Andrea Alù
IMAGE LICENSED BY INGRAM PUBLISHING
Over the past 20 years, metamaterials have evolved into a powerful platform for wave manipulation, demonstrating a plethora of exciting functionalities relevant to a wide range of technologies. Yet, most of the work on metamaterials to date has been limited to carefully patterning materials in space, enabled by advances in micro- and nano-fabrication and in the understanding of complex wave-matter interactions at subwavelength scales. The complex wave transformations enabled by metamaterials are typically associated with multiple scattering events, driving complex interference and resonance phenomena associated with the multiple spatial interfaces that form their microstructure. Spatial metamaterials are, however, fundamentally limited in the way they can transform and control waves; in the linear regime, the frequency content of the incoming waves is conserved, and time-reversal symmetry, reciprocity, and passivity impose further constraints [1]. Recent developments have demonstrated that many of these limitations may be bypassed by adding time as a relevant “fourth” dimension—beyond the three spatial ones—in the design of metamaterials. For instance, tailored time variations can break time-reversal symmetry and reciprocity [2], and they can transform frequencies and impart gain through parametric effects. These concepts have recently been converging into a new paradigm for metamaterials in which space and time can be combined together to drastically expand the palette of degrees of freedom available for wave control [3].
The idea of using time as a dimension for wave control can be traced back to the late 1950s, when Morgenthaler [4] introduced the concept of a time interface. Dual to the familiar concept of a spatial interface, which consists of a sharp transition in space that does not change in time, a time interface is everywhere in space, but it exists only at one instant in time. It is formed when the material properties of the medium supporting an input wave are abruptly and largely changed. Such a time interface sustains phenomena, such as time reflection and time refraction, that are somewhat related to the familiar scattering processes occurring at a spatial interface. At a time interface, backward and forward waves are generated, but their frequency and energy are not conserved, providing an efficient and inherently fast platform to realize signal amplification and frequency transformations. In addition, time-reflected signals are time-reversed without distortions, offering a frequency-agnostic and efficient form of phase conjugation, relevant for applications from imaging to communications and computing.
Progress in the technologies that allow us to change and control the material properties in time has recently revived interest in these phenomena, supporting the fast and efficient tuning of the electromagnetic response of circuit elements and materials. In turn, exciting proposals to leverage these phenomena for exotic wave control have been appearing in the recent literature [5], [6], [7]. Inspired by how combinations of spatial interfaces enable sophisticated wave manipulation, e.g., sharp resonances and bandgaps in photonic crystals, combinations of time interfaces have been shown to support new forms of wave interference and resonances, and when combined, they can form the basis for time crystals [8] and time metamaterials [9]. The recent experimental demonstration of a time interface for electromagnetic waves, obtained in a transmission-line metamaterial loaded with a dense array of switches and reservoir capacitors, has enabled the observation of the powerful opportunities of these concepts, for instance, realizing broadband, fast phase conjugation, and frequency conversion [10], spearheading further excitement in this field of research. The overarching vision consists of combining tailored spatial and temporal interfaces in 4D metamaterials, enabling seamless wave transformations in space, time, frequency, and momentum, and hence, opening unchartered opportunities for the future of metamaterials.
Within this background, it has been exciting to edit this special issue that aims to offer an overview of these recent advances and an introduction to this emerging field of research for the benefit of the broad antennas and propagation community. G. Ptitcyn et al. [A1] present an excellent tutorial on the basics of time-varying systems and circuits, pointing out the relevant opportunities that time variations offer in the quest of manipulating electromagnetic signals and the new challenges that emerge in their modeling. S. Yin et al. [A2] discuss time interfaces and wave interference enabled by their combinations in the framework of scattering and transmission-line theory, shedding physical insights on the associated phenomena within a framework that can be accessible to electrical and antenna engineers. Z. Hayran and F. Monticone [A3] showcase ways in which, by adding the temporal dimension, we can overcome some of the inherent limitations of linear time-invariant structures, offering a vista over the new opportunities that time- and space-time metamaterials may offer. V. Pacheco-Peña and N. Engheta [A4] discuss homogenization principles and effective-medium theory for time metamaterials, comparing them with classical homogenization schemes for layered media and offering interesting physical insights into the new phenomena enabled by periodic combinations of time interfaces. C. Caloz et al. [A5] discuss the opportunities enabled by the combination of space and time interfaces in space-time metamaterials, unveiling physical insights and engineering perspectives for applications. Finally, S. Taravati and G. V. Eleftheriades [A6] present the modeling, design, and applications of space-time metasurfaces, which tailor waves by combining variations in space and time over a thin platform. As a collection, this series of articles aims at providing an introduction to these topics for the benefit of the broad electrical engineering and antennas and propagation communities, offering a snapshot of the state of the art and a perspective on the evolution of this field.
