Observation of optical second-harmonic generation in porous-silicon-based photonic crystals in the Laue diffraction scheme

Second-harmonic generation (SHG) in the Laue scheme of the dynamical Bragg diffraction in one-dimensional photonic crystal (PhC) is studied. The experiments are performed for partially annealed porous-silicon PhC containing 250 periods of the structure. Our measurements confirm that the phase-matched optical SHG is observed under the Bragg conditions, which is evidenced by a narrow angular and spectral distribution of the diffracted SHG outgoing the PhC. This is confirmed by both the analytical description of the SHG process performed in the two-wave approximation, and by direct calculations of the PhC dispersion curves for the fundamental and SHG wavelengths by the revised plane wave method. Possible types of phase- and quasi-phase-matching realized in the studied PhC under the Laue diffraction scheme are discussed.