Fig. 1. Operating principle of a spaceplate.
a A spaceplate can compress a propagation length of deff into a thickness d. For example, a beam incident on the spaceplate at angle θ will emerge at that same angle and be transversely translated by length w (resulting in a lateral beam shift Δx), just as it would for deff of free space. b Adding a spaceplate to an imaging system such as a standard camera (top) will shorten the camera (center). An ultrathin monolithic imaging system can be formed by integrating a metalens and a spaceplate directly on a sensor (bottom). c A lens focuses a collimated beam at a working distance corresponding to its focal length f. d A spaceplate will act to shorten the distance from the lens to the focus by a distance |Δ|. The emerging rays are parallel to the original incident rays, which preserves the lens strength. The plate therefore effectively propagates light for a longer length than the physical space it occupies. This effect can be achieved using e, a nonlocal metamaterial, or f, for the extraordinary ray for propagation along the fast axis (e) of a uniaxial birefringent medium with nBG = ne. g A spaceplate can be made of a homogeneous medium with any of these angle-dependent refractive index curves, parametrized by the quantity C.