Second-harmonic generation in nonlinear materials can be greatly enhanced by realizing doubly resonant cavities with high quality factors. However, fulfilling such doubly resonant condition in photonic crystal (PhC) slab cavities is a long-standing challenge, because of the difficulty in engineering photonic bandgaps around both frequencies. Here, by implementing a second-harmonic bound state in the continuum (BIC) and confining it with a heterostructure design, we show the first doubly resonant PhC slab cavity with $2.4 \times {10^{- 2}}\;{{\rm W}^{- 1}}$ intrinsic conversion efficiency under continuous-wave excitation. We also report the confirmation of highly normal-direction concentrated far-field emission pattern with radial polarization at the second harmonic frequency. These results represent a solid verification of previous theoretical predictions and a cornerstone achievement, not only for nonlinear frequency conversion but also for vortex beam generation and prospective nonclassical sources of radiation.

中文翻译：

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从连续体中的束缚态产生双共振二次谐波

通过实现具有高品质因数的双谐振腔，可以大大增强非线性材料中的二次谐波产生。但是，由于很难在两个频率附近设计光子带隙，因此在光子晶体（PhC）平板型腔中实现这种双共振条件是一项长期的挑战。在这里，通过在连续体（BIC）中实现第二谐波束缚态并将其限制在异质结构设计中，我们展示了第一个双共振PhC平板腔，其空腔为$ 2.4乘以{10 ^ {-2}} \; {{\ rm W} ^ {-1}} $连续波激励下的固有转换效率。我们还报告了在二次谐波频率下具有径向极化的高度法向集中的远场发射图的确认。这些结果代表了对先前理论预测和基础成就的可靠验证，不仅对于非线性频率转换，而且对于涡旋束生成和预期的非经典辐射源也是如此。