Enhanced nonlinear optical responses of graphene in multi-frequency topological edge modes

We propose a hybrid structure where graphene is inserted to the interface of two one-dimensional photonic crystals (1D PCs). The two PCs are designed to have opposite topological properties, and at the interface, topological edge modes exist. The edge modes exist at both the fundamental frequency (FF) and the third harmonic (TH) frequency. This double resonant structure will enhance the nonlinear responses of graphene greatly, including Kerr nonlinearity and TH generation. We discuss these two kinds of nonlinearities both at terahertz (THz) and near-infrared (NIR) frequencies. The influence of Kerr nonlinearity on the resonant frequencies is considered, when we calculate the TH generation. At THz frequency, low-threshold bistability (about 8MW/cm²) is obtained and the TH generation efficiency of 2.5% is achieved with incident intensity of 10MW/cm². At NIR frequency, the nonlinear conductivities of graphene are about 7 orders lower. Bistability is unlikely to happen with incident intensity below 1GW/cm². The TH generation efficiency is only about 5×10^-6 with incident intensity of 25MW/cm². The proposed structure is more suitable to work as a low-threshold saturable absorber at NIR frequency. These results may be helpful both for a better understanding of graphene's nonlinear responses in a double resonant structure and for potential applications in THz nonlinear devices and NIR nanophotonics.