Nonlocal effects in temporal metamaterials

Nonlocality is a fundamental concept in photonics. For instance, nonlocal wave-matter interactions spatially modulated metamaterials enable novel effects, such as giant electromagnetic chirality, artificial magnetism, and negative refraction. Here, we investigate the effects induced by spatial nonlocality {\em temporal} metamaterials, i.e., media with dielectric permittivity rapidly time. Via rigorous multiscale approach, introduce general compact formalism for effective medium theory of temporally periodic metamaterials. In particular, study two scenarios: i)} temporal modulation, {{\em ii)}} boundary where abruptly changed time subject to modulation. We show that these configurations can give rise peculiar highlight similarities differences respect spatial-metamaterial counterparts. Interestingly, tailoring interactions, also identify an intriguing configuration which metamaterial perform first-order derivative incident wavepacket. Our theoretical results, backed full-wave numerical simulations, key physical ingredients may pave way applications. By fully exploiting time-reversal symmetry breaking, promise great potential efficient, tunable optical computing devices.