Larger enhancement in four-wave mixing from graphene embedded in one-dimensional photonic crystals

We demonstrate theoretically that the efficiency of four-wave mixing (FWM) can be enhanced by more than several orders in monolayer graphene by inserting it in a properly designed photonic crystal (PC). Two kinds of cases are considered. One is monolayer graphene embedded in defect PC, and the other is a stack of monolayer graphene in a dielectric multilayer structure. It is found that a larger enhancement of the efficiency in the FWM from the monolayer graphene can be obtained in two cases. Such an effective enhancement utilizes the improved field localization within the defect state or at the band-edge state. Due to the presence of a feedback mechanism at each interface of the multilayer, we demonstrate that the tunable phase conjugation by an external voltage can be effectively generated when only one pump wave is used.