Complex third-order nonlinear susceptibility of single-layer graphene governing third-harmonic generation

The resonant process of the third-order nonlinear optical response of single-layer graphene has been investigated using various approaches. The complex third-order nonlinear susceptibility (χ(3)) directly reflects the resonance effects in third-order nonlinear processes. We measured the modulus and phase of χ(3) governing the third-harmonic generation (THG) of graphene using the Maker fringe method. First, we observed the incident photon energy dependence of THG in the energy range from 0.57 to 0.81 eV. The modulus values of χ(3) decreased from 7×10-10 to 2×10-10 esu, with an increase in photon energy. The phase values increased from 330 ° to 360 ° in the corresponding energy range. When the experimental result and the model calculation were compared, we found that the THG process in graphene can be described by the superposition of one-, two-, and three-photon resonant components. Experimental results demonstrate that the two-photon resonant process comprising interband and intraband transitions is the most significant among the three components for THG in graphene. Second, we measured the Fermi energy (EF) dependence of THG in the range of -568meV≤EF≤+133meV at incident photon energies of 0.60 and 0.72 eV. The modulus of χ(3) changed from 5.4×10-11 to 6.4×10-10 esu with doping. This result is due to the reduction of the one-photon resonant component by Pauli blocking. The complex χ(3) has positive real and negative imaginary parts regardless of EF. We also analyzed the laser power dependence of THG intensity via model calculation taking account of the electron temperature. The experimental results and discussion of the complex χ(3) of graphene can be a basis for understanding nonperturbative harmonic generation and other third-order nonlinear optical responses in Dirac materials.