  We introduce an approach to the design of three-dimensional transformation
optical (TO) media based on a generalized quasi-conformal mapping approach. The
generalized quasi-conformal TO (QCTO) approach enables the design of media that
can, in principle, be broadband and low-loss, while controlling the propagation
of waves with arbitrary angles of incidence and polarization. We illustrate the
method in the design of a three-dimensional "carpet" ground plane cloak and of
a flattened Luneburg lens. Ray-trace studies provide a confirmation of the
performance of the QCTO media, while also revealing the limited performance of
index-only versions of these devices.
