arXiv2026
A challenge in optics, which is shared by other sources of radiation, is to direct a coherent beam to impinge on a target behind an obstacle intervening in the line-of-sight (LoS). While self-accelerating or bending beams can help avoid an LoS obstacle, the beam does not reach the LoS target downstream beyond the obstacle. If one instead avoids the obstacle by projecting a \textit{transverse} null or shadow onto the axial plane at which it is located, an associated \textit{axial} shadow is cast that extends over the effective Rayleigh length, which reduces the utility of this approach. Unless either the wavelength or the transverse shadow width is changed, this Rayleigh length can only be reduced by modifying the structure of the illumination beam. Here we show that space-time wave packets (STWPs), in which each spatial frequency is tightly associated with a single wavelength, when used as an illumination beam, can dramatically reduce the axial extent of the cast shadow. Indeed, by utilizing STWPs we produce deep sub-Rayleigh-length shadows, in some cases with a more than two orders-of-magnitude reduction below the conventional Rayleigh length. For example, a 5-mm-wide transverse shadow in a Gaussian beam at a wavelength of $\sim1$~$\mu$m has a Rayleigh length of $\sim25$~m, whereas the same shadow projected by an STWP extends only $\sim0.15$~m. We demonstrate this sub-Rayleigh-length reduction in the axially cast shadow accompanying transverse nulls whose widths extend over a broad span of widths from 80~$\mu$m to 48~mm -- almost three orders-of-magnitude. These results may lead to advances in safe radiation therapy, non-LoS optical and wireless communications, selective stand-off detection, three-dimensional photolithography, and laser ablation and micro-machining.