Metasurface spaceplates reach a millimeter-scale squeezed length of free space
Metasurfaces offer compact flat lenses (metalenses) for miniaturized imaging systems; however, the utmost miniaturization requires not only metalenses but also a substantial reduction of free space. A Spaceplate is a flat-optics element designed to mimic free-space propagation, effectively propagating light over a distance far exceeding its physical thickness, with the induced squeezed length serving as the key figure of merit. Despite substantial progress, most existing spaceplate designs have been fundamentally constrained by a trade-off between squeezed length and numerical aperture, and none has demonstrated a feasible structure supporting both a moderate numerical aperture and a millimeter-scale squeezed length. We report a metasurface spaceplate reaching the milestone of a millimeter-scale squeezed length with a practical numerical aperture. We achieved this by combining advantageous elements from existing approaches: high compression ratios and inverse-design flexibility in optimized multilayer metasurfaces, serving as the spaceplate unit structure, and preserving its numerical aperture by coupling its replicas, to construct a coupled cascaded spaceplate with an increased thickness. For operation in the mid-wave infrared, we demonstrated an optimized spaceplate exhibiting a high compression ratio of ~14 with a physical thickness of ~80 {\mu}m, resulting in a squeezed length of 1.09 mm, for a numerical aperture of 0.13. We developed a general framework for calculating the transmission characteristics of multilayered spaceplates while optimizing their layer thicknesses to accurately reproduce the target free space. Strikingly, millimeter-scale squeezed lengths with practical numerical apertures via metasurface spaceplates pave the way for ultrathin imaging systems through their utmost miniaturization, opening a new paradigm for augmented reality headsets, cellphones, and many more.