Space-time wave packets propagating a kilometer in air

We report on the diffraction-free propagation of space-time wave packets (STWPs) – a class of propagation-invariant pulsed beams – for $\sim \text{\hspace{0.17em}⁣}1$ km in an open-air laser range in a low-turbulence scenario. Making use of $\approx \text{\hspace{0.17em}⁣}100$-fs pulses (bandwidth $\sim \text{\hspace{0.17em}⁣}25$ nm) at a wavelength of $\approx \text{\hspace{0.17em}⁣}1$ $\mu$m, we construct an STWP with a transverse width of $\approx \text{\hspace{0.17em}⁣}2$ mm that expands to $\approx \text{\hspace{0.17em}⁣}3$ mm after $\sim \text{\hspace{0.17em}⁣}500$ m, and another that expands from $\approx \text{\hspace{0.17em}⁣}8$ mm to $\approx \text{\hspace{0.17em}⁣}10$ mm after 1 km. The propagation of the STWPs is compared to Gaussian wave packets of the same transverse spatial width and bandwidth. We establish a theoretical model that accounts for the significant factors limiting the STWP propagation distance and suggests the path to further extending this distance.