We study the dynamics of space-time nondiffracting wave packets, commonly known as light bullets, in a spatiotemporally varying medium. We show that by spatiotemporal refraction, a monochromatic focused beam can be converted to a light bullet that propagates at a given velocity. By further designing the index profile of the spatiotemporal boundary, the group velocity and the propagation direction of the light bullet can be engineered in a programmable way. All effects mentioned above cannot be achieved by spatial or temporal boundaries, and are only possible with spatiotemporal boundaries. These findings provide unique ways to engineer the dynamics of electromagnetic wave packets in space-time. Such wave packets with engineered space-time trajectory may find potential applications in the spatiotemporal control of material properties or particles, or for use as a way to emulate relativistic physics in the laboratory.
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