Experimental determination of the complex third-order nonlinear optical susceptibility in graphene

Research of the electronic process governing optical third-harmonic generation (THG) in single-layer graphene is essential for understanding high-harmonic generation or other nonlinear optical responses of graphene-related materials. In this research, we investigated the electronic transition dominating THG in single-layer graphene from a spectral measurement of THG. To determine absolute values and phases of third-order nonlinear susceptibility χ⁽³⁾ quantitatively, we adopted the Maker fringe method. As a result of the experiment, we obtained the χ⁽³⁾ spectrum of graphene in the range from 0.55 eV to 1.15 eV in fundamental photon energy. Here, as we analyzed the fringe patterns, we determined the phases of χ⁽³⁾. The phase spectrum of χ⁽³⁾ reveals the resonance processes and the electronic processes governing THG in graphene. On the basis of the experimental results, we discuss the electronic processes of the nonlinear optical response related to a Dirac-cone type electronic state.