Fig. 1.

Spatio-temporal spectral engineering for arbitrary group velocity control. a–c Conic-section trajectories at the intersection of the free space light-cone with a spectral hyperplane $\mathcal{P}\left(\theta \right)$ are spatio-temporal spectral loci of space-time (ST) wave packets with tunable group velocities v_g in free space: a subluminal, b superluminal, and c negative-superluminal v_g. For each case we plot the projection of the spatio-temporal spectrum onto the (k_x, k_z) plane restricted to k_z > 0 (white curve). d Projections of the spatio-temporal spectra from (a–c) onto the $\left(k_z,\frac{\omega }{c}\right)$ plane. The slope of each projection determines the group velocity of each ST wave packet along the axial coordinate z, v_g = ctanθ