Enhanced Second and Third Harmonic Generations in Metasurfaces Enabled through Point Group Design and Accidental Bound States in the Continuum

Here, we investigate enhanced second- and third-harmonic generation (SHG and THG) in GaAs metasurfaces by combining electromagnetic point-group designs with accidental bound states in the continuum (BICs). Using group theory, we predict the existence, suppression, and polarization selection rules of SHG and THG for metasurfaces belonging to the D2h and C2v point groups. In D2h metasurfaces, inversion symmetry suppresses SHG while enabling polarization-selective THG, which is strongly enhanced near accidental BICs with ultrahigh Q-factors approaching 107. By breaking inversion symmetry to form C2v metasurfaces through the introduction of nanogaps, SHG is now allowed and is dramatically enhanced near accidental BICs. Importantly, accidental BICs preserve polarization selection rules while providing a robust parameter range for high-Q resonances, in contrast to quasi-BICs induced by symmetry breaking. Our results demonstrate that the combination of point-group theory and accidental-BIC engineering offers a predictive and robust route toward highly efficient nonlinear metasurfaces.