  Maxwell's equations in curved space-time are invariant under electromagnetic
duality transformations. We exploit this property to constraint the design
parameters of metamaterials used for transformations optics. We show that a
general transformation must be implemented using a dual-symmetric metamaterial.
This can be accomplished constraining the polarisability tensors of their
individual constituents, i.e. the meta atoms. We obtain explicit expressions
for these constraints. We also show that the spatial part of the coordinate
transformation depends only on the electric-electric tensorial coupling of the
polarisability tensor, while the spatio-temporal part depends only on the
electric-magnetic tensorial coupling. In our derivations, we find that two
dipoles located at the same point, one electric (p) and one magnetic (m), are
needed to produce a total field with well defined helicity equal to +1 or -1,
and that they must be related as p=im/c or p=-im/c, respectively.
