We study a class of temporal metamaterials characterized by time-varying dielectric permittivity waveforms of duration much smaller than the characteristic wave-dynamical timescale. In the analogy between spatial and temporal metamaterials, such a short-pulsed regime can be viewed as the temporal counterpart of metasurfaces. We introduce a general and compact analytical formalism for modeling the interaction of a short-pulsed metamaterial with an electromagnetic wave packet. Specifically, we elucidate the role of local and nonlocal effects, as well as the time-reversal symmetry breaking, and we show how they can be harnessed to perform elementary analog computing, such as first and second derivatives. Our theory validated against full-wave numerical simulations suggests a novel route for manipulating electromagnetic waves without relying on long, periodic temporal modulations. Just as metasurfaces have played a pivotal role in the technological viability and practical applicability of conventional (spatial) metamaterials, short-pulsed metamaterials may catalyze the development of temporal and space-time metamaterials.

中文翻译：

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短脉冲超材料

我们研究了一类时间超材料，其特征是随时间变化的介电常数波形，其持续时间远小于特征波动态时间尺度。在空间和时间超材料之间的类比中，这种短脉冲状态可以被视为超表面的时间对应物。我们介绍了一种通用且紧凑的分析形式，用于模拟短脉冲超材料与电磁波包的相互作用。具体来说，我们阐明了局部和非局部效应的作用，以及时间反演对称性破坏，并展示了如何利用它们来执行基本的模拟计算，例如一阶和二阶导数。我们的理论针对全波数值模拟进行了验证，提出了一种无需长期依赖即可操纵电磁波的新途径，周期性时间调制。正如超表面在常规（空间）超材料的技术可行性和实际适用性中发挥了关键作用一样，短脉冲超材料可能会催化时空超材料的发展。