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