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Most optical systems involve a combination of lenses separated by free-spaceregions where light acquires the required angle-dependent phase delay for acertain functionality. Very recently, flat-optics structures have been proposedto compress these large free-space volumes and miniaturize the overall opticalsystem. However, these early designs can only replace free-space volumes oflimited length, or operate in a very narrow angular range, or require ahigh-index background. These issues raise questions about the applicability ofthese devices in practical scenarios. Here, we first derive a fundamentaltrade-off between the length of compressed free space and the operating angularrange, which explains some of the limitations of earlier designs, and we thenpropose a solution to relax this trade-off using nonlocal metasurfacestructures composed of suitably coupled resonant layers. This strategy,inspired by coupled-resonator-based band-pass filters, allows replacingfree-space volumes of arbitrary length over wide angular ranges, and with veryhigh 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 notdictate the actual distance at which focusing is achieved. Our findings areexpected to extend the reach of the field of metasurfaces and open newunexplored opportunities.

Dielectric nonlocal metasurfaces for fully solid-state ultra-thin optical systems