Nonlocal effects in temporal metamaterials

TL;DR

This paper explores how nonlocal effects in temporally modulated metamaterials lead to unique wave interactions, revealing new physical phenomena and potential applications in optical computing.

Contribution

It introduces a formalism for nonlocal effective medium theory in temporal metamaterials and analyzes novel effects arising from temporal nonlocality and boundary interactions.

Findings

Temporal nonlocal effects induce unusual wave phenomena.

Tailored boundary interactions enable wavepacket derivatives.

Full-wave simulations confirm theoretical predictions.

Abstract

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