Non-dispersive short pulses supported by quasiperiodic spatiotemporal gratings

It is shown that a quasiperiodic spatiotemporal grating formed in a dispersive medium enables the propagation of linear localized pulses of the probe field without dispersive spreading. Increasing the amplitude or modulation depth of the grating allows for the accommodation of a larger number of probe pulses. In the case of a formally infinite grating, these pulses propagate without distortion at the velocity of the spatiotemporal lattice. When the grating has finite spatial and temporal extents, a wide Gaussian probe pulse evolves into a sequence of non-interacting localized pulses that propagate over long distances with significantly reduced dispersion.