  The development of optical metamaterials has resulted in the demonstration of
remarkable physical properties, including cloaking, optical magnetism, and
negative refraction. The latter has attracted particular interest, mainly
because of its promise for super-resolution imaging. In recent years, negative
refraction has been demonstrated with plasmonic materials and nonlinear
discrete elements. However, the widespread use of negative refraction at
optical frequencies is limited by high losses and strong dispersion effects,
which typically limits operation to narrow frequency bands. Here we use
degenerate four-wave mixing (d-4WM) to demonstrate controllable negative
refraction at a graphene interface, which acts as a highly efficient
phase-conjugating surface. The scheme has very low loss because of the very
small thickness of the nonlinear material and it ensures broadband operation
due to the linear bandstructure of graphene.
