Giant Enhancement of Second Harmonic Generation at Photonic Band Gap Edges

Second harmonic generation （SHG） in one-dimensional nonlinear photonic crystals made from periodically alternating ferroelectric and dielectric layers is investigated by means of the transfer matrix method. When tuned at the photonic band gap （PBG） edges, the fundamental wave and second harmonic wave slow down, and the filed enhancement takes place within the nonlinear photonic crystal. The phase mismatching can be compensated for to some extent and the second harmonic process will be enhanced. Numerical results show that the enhancement of SHG in the PBG structure can be up to four orders of magnitude compared with the traditional quasi-phase-matching structure.