The parametric quadratic nonlinear interaction is considered within three-dimensional photonic crystals. A theoretical model that includes the full three-dimensional aspect of such nonlinear interaction is developed. Results from the study prove that second-order processes are possible in centrosymmetric three-dimensional photonic crystals and that the contribution to this nonlinear interaction is localized at the interfaces separating the two materials of the photonic lattice. In fact, such structures provide an independent solution to some of the most basic requirements for an efficient second-order nonlinear interaction: a nonvanishing interaction in the dipole approximation, a phase-matching mechanism, and a high nonlinear susceptibility not linked to the specific properties of the crystalline structure. Numerical results show that efficient parametric processes are achievable by use of short three-dimensional photonic crystals when realistic parameters for such nonlinear structures are used.
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