Simultaneous High-Efficiency Second- and Third-Harmonic Generation in a 1-D Semiconductor Photonic Crystal

We show that very high-efficiency second- and third- harmonic conversions can be generated simultaneously in 1-D semiconductor photonic crystals that possess both chi⁽²⁾ and chi⁽³⁾ nonlinearities. This is theoretically demonstrated in a CdS-SiO₂ photonic crystal. The total conversion efficiency can be as large as ~30% for both second- and third-harmonic generations in a small sample with ~14 mum thickness and an input power of ~300 MW/cm². Such high conversion efficiency is the result of 1) the improved phase matching induced by the Kerr effect and 2) the formation of coupled localized states for the fundamental and second- and third-harmonic waves. From our calculation results, we have also observed the tristability of the output intensity as a function of the input power for each of the fundamental, second-harmonic and third-harmonic waves. The origin of the tristability can be understood from the merging of two bistabilities of the fundamental and higher harmonic waves.