Nonlocal metasurfaces: universal modal maps governed by a nonlocal generalized Snell's law

In this opinion, we describe the potential of an emerging class of flat optics known as "nonlocal metasurfaces" to manipulate light in both real space and momentum space. While the ultimate form of a conventional "local" metasurface can be viewed as a universal generator of any desired waveform from a fixed input wavefront, the ultimate form of a nonlocal metasurface would instead act as a universal "map" from a given set of input waveforms to a set of orthogonal output waveforms. Here, we discuss how this implies four-dimensional information capacity, drastically enhancing information density compared to local metasurfaces. We discuss a framework using scattering matrices and a nonlocal generalized Snell's law to describe nonlocal metasurfaces. We comment on the potential, progress, and practicality of this ambitious vision, suggesting limitations and next steps.