Coherent Nonlinear Optical Response of Graphene

We investigate the nonlinear optical properties of graphene flakes using four-wave mixing. The corresponding third-order optical susceptibility is found to be remarkably large and only weakly dependent on the wavelength in the near-infrared frequency range. The magnitude of the response is in good agreement with our calculations based on the nonlinear quantum response theory.

Figure 1

(a) Schematic of the experimental layout, indicating the pump beams with frequencies ${\omega }_1$, ${\omega }_2$, and the emission beam with frequency ${\omega }_e$. (b) Diagram of energy conservation in the four-wave mixing process. (c) Band structure of graphene with the three resonant photon energies (arrows) involved in four-wave mixing.

Figure 2

Emission spectra of a graphene flake excited with pump pulses of different wavelengths, (${\lambda }_1$, ${\lambda }_2$): (940 nm, 1224 nm), (950 nm, 1210 nm), (958 nm, 1196 nm), (967 nm, 1183 nm), and (977 nm, 1168 nm). The dashed line represents the wavelength dependence predicted by Eq. (4).

Figure 3

Emission spectra of a graphene monolayer excited with pump wavelengths (969 nm, 1179 nm), compared to the emission of a 4 nm thick gold film under the same experimental conditions.

Figure 4

(a) Standard green light (550 nm) reflection images of two graphene flakes. (b) Nonlinear optical images measured with pump wavelengths of 969 nm and 1179 nm. Image acquisition times are approximately 0.6 s. (c) The contrast in four-wave mixing images as a function of the number of graphene layers.