Merging bound states in the continuum in the geometrical parameter space

Optical resonators can support bound states in the continuum (BICs) with infinite quality (Q) factors by eliminating radiation losses. However, practical optical resonators only support quasi-BICs with finite Q factors due to the scattering losses caused by inevitable fabrication defects. Merging multiple BICs in momentum space can improve the Q factors of resonators over a broad wavevector range. The dependence of a resonator on high-precision nanofabrication can also be decreased by improving the robustness of the Q factors of quasi-BICs against asymmetric structural parameters, which is much easier to realize high Q factors. Here, we propose an efficient method to merge multiple BICs in the geometrical parameter space by engineering a folded mode induced by Brillouin zone folding. Along with the topological charge evolution process in momentum space, this approach significantly improves the robustness of the Q factor of resonators against perturbations caused by geometric symmetry breaking and wavevector. Compared with fundamental isolated BICs, the merged BICs are more immune to structural disorders. Our approach provides a path to achieve robust ultrahigh-Q resonances, which holds immense potential in enhancing quantum and nonlinear effects, as well as improving the performance of optical sensors and nanolasers.