Negative Kerr Nonlinearity of Graphene as seen via Chirped-Pulse-Pumped Self-Phase Modulation

We experimentally demonstrate a negative Kerr nonlinearity for quasiundoped graphene. Hereto, we introduce the method of chirped-pulse-pumped self-phase modulation and apply it to graphene-covered silicon waveguides at telecom wavelengths. The extracted Kerr-nonlinear index for graphene equals $n_{2,\mathrm{gr}}=-{10}^{-13}{\mathrm{m}}^2/\mathrm{W}$. Whereas the sign of $n_{2,\mathrm{gr}}$ turns out to be negative in contrast to what has been assumed so far, its magnitude is in correspondence with that observed in earlier experiments. Graphene’s negative Kerr nonlinearity strongly impacts how graphene should be exploited for enhancing the nonlinear response of photonic (integrated) devices exhibiting a positive nonlinearity. It also opens up the possibility of using graphene to annihilate unwanted nonlinear effects in such devices, to develop unexplored approaches for establishing Kerr processes, and to extend the scope of the “periodic poling” method often used for second-order nonlinearities towards third-order Kerr processes. Because of the generic nature of the chirped-pulse-pumped self-phase modulation method, it will allow fully characterizing the Kerr nonlinearity of essentially any novel (2D) material.

Figure 1

Illustration of the broadening factor dependence on the input chirp parameter for a silicon waveguide and for Gaussian and ${\mathrm{sech}}^2$ input pulses as used in our experiments.

Figure 2

(a) Outline of the employed waveguide structures. (b) Experimental setup for the SPM measurements.

Figure 3

FROG-measured temporal power profile (solid blue line) and phase profile (solid red line) of the input pulses with positive chirp. The dotted green line is the quadratically fitted phase.

Figure 4

Broadening factor vs graphene length for a positive input chirp. The analytical dashed curves serve for fitting.

Figure 5

FROG-measured (solid lines) and numerically simulated (dashed lines) temporal power profile (blue) and phase profile (red) of the input pulses with negative chirp. The dotted green line is the quadratically fitted phase.

Figure 6

Broadening factor vs graphene length for a negative input chirp. The analytical dashed curves serve for fitting.