Simultaneously phase-matched enhanced second and third harmonic generation

Second and third harmonic generation via a chi ((2)) three-wave mixing process can occur with high conversion efficiency in a one-dimensional photonic band gap structure. We find that it is possible to simultaneously achieve enhancement and exact phase-matching conditions of second harmonic and sum frequency generation, omega +2 omega-->3 omega. It is also remarkable that high conversion efficiencies persist under tuning conditions that correspond to a phase mismatch. While these conditions are quite unusual and cannot be achieved in any known bulk material, we show that they can be easily obtained in finite layered structures by using and balancing an interplay between material dispersion and the geometrical dispersion introduced by the structure.