  In this paper, we proposed and numerically demonstrated a giant enhancement
up to 108 in both forward and backward propagation of the Second Harmonic
Generation by combining the high-quality factor cavities of the Bound States in
the Continuum and the excellent nonlinear optical crystal of lithium niobate.
The enhancement factor is defined as the ratio of the second harmonic signal
generated by the structure (lithium niobate membrane with Si grating) divided
by the signal generated by lithium niobate membrane alone. Furthermore, a
minimum interaction time of 350 ps is achieved despite the etching less lithium
niobate membrane with a conversion efficiency of 4.77x10-6. The origin of the
enhancements is linked to the excitation of a Fano-like shape
Symmetry-Protected Mode (SPM) that is revealed by Finite Difference Time Domain
(FDTD) simulations. The proposed platform opens the way to a new generation of
efficient integrated optical sources compatible with nanophotonic devices for
classical and quantum applications.
