We demonstrate a tunable plasmonic metasurface by considering a graphene sheet
subject to a periodically patterned doping level. The unique optical properties of
graphene result in electrically tunable plasmons that allow for extreme confinement
of electromagnetic energy in the technologically significant regime of THz frequencies.
Here we add an extra degree of freedom by using graphene as a metasurface, proposing
to dope it with an electrical gate patterned in the micron or sub-micron scale. By
extracting the effective conductivity of the sheet we characterize metasurfaces periodically
modulated along one or two directions. In the first case, and making use of the
analytical insight provided by transformation optics, we show an efficient control of
THz radiation for one polarization. In the second case, we demonstrate a metasurface
with an isotropic response that is independent of wave polarization and orientation.