I would like to take this opportunity to thank all the authors and reviewers of these articles, which form a great collection. Sincere thanks also go to IEEE Antennas and Propagation Magazine Editor-in-Chief Prof. Francesco Andriulli for encouragement and support and to Editorial Assistant Christina Tang-Bernas for all of the support and patience. I hope that many of you will enjoy reading this collection and that it may be useful to introduce the broad readership of this journal to a topic that is rapidly becoming an exciting direction in the context of electromagnetic wave manipulation and of metamaterials.
Andrea Alù (aalu@gc.cuny.edu) is with the Photonics Initiative, Advanced Science Research Center, City University of New York, New York, NY 10031 USA and with the Physics Program, Graduate Center, City University of New York, New York, NY 10016 USA.
[1] A. Krasnok, N. Nefedkin, and A. Alù, “Parity-time symmetry and exceptional points,” IEEE Antennas Propag. Mag., vol. 63, no. 6, pp. 110–121, Dec. 2021, doi: 10.1109/MAP.2021.3115766.
[2] A. Kord and A. Alù, “Magnetless circulators based on synthetic angular-momentum bias: Recent advances and applications,” IEEE Antennas Propag. Mag., vol. 63, no. 6, pp. 51–61, Dec. 2021, doi: 10.1109/MAP.2020.3043437.
[3] N. Engheta, “Four-dimensional optics using time-varying metamaterials,” Science, Vol. 379, No. 6638, pp. 1190–1191, Mar. 2023, doi: 10.1126/science.adf1094.
[4] R. Morgenthaler, “Velocity modulation of electromagnetic waves,” IRE Trans. Microw. Theory Techn., vol. 6, no. 2, pp. 167–172, Apr. 1958, doi: 10.1109/TMTT.1958.1124533.
[5] A. Akbarzadeh, N. Chamanara, and C. Caloz, “Inverse prism based on temporal discontinuity and spatial dispersion,” Opt. Lett., vol. 43, no. 14, pp. 3297–3300, Jul. 2018, doi: 10.1364/ol.43.003297.
[6] V. Pacheco-Peña and N. Engheta, “Antireflection temporal coatings,” Optica, vol. 7, no. 4, pp. 323–331, Apr. 2020, doi: 10.1364/optica.381175.
[7] E. Galiffi et al., “Photonics of time-varying media,” Adv. Photon., vol. 4, no. 1, Feb. 2022, Art. no. 014002, doi: 10.1117/1.AP.4.1.014002.
[8] K. Sacha and J. Zakrzewski, “Time crystals: A review,” Rep. Prog. Phys., vol. 81, no. 1, Jan. 2018, Art. no. 016401, doi: 10.1088/1361-6633/aa8b38.
[9] S. Yin, E. Galiffi, and A. Alù, “Floquet metamaterials,” eLight, vol. 2, no. 1, May 2022, Art. no. 8, doi: 10.1186/s43593-022-00015-1.
[10] H. Moussa, G. Xu, S. Yin, E. Galiffi, Y. Ra’di, and A. Alù, “Observation of temporal reflection and broadband frequency translation at photonic time interfaces,” Nature Phys., early access, 2023, doi: 10.1038/s41567-023-01975-y.
Digital Object Identifier 10.1109/MAP.2023.3262101