  We report on nonlinear frequency conversion from the telecom range via second
harmonic generation (SHG) and third harmonic generation (THG) in suspended
gallium nitride slab photonic crystal (PhC) cavities on silicon, under
continuous-wave resonant excitation. Optimized two-dimensional PhC cavities
with augmented far-field coupling have been characterized with quality factors
as high as 4.4$\times10^{4}$, approaching the computed theoretical values. The
strong enhancement in light confinement has enabled efficient SHG, achieving
normalized conversion efficiency of 2.4$\times10^{-3}$ $W^{-1}$, as well as
simultaneous THG. SHG emission power of up to 0.74 nW has been detected without
saturation. The results herein validate the suitability of gallium nitride for
integrated nonlinear optical processing.

Optics