Merging bound states in the continuum for high-efficiency second-harmonic generation

Subwavelength resonant metasurfaces empowered by bound states in the continuum (BICs) have recently emerged as promising platforms for boosting optical nonlinearities as they support high-quality ($Q$) quasi-BIC resonances with strong electromagnetic-field confinement. To date, most such studies have focused on optical resonances, termed symmetry-protected quasi-BICs, because they can be readily accessible in broken-symmetry structures. However, for traditional designs of which meta-atoms are placed on low-refractive-index substrates, their smallest achievable geometric symmetries impose a limitation on the realization of ultrahigh-$Q$ resonances and thereby on the harmonic generation efficiency. Here we demonstrate a strategy that allows us to improve the $Q$ factors of quasi-BICs over a broad range of geometrical asymmetry parameter values. Specifically, using asymmetric dielectric metasurfaces placed above a perfectly reflecting mirror, we construct merging BICs in the geometrical parameter space, which pushes the square asymptotic behavior of the $Q$ factors of traditional configurations into the power of 4 or even 6. We demonstrate that merging-BIC designs can remarkably enhance the second-harmonic generation efficiency. This work suggests a route to suppress out-of-plane radiation losses of metasurfaces with potential applications to nonlinear optics, lasing, and sensing.