Recovery of topologically robust merging bound states in the continuum in photonic structures with broken symmetry

Optical bound states in the continuum (BICs) provide a unique mechanism of light confinement that holds great potential for fundamental and applied research in optics and photonics. Of particular interest are merging BICs realized in planar periodic structures by merging accidental and symmetry-protected BICs. Topological nature of merging BICs renders their $Q$ factors exceptionally high and robust. However, the existence of accidental BICs relies on the up-down mirror symmetry of the structure. If this symmetry is broken, e.g., by a substrate, the $Q$ factor of the mode drops down. Consequently, ultrahigh-$Q$ merging BICs cannot be achieved in substrate-supported structures. Here, by studying the case of a one-dimensional periodic dielectric grating, we discover a simple method to fully compensate for the detrimental effect of breaking the up-down mirror symmetry. The method makes use of a thin layer of a high-refractive-index dielectric material on one side of the structure, allowing one to restore the diverging $Q$ factor of the accidental BIC and fully recover the merged BIC. By investigating the far-field polarization patterns of the modified gratings, we show that the integer-charge polarization vortices of the accidental BICs are restored by intersecting the momentum-space trajectories of circularly polarized half-vortices simultaneously in the upward and downward radiation directions. Our approach can enable flexible design, feasible realization, and extended applications of topologically robust BICs in various systems.