  Vector vortex beams have played a fundamental role in the better
understanding of coherence and polarization. They are described by spatially
inhomogeneous polarization states, which present a rich optical mode structure
that has attracted much attention for applications in optical communications,
imaging, spectroscopy and metrology. However, this complex mode structure can
be quite detrimental when propagation effects such as turbulence and
birefringence perturb the beam. Optical phase conjugation has been proposed as
a method to recover an optical beam from perturbations. Here we demonstrate
full phase conjugation of vector vortex beams using three-wave mixing. Our
scheme exploits a fast non-linear process that can be conveniently controlled
via the pump beam. Our results pave the way for sophisticated, practical
applications of vector beams.
