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The work harnesses principles of spatial state tomography to fully characterise an optical beam in space, time, spectrum, and polarisation. Analysis of the output of a vertical-cavity surface-emitting laser illustrates the technique’s capabilities.

Truly arbitrary spatiotemporal wavefront shaping has many potential applications in optics. Here the authors develop a system capable of arbitrary waveshaping to the extent of full time reversal of spatiotemporal optical beams.

Here, the authors describe the control of the temporal shape and polarization of the total transmission through a multimode fibre. Most of the previous works studied spatial control of the output field at the expense of the temporal behaviour.

A Correction to this paper has been published: https://doi.org/10.1038/s41467-021-20944-8.