  Lossless linear wave propagation is symmetric in time, a principle which can
be used to create time reversed waves. Such waves are special 'pre-scattered'
spatiotemporal fields, which propagate through a complex medium as if observing
a scattering process in reverse, entering the medium as a complicated
spatiotemporal field and arriving after propagation as a desired target field,
such as a spatiotemporal focus. Time reversed waves have previously been
demonstrated for relatively low frequency phenomena such as acoustics, water
waves and microwaves. Many attempts have been made to extend these techniques
into optics. However, the much higher frequencies of optics make for very
different requirements. A fully time reversed wave is a volumetric field with
arbitrary amplitude, phase and polarisation at every point in space and time.
The creation of such fields has not previously been possible in optics. We
demonstrate time reversed optical waves with a device capable of independently
controlling all of light's classical degrees of freedom simultaneously. Such a
class of ultrafast wavefront shaper is capable of generating a sequence of
arbitrary 2D spatial/polarisation wavefronts at a bandwidth limited rate of 4.4
THz. This ability to manipulate the full field of an optical beam could be used
to control both linear and nonlinear optical phenomena.
