Space–time wave packets violate the universal relationship between angular dispersion and pulse-front tilt

Introducing angular dispersion into a pulsed field tilts the pulse front with respect to the phase front. There exists between the angular dispersion and the pulse-front tilt a universal relationship that is device-independent, and also independent of the pulse shape and bandwidth. We show here that this relationship is violated by propagation-invariant space-time (ST) wave packets, which are pulsed beams endowed with precise spatio-temporal structure corresponding to a particular form of angular dispersion. We demonstrate theoretically and experimentally that underlying ST wave packets is -- to the best of our knowledge -- the first example in optics of non-differentiable angular dispersion, resulting in pulse-front tilt that depends on the pulse bandwidth even at fixed angular dispersion.