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

Time reversed optical waves by arbitrary vector spatiotemporal field generation