Enhanced Cerenkov SHG in planar nonlinear waveguide reproducing a 1-D PBG

Second harmonic generation (SHG) in Cerenkov configuration is investigated under conditions for which the use of a linear grating fabricated on top of the waveguide reproduces a photonic band-gap structure. The fundamental mode of the guide, at the fundamental frequency, is timed at the photonic band edge resonance thus experiencing a great confinement and enhancement of the electromagnetic field inside the structure. The conversion efficiency achieved in both forward and backward direction is at least one order of magnitude greater than that of a ``conventional'' Cerenkov emission in a waveguide of the same length.