Axial spectral encoding of space-time wave packets

Space-time (ST) wave packets are propagation-invariant pulsed optical beams whose group velocity can be tuned in free space by tailoring their spatio-temporal spectral structure. To date, efforts on synthesizing ST wave packets have striven to maintain their propagation invariance. Here, we demonstrate that one degree of freedom of a ST wave packet -- its on-axis spectrum -- can be isolated and purposefully controlled independently of the others. Judicious spatio-temporal spectral amplitude and phase modulation yields ST wave packets with programmable spectral changes along the propagation axis; including red-shifting or blue-shifting spectra, or more sophisticated axial spectral encoding including bidirectional spectral shifts and accelerating spectra. In all cases, the spectral shift can be larger than the initial on-axis bandwidth, while preserving the propagation-invariance of the other degrees of freedom, including the wave packet spatio-temporal profile. These results may be useful in range-finding in microscopy or remote sensing via spectral stamping.