  Photonic crystal point-defect cavities were fabricated in a GaN free-standing
photonic crystal slab. The cavities are based on the popular L3 design, which
was optimized using an automated process based on a genetic algorithm, in order
to maximize the quality factor. Optical characterization of several individual
cavity replicas resulted in an average unloaded quality factor Q = 16,900 at
the resonant wavelength {\lambda} $\sim 1.3$ {\mu}m, with a maximal measured Q
value of 22,500. The statistics of both the quality factor and the resonant
wavelength are well explained by first-principles simulations including
fabrication disorder and background optical absorption.
