  We demonstrate that the effective third-order nonlinear susceptibility of a
graphene sheet can be enhanced by more than two orders of magnitude by
patterning it into a graphene metasurface. In addition, in order to gain deeper
physical insights into this phenomenon, we introduce a novel homogenization
method, which is subsequently used to characterize quantitatively this
nonlinearity enhancement effect by calculating the effective linear and
nonlinear susceptibility of graphene metasurfaces. The accuracy of the proposed
homogenization method is demonstrated by comparing its predictions with those
obtained from the Kramers-Kronig relations. This work may open up new
opportunities to explore novel physics pertaining to nonlinear optical
interactions in graphene metasurfaces.
