In general, space-time wave packets with correlations between transverse
spatial fields and temporal frequency spectra can lead to unique spatiotemporal
dynamics, thus enabling control of the instantaneous light properties. However,
spatiotemporal dynamics generated in previous approaches manifest themselves at
a given propagation distance yet not arbitrarily tailored longitudinally. Here,
we propose and demonstrate a new versatile class of judiciously synthesized
wave packets whose spatiotemporal evolution can be arbitrarily engineered to
take place at various predesigned distances along the longitudinal propagation
path. Spatiotemporal synthesis is achieved by introducing a 2-dimensional
spectrum comprising both temporal and longitudinal wavenumbers associated with
specific transverse Bessel-Gaussian fields. The resulting spectra are then
employed to produce wave packets evolving in both time and axial distance - in
full accord with the theoretical analysis. In this respect, various light
degrees of freedom can be independently manipulated, such as intensity,
polarization, and transverse spatial distribution (e.g., orbital angular
momentum). Through a temporal-longitudinal frequency comb spectrum, we simulate
the synthesis of the aforementioned wave packet properties, indicating a
decrease in relative error compared to the desired phenomena as more spectral
components are incorporated. Additionally, we experimentally demonstrate
tailorable spatiotemporal fields carrying time- and longitudinal-varying
orbital angular momentum, such that the local topological charge evolves every
~1 ps in the time domain and 10 cm axially. We believe that our space-time wave
packets can significantly expand the exploration of spatiotemporal dynamics in
the longitudinal dimension, and potentially enable novel applications in
ultrafast microscopy, light-matter interactions, and nonlinear optics