the presence of manufacturing defects, the merging BICs demonstrate exceptional robustness. This provides new insights for the flexible control of BICs in diversified applications while also expanding their potential in a broader momentum space.