Abstract
In order to determine the angular geometry that satisfies quasi-phase matching conditions for enhanced second-harmonic generation (SHG), the equi-frequency surfaces of the resonant photonic modes (that lie above the light line) of a one-dimensional GaN photonic crystal have been experimentally and theoretically studied as a function of frequency, angle of incidence, and azimuthal direction. Enhancement of the SHG has been observed when the angular configuration satisfies the quasi-phase matching conditions, i.e., when both the fundamental and second-harmonic fields coincide with resonant modes of the photonic crystal. The SHG enhancement achieved to the double resonance was 5000 times with respect to the unpatterned GaN layer. A smaller, but still substantially enhanced SHG level was also observed when the fundamental field is coupled into a resonant mode, while the second-harmonic field is not.