A diffractive study of optical parametric interactions in nonlinear photonic crystals

With the nonlinear diffraction concept, we present a diffractive study of optical parametric interactions in nonlinear photonic crystals. The nonlinear diffraction concept enables the design of complicated nonlinear photonic crystal structures in an intuitive way. We show that there are two basic linear sequences, the anti-stacking and the para-stacking sequences, existing in a one-dimensional structure; and we present the realization of multiple phase-matching resonances in the combination of the two basic sequences. The parameters affecting the structure factor of a two-dimensional nonlinear photonic crystal are investigated, which indicate that not only the Ewald construction but also the relative domain size determines two-dimensional nonlinear diffractions.