Free-space group-velocity dispersion induced in space-time wave packets by V-shaped spectra

Introducing precise spatiotemporal 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 class of ST wave packets that we call V-waves (so named because of their characteristically V-shaped spatiotemporal 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 spatiotemporal structure of the field itself. These results are of interest for optical signal processing and nonlinear optics.