  In this work, a doubly resonant photonic crystal (PhC) cavity using the
merged bound states in the continuum (BICs) is proposed to obtain a higher
second harmonic generation (SHG) efficiency. Firstly by scanning geometry
parameters the accidental BICs and a band-edge mode outside the light cone can
be obtained. Then as the lattice constant or the thickness of the slab is
adjusted the accidental BICs will merge. A supercell with large and small holes
is constructed and the band-edge mode outside the light cone can be
mode-matched with the merged BICs mode. Finally the heterostructure PhC cavity
is designed. The merged BICs show a high quality factor for the photonic
crystal with finite size. Consequently, the SHG efficiency of the lattice
constant near merged BICs of ~6000% W-1 is higher than the one of the isolated
BIC.
