Nonlinear diffraction in enhanced second-harmonic generation from 3D opal-Si and opal-GaN photonic crystals

Realization of enhancement of second-harmonic generation (SHG) in three-dimensional (3D) photonic crystals utilizing nonlinear diffraction is demonstrated. The samples are composed from close-packed silicon oxide spheres with diameter of 250 to 300 nm in each sample forming an ordered fcc opal matrix. The opal voids are filled by noncentrosymmetric gallium nitride and centrosymmetric silicon with filling factor close to unit. The photonic band gap (PBG) is obtained for light reflected from the (111) face and localized in the spectral region from 800 to 950 nm for different samples. SHG spectra show pronounced peaks as the fundamental radiation is tuned across the photonic band gap. The intensity enhancement in SHG is about 100 and the spectral width of the SHG resonances is approximately 15 nm. The SHG enhancement is attributed to combination of linear diffraction of the fundamental radiation from the (111) opal layers and nonlinear diffraction utilizing the 3D periodicity of the quadratic susceptibility of silicon and gallium nitride nanocrystals in opal voids. The spectral position of the SHG peak is slightly red-shifted in comparison with the PBG center and attributed to condition of the group velocity minima.