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To date, second-harmonic generation (SHG) at nanoscale has been concentratedon employing high-refractive-index nanostructures, owing to the strong fieldconfinement at deep subwavelength scales based on optically resonant effects.However, low-index nanostructures generally exhibit weaker resonant effects andlower field confinement. To address this issue, by harnessing the largenonlinearity of LiNbO$\mathrm{_3}$, we propose a novel approach to employguided resonances and bound states in the continuum (BICs) with aLiNbO$\mathrm{_3}$ metasurface consisting of a LiNbO$\mathrm{_3}$ disk arraysitting on a LiNbO3 thin film. Such a system can transform the guided modessupported by LiNbO$\mathrm{_3}$ thin film into high-quality guided resonanceswhich can be excited directly under plane-wave illumination. Importantly, wefurther demonstrate strong field confinement inside LiNbO3 thin film withtailorable Q-factor by realising a Friedrich-Wintgen BIC. Such a unique modeengineering enables a record-high SHG efficiency of 5\% under a pump intensityas low as 0.4 $\mathrm{MW/cm^{2}}$. Moreover, we reveal the influence ofnonlinear resonances and cross-coupling on the SHG by showing the anomalous SHGand efficiency tuning with the rotation of the crystal axis. Our work offers anew route to constructing enhanced SHG based on high-Q guided resonances andBICs, including low-index and high-index nonlinear materials.

Boosted second-harmonic generation in the LiNbO$\mathrm{_3}$ metasurface governed by high-Q guided resonances and bound states in the continuum