Second and third harmonic generation via a chi ((2)) three-wave mixing proc
ess 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 correspon
d 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 obt
ained in finite layered structures by using and balancing an interplay betw
een material dispersion and the geometrical dispersion introduced by the st
ructure.