To allow significant nonlinear responses to build up, usually bulky materials with enlarged interaction length and intense light are used. However, optical nonlinearities of common materials are inherently weak. Various phenomena and important applications arise with sufficiently high field strength ranging from frequency conversion, all-optical signal processing to ultrafast switching. Nonlinear optical effects, which occur with strong light illumination, are indispensable in modern physics. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement 1. 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. The proposed structure is more suitable to work as a low-threshold saturable absorber at NIR frequency. The TH generation efficiency is only about 5×10 −6 with incident intensity of 25MW/cm 2. Bistability is unlikely to happen with incident intensity below 1GW/cm 2. At NIR frequency, the nonlinear conductivities of graphene are about 7 orders lower. At THz frequency, low-threshold bistability (about 8MW/cm 2) is obtained and the TH generation efficiency of 2.5% is achieved with incident intensity of 10MW/cm 2. The influence of Kerr nonlinearity on the resonant frequencies is considered, when we calculate the TH generation. We discuss these two kinds of nonlinearities both at terahertz (THz) and near-infrared (NIR) frequencies. This double resonant structure will enhance the nonlinear responses of graphene greatly, including Kerr nonlinearity and TH generation. The edge modes exist at both the fundamental frequency (FF) and the third harmonic (TH) frequency. The two PCs are designed to have opposite topological properties, and at the interface, topological edge modes exist. We propose a hybrid structure where graphene is inserted to the interface of two one-dimensional photonic crystals (1D PCs). Note: Author names will be searched in the keywords field, also, but that may find papers where the person is mentioned, rather than papers they authored.Use a comma to separate multiple people: J Smith, RL Jones, Macarthur.Use these formats for best results: Smith or J Smith.For best results, use the separate Authors field to search for author names.Use quotation marks " " around specific phrases where you want the entire phrase only.Question mark (?) - Example: "gr?y" retrieves documents containing "grey" or "gray".