Nonlinear Interactions in Periodic and Quasi-Periodic Nonlinear Photonic Crystals

Nonlinear photonic crystals are materials in which the second order susceptibility is modulated in an ordered fashion, usually in one or two dimensions, while the linear susceptibility remains constant. Here, a general analysis of quasi-phase-matched interactions in a nonlinear photonic crystal is derived for the cases of periodic and quasiperiodic structures. The effects of the lattice, motif and interaction area on the generated electric field and intensity are analyzed in a periodic nonlinear photonic crystal. For the case of a quasiperiodic frequency converter, a systematic procedure is described, enabling to phase match any set of interacting waves. Nonlinear photonic crystals with radial symmetry are introduced. These structures have continuous rotation symmetry, but no translation symmetry, in contrary to the lattice based structures. Finally, several applications of quasiperiodic nonlinear frequency converters are reviewed.