Finite-Size Effects in Nonlocal Metasurfaces.

Metasurfaces leveraging nonlocal resonances enable narrowband spectral control and strong near-fields, with applications spanning augmented reality, biosensing, and nonlinear optics. However, the large spatial extent of these modes also poses new challenges: finite-size effects often deteriorate the performance of practical, footprint-limited devices. Here, we develop a spatiotemporal coupled-mode theory model that intuitively and quantitatively captures how finite size affects the scattering response of nonlocal metasurfaces. This reveals that, when the modal propagation length becomes constrained by the physical interaction length, the scattered field shows strong interference fringes and line width broadening. We derive an expression for the quality factor that incorporates an additional edge-loss channel, demonstrating that the stored energy and effective lifetime scale exponentially with the interaction length. We validate these predictions experimentally using position- and momentum-resolved spectroscopy on a 30-μm-wide metasurface. Overall, this work formalizes the impact of finite size on the scattering response of nonlocal photonic systems, and provides handles on how to minimize the impact of finite-size effects in metasurface design.