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We report a general description of quasi-phase-matched parametric process innonlinear photonic crystals (NLPC) by extending the conventional X-raydiffraction theory in solids. Under the virtual wave approximation,phase-matching resonance is equivalent to the diffraction of the scatteredvirtual wave. Hence a modified NLPC Ewald construction can be built up, whichillustrates the nature of the accident for the diffraction of the virtual wavein NLPC and further reveals the complete set of diffractions of the virtualwave for both of the air-dielectric and dielectric-dielectric contacts. We showthe two basic linear sequences, the anti-stacking and para-stacking linearsequences, in one-dimension (1D) NLPC and present a general rule for multiplephase-matching resonances in 1D NLPC. The parameters affecting the NLPCstructure factor are investigated, which indicate that not only the Ewaldconstruction but also the relative NLPC atom size together determine whether adiffraction of the virtual wave can occur in 2D NLPC. The results also showthat 1D NLPC is a better choice than 2D NLPC for a single parametric process.

A Diffractive Study of Parametric Process in Nonlinear Photonic Crystals