  Most optical systems involve a combination of lenses separated by free-space
regions where light acquires the required angle-dependent phase delay for a
certain functionality. Very recently, flat-optics structures have been proposed
to compress these large free-space volumes and miniaturize the overall optical
system. However, these early designs can only replace free-space volumes of
limited length, or operate in a very narrow angular range, or require a
high-index background. These issues raise questions about the applicability of
these devices in practical scenarios. Here, we first derive a fundamental
trade-off between the length of compressed free space and the operating angular
range, which explains some of the limitations of earlier designs, and we then
propose a solution to relax this trade-off using nonlocal metasurface
structures composed of suitably coupled resonant layers. This strategy,
inspired by coupled-resonator-based band-pass filters, allows replacing
free-space volumes of arbitrary length over wide angular ranges, and with very
high transmittance. Finally, we theoretically demonstrate, for the first time,
the potential of combining local and nonlocal metasurfaces to realize compact,
fully solid-state, planar structures for focusing, imaging, and magnification,
in which the focal length of the lens (and hence its magnifying power) does not
dictate the actual distance at which focusing is achieved. Our findings are
expected to extend the reach of the field of metasurfaces and open new
unexplored opportunities.
