Spatio-temporal coupled mode theory for nonlocal metasurfaces

Diffractive nonlocal metasurfaces have recently opened a broad range of exciting developments in nanophotonics research and applications, leveraging spatially extended-yet locally patterned-resonant modes to control light with new degrees of freedom. While conventional grating responses are elegantly captured by temporal coupled mode theory, current approaches are not well equipped to capture the arbitrary spatial response observed in the nascent field of nonlocal metasurfaces. Here, we introduce spatio-temporal coupled mode theory (STCMT), capable of elegantly capturing the key features of the resonant response of wavefront-shaping nonlocal metasurfaces. This framework can quantitatively guide nonlocal metasurface design while maintaining compatibility with local metasurface frameworks, making it a powerful tool to rationally design and optimize a broad class of ultrathin optical components. We validate this STCMT framework against full-wave simulations of various nonlocal metasurfaces, demonstrating that this tool offers a powerful semi-analytical framework to understand and model the physics and functionality of these devices, without the need for computationally intense full-wave simulations. We also discuss how this model may shed physical insights into nonlocal phenomena in photonics and the functionality of the resulting devices. As a relevant example, we showcase STCMT's flexibility by applying it to study and rapidly prototype nonlocal metasurfaces that spatially shape thermal emission.