  We experimentally demonstrate a negative Kerr nonlinearity for quasi-undoped
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 n2,gr =
-10^(-13) m^2/W. Whereas the sign of n2,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.
