Parametric interactions in 3-dimensional photonic crystals

The quadratic nonlinear interaction is considered within 3-dimensional photonic crystals. Results from a theoretical model that includes the full 3-dimensional aspect of such nonlinear interaction prove that second order processes are possible in centrosymmetric 3-dimensional photonic crystals, where the contribution to this nonlinear interaction is localized at the interfaces separating the two materials of the photonic lattice. It is shown also that the intrinsic periodicity of the material provides the mechanism of phase matching. Additional numerical results from the same model show that efficient parametric processes are achievable using very short 3-dimensional photonic crystals, when realistic pararmeters for such nonlinear structures are used.