Abstract
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 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: (i) a periodic temporal modulation, and (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.
Highlights
Spatial dispersion [1, 2] implies that the electromagnetic (EM) constitutive relationships are nonlocal, i.e., the electric and/or magnetic inductions at a given point depend on the fields applied in a spatial neighborhood
We investigate the effects induced by spatial nonlocality in temporal metamaterials, i.e., media with a dielectric permittivity rapidly modulated in time
In some cases nonlocality is viewed as a detrimental effect to suppress or mitigate [7], its proper harnessing can be very beneficial in a variety of application scenarios, including artificial magnetism [8], chirality [6], ultrafast nonlinear optics [9], advanced dispersion engineering [10, 11], and wave-based analog computing [12]
Summary
Spatial dispersion [1, 2] implies that the electromagnetic (EM) constitutive relationships are nonlocal, i.e., the electric and/or magnetic inductions at a given point depend on the fields applied in a spatial neighborhood (and, because of causality, at previous time instants). In metamaterials engineering, there is a surge of interest in exploiting the temporal dimension as well, motivated by the increasing availability of fast, reconfigurable “meta-atoms” whose response can be dynamically modulated in time [13–16]. This has led to revisiting with renewed attention some old studies on wave interactions with time-varying media or structures [17–19], and to the demonstration of a variety of intriguing effects and applications, ranging from nonreciprocity to broadband light manipulation (see, e.g., [20–38] for a sparse sampling)
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