Optical Bloch-mode-induced quasi phase matching of quadratic interactions in one-dimensional photonic crystals

We examine in detail the quasi-phase-matching process obtained as a stationary modulation of the fundamental field at the band edge of a finite one-dimensional photonic crystal. The treatment is carried out in terms of the structure Bloch waves and fully explains the behavior of second-harmonic generation in the grating. An integrated microstructured AlGaAs mesa waveguide is proposed that gives efficient second-harmonic and difference-frequency generation in virtue of the combined presence of a periodic modulation of the fundamental-field amplitude and of the photonic bandgap edge.