  Spaceplates are novel flat-optic devices that implement the optical response
of a free-space volume over a smaller length, effectively "compressing space"
for light propagation. Together with flat lenses such as metalenses or
diffractive lenses, spaceplates have the potential to enable a drastic
miniaturization of any free-space optical system. While the fundamental and
practical bounds on the performance metrics of flat lenses have been well
studied in recent years, a similar understanding of the ultimate limits of
spaceplates is lacking, especially regarding the issue of bandwidth, which
remains as a crucial roadblock for the adoption of this platform. In this work,
we derive fundamental bounds on the bandwidth of spaceplates as a function of
their numerical aperture and compression ratio (ratio by which the free-space
pathway is compressed). The general form of these bounds is universal and can
be applied and specialized for different broad classes of space-compression
devices, regardless of their particular implementation. Our findings also offer
relevant insights into the physical mechanism at the origin of generic
space-compression effects, and may guide the design of higher performance
spaceplates, opening new opportunities for ultra-compact, monolithic, planar
optical systems for a variety of applications.
