Optical effects in spatiotemporal metasurfaces and metamaterials

In the realm of metamaterials, time-varying media have opened new frontiers. By altering material properties at time scales comparable to the oscillation period of light or even shorter, intriguing phenomena like momentum band gaps and parametric amplification emerge. Spatially and temporally modulated materials create four-dimensional metamaterials, offering complete control over light. In this contribution, we present a scattering theory for spatiotemporal metamaterials. It begins with eigenmodes in time-varying homogenous media, addressing light scattering by time-varying spheres. We extend this to 2D and 3D periodic structures using a T-matrix-based approach. These materials constitute spatiotemporal metasurfaces and metamaterials. We introduce theoretical and computational tools, exploring homogenization, resonances, and momentum band gaps. In the latter part, we exploit spatial resonances to lower the required modulation amplitude of the time-varying media to observe a notable momentum band gap. With that, our approach simplifies the experimental observation of time-varying media effects.