  Temporal waveform manipulation is a fundamental functionality in optics and
crucial for applications like optical communications, microwave photonics and
quantum optics. Traditional IQ- or phase-amplitude modulators shape light by
carving energy from the input lightwave and are thus fundamentally lossy, and
cannot apply independent modulation to multiple input wavelengths
simultaneously. Taking inspiration from the space-time duality, we produce
arbitrary unitary spectro-temporal transformations on multiple temporal input
vectors with a modulation structure comprising of only lossless phase
modulation and dispersive allpass filtering. The bandwidth of the output
waveforms is not restricted by the driving electronics and independent
transformations can be performed simultaneously on multiple orthogonal inputs
such as spectrally separated frequency tones. This overcomes the main
limitations of traditional electro-optic modulators and offers fundamental new
insight into temporal wave manipulation.
