  Introducing precise spatio-temporal structure into a pulsed optical field can
lead to remarkable changes with its free propagation. `Space-time' (ST) wave
packets, for example, propagate rigidly at a tunable group velocity in free
space by inculcating a one-to-one relationship between the axial wave numbers
and the temporal frequencies. Here we introduce a new class of ST wave packets
that we call V-waves (so named because of their characteristically V-shaped
spatio-temporal spectrum) in which a linear one-to-one relationship is
introduced between the temporal frequencies and the transverse wave numbers (or
spatial frequencies). We confirm experimentally that V-waves experience
anomalous group velocity dispersion in free space, all the while maintaining
the group velocity fixed at the speed of light in vacuum. Extremely large
values of group velocity dispersion can be easily realized, which are not
accessible with traditional optical materials or photonic structures. Moreover,
V-waves are the unique optical wave packets whose diffraction and dispersion
lengths are intrinsically equal by virtue of the spatio-temporal structure of
the field itself. These results are of interest for optical signal processing
and nonlinear optics.
