Doubly resonant photonic crystal cavity using merged bound states in the continuum

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.