  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.
