Doubly resonant second-harmonic generation of a vortex beam from a bound state in the continuum

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.