  We present a study on photonic vertical cavities consisting of nonlinear
materials embedded in photonic crystals (PhCs) for resonantly enhancing second
harmonic generation (SHG). Previous attempts at SHG in such structures have
been limited to efficiencies of 10$^{-7}$ to 10$^{-5}$, but we demonstrate here
a high SHG efficiency of 0.28% by constructing a vertical cavity with a lithium
niobate membrane placed between two PhCs, which exhibits high quality
resonances. Our results open up new possibilities for compact laser frequency
converters that could have a revolutionary impact on the fields of nonlinear
optics and photonics.
