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Spatial structuring of an optical pulse can lead in some cases upon freepropagation to changes in its temporal profile. For example, introducingconventional angular dispersion into the field results in the pulseencountering group-velocity dispersion in free space. However, only limitedcontrol is accessible via this strategy. Here we show that precise andversatile control can be exercised in free space over the dispersion profile ofso-called `space-time' wave packets: a class of pulsed beams undergirded bynon-differentiable angular dispersion. This abstract mathematical featureallows us to tune the magnitude and sign of the different dispersion orderswithout introducing losses, thereby realizing arbitrary dispersion profiles,and achieving dispersion values unattainable in optical materials away fromresonance. Unlike optical materials and photonic structures in which the valuesof the different dispersion orders are not independent of each other, theseorders are addressable separately using our strategy. These results demonstratethe versatility of space-time wave packets as a platform for structured lightand point towards their utility in nonlinear and quantum optics.

Engineering the optical vacuum: Arbitrary magnitude, sign, and order of dispersion in free space using space-time wave packets