Doubly resonant photonic crystal cavity (PCC) can trap the light within the sub-wavelength scale. It can support the resonant modes both at the fundamental and the second harmonic frequency. As a result, doubly resonant PCC usually shows a higher nonlinear conversion efficiency. Previous doubly resonant PCCs were constructed by the band-edge mode and the bound states in the continuum (BIC) mode, and were realized in the simulation and the experiment. However, these works generally analyze how to achieve the doubly resonant PCC qualitatively based on various materials. The method of enhancing the value of nonlinear conversion efficiency in the doubly resonant PCC is still not reported.

To solve the problem, we design a doubly resonant PCC based on the merged BIC. For a PCC slab, the merged BIC shows a higher quality factor compared with the one in common BIC, which is beneficial for frequency conversion. We constructed heterostructure PCC based on z-cut lithium niobate slab. The PCC includes the outer region, the transition region, and the core region. The supercell of large and small holes are used to construct core region to help matching the band-edge mode and the merged BIC mode. The lattice constant is adjusted to determine the BIC to be the common state or the merged state. In the simulation the quality factor of 1.5×10^5 is obtained at the fudamental frequency and the quality factor of 2000 is obtained at the second harmonic frequency. The nonlinear conversion efficiency of 48 W^-1 is obtained using the theoretical formula, which is 5 times larger than the one in the common BIC state. This work is expected to provide guidance to the application of BIC in nonlinear photonic area.

Fig. 1 (a) Schematic of the proposed doubly resonant PCC based on merged BIC. (b)The trend of quality factors at the fudamental and second harmonic frequencies in PCC versus the lattice constant. (c) The trend of the product of, the square of the quality factor of the band-edge mode, and the quality factor of the BIC mode versus lattice constants. The trend of the square of the nonlinear overlapping factors versus the lattice constant. (d) The trend of theoretical nonlinear efficiency versus lattice constant.

The work was published in “Rui Ge, Xiangmin Liu, Xiongshuo Yan, Xianfeng Chen and Yuping Chen. Doubly resonant photonic crystal cavity using merged bound states in the continuum, Physical Review B, 107(16):165406 (2023)”.

Link: https://doi.org/10.1103/PhysRevB.107.165406