Photonic-bandgap structures in planar nonlinear waveguides: application to second-harmonic generation

Second-harmonic generation (SHG) is investigated in a planar waveguide geometry under conditions for which the use of a linear grating fabricated on top of the waveguide reproduces a photonic-bandgap structure. The fundamental mode of the guide, which coincides with the fundamental pump frequency, is tuned at the photonic band-edge resonance in order to enhance field-localization effects. However, the linear grating alone is not able to produce both field confinement and phase matching of the second-harmonic-generation process. Phase matching is obtained with the additional modulation of the nonlinear susceptibility ${\chi }^{(2)},$ as in conventional quasi-phase-matching schemes. The conversion efficiency achieved with both linear and nonlinear gratings is orders of magnitude greater than that of a quasi-phase-matched device of the same length.