Inverting and canceling normal and anomalous group velocity dispersion using space-time wave packets

Chromatic dispersion is an intrinsic property of optical materials that broadens and deforms optical pulses. Well known methodologies may compensate (pre-compensate) for dispersion after (before) propagation through the medium, typically by exploiting angular dispersion. Dispersion cancellation, on the other hand refers to modifying the field structure so that it propagates invariantly in a dispersive medium. In this context, a fundamental theorem indicates that angular dispersion can cancel normal group-velocity dispersion (GVD) but not anomalous GVD. We show that so-called non-differentiable angular dispersion unique to a class of pulsed beams dubbed space-time wave packets helps overcome this limitation and helps cancel normal or anomalous GVD symmetrically. We demonstrate this capability experimentally by synthesizing space-time wave packets that are dispersive in free space but become dispersion-free once coupled to the appropriate medium whether in the normal- or anomalous-GVD regime – all while maintaining independent control over the group velocity of the wave packet.