Experimental realization of Lorentz boosts of space-time wave packets

It is now well-understood that a Lorentz boost of a spatially coherent monochromatic optical beam yields a so-called space-time wave packet (STWP): a propagation-invariant pulsed beam whose group velocity is determined by the relative velocity between the source and observer. Moreover, the Lorentz boost of an STWP is another STWP, whose group velocities are related by the relativistic law for addition of velocities typically associated with massive particles. We present an experimental procedure for testing this prediction in both the subluminal and superluminal regimes that makes use of spatio-temporal Fourier synthesis via a spatial light modulator. Our approach enables realizing the change in temporal bandwidth, the invariance of the spatial bandwidth, the concomitant change in the spatio-temporal wave-packet envelope, and the change in group velocity that all accompany a Lorentz boost of a monochromatic optical beam. The only consequence of the Lorentz boost not captured by this methodology is the Doppler shift in the optical carrier. This work may provide an avenue for further table-top demonstration of relativistic transformations of optical fields.