Engheta N

Pacheco-Peña V

English

Newcastle University E-Prints

  17th International Congress on Artificial Materials for Novel Wave Phenomena – Metamaterials 2023 Crete, Greece, Sep. 11th –16th, 2023 Space-Time Effective Media Enabled by Spatial Interfaces and Temporal boundaries:         A Four-Dimensional Approach   V. Pacheco-Peña 1, and N. Engheta 2  1 School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom 2 Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA victor.pacheco-pena@newcastle.ac.uk, engheta@seas.upenn.edu   Abstract  –  In this contribution, we will present our recent efforts on four-dimensional (4D) metamaterials by merging both spatial and temporal boundaries. We make use of spatial multilayers (arranged either vertically or horizontally within a parallel plate cavity) with some of the layers being filled with temporal metamaterials having rapid periodic changes between two permittivity values. A closed-form solution for the space-time effective medium will be presented demonstrating the higher degrees of freedom enabled by metamaterials modulated both in space and time.   I. INTRODUCTION  The arbitrary manipulation of light-matter interactions has been at the heart of the field of metamaterials, photonics and optics[1]. Innovation in this field has expanded to break discipline boundaries over the years, enabling the implementation of artificially engineered media for new and improved applications including lenses and antennas[2], [3], sensors[4], [5], artificial intelligence-based designs[6]–[8], computing with waves[9]–[12], and medicine[13], among others. All these have been possible due to the degrees of freedom provided by metamaterial and metasurfaces-based devices where, for instance, subwavelength geometries in periodic or aperiodic arrangements can be used to generate effective electromagnetic parameters of permittivity (εreff) and permeability (µreff). Spatially arranged subwavelength multilayers is an example of this realm where the effective εreff can be controlled by parameters such as the thickness of the layers and the materials involved in the design[14]. The ability to achieve effective electromagnetic parameters has been widely exploited with demonstrations of effective media with values of εreff near-zero or even negative[15]–[17].  Research and developments in the field has been focused on the time-harmonic scenario where spatial inhomogeneities are engineered to manipulate light-matter interactions. While first explored back in the middle of the last century[18], [19], temporal variations of the electromagnetic properties of media has recently become a hot research topic[20]–[27]. This has been of particular interest to the metamaterials and photonics communities as media controlled in space and time can enable new avenues for arbitrary manipulation of fields and waves. In this work, we will present our recent efforts in exploration of interesting physical phenomena that occur when metamaterials are controlled both in space and time. Recently, we have demonstrated how an unbounded, isotropic, and homogeneous medium periodically modulated in time using rapid changes of εr can enable the deign of effective medium concepts in the time domain (a concept that we called temporal effective medium[28]). Here, we will show how such temporal effective medium concepts can be merged with spatial multilayers to achieve an effective medium in 4D; i.e., the expansion of effective medium concepts for space-time metamaterials[29]. These results may open new research avenues for a complete control of the propagation of electromagnetic waves both in space and time.      17th International Congress on Artificial Materials for Novel Wave Phenomena – Metamaterials 2023 Crete, Greece, Sep. 11th –16th, 2023 II. DISCUSSION  An example of the proposed space-time effective medium approach is shown in Fig. 1. Here, we consider a parallel plate cavity filled with a multilayered metamaterial composed of alternating layers of material A and material B (green and light-blue blocks). The material A has a constant permittivity in time with a value εrA(t)= εr1 =1. The spatial layers B are filled with a temporal medium with a permittivity modeled as a single step function. Here, εrB(t) is changed from 1 to 30 at t = t0. Note that the large values of permittivity are chosen here to better observe the concept of effective medium properties. We then obtain the spectrum of the electric field distribution (Ey) within a layer A and the results are shown in Fig. 1c as black solid line where it can be seen how the frequency is changed, as expected. Interestingly, this space-time medium can be replaced by an effective medium modeled as a single step function of permittivity that is changed from 1 to 9 as a single step. The spectrum of the numerically calculated field distribution for this space-time effective medium is shown as dashed-red line in Fig. 1c demonstrating an excellent agreement with the previous results. During the conference we will provide an in-depth analysis of this approach showing a close form solution for the effective space-time medium as well as further cases such as periodically rapid modulation of temporal functions of some spatial layers and the effect of filling fraction both in space and time, among other features.   Fig. 1. Space-time effective medium approach. The spatial multilayers have alternating layers of material A (time-independent) and material B (time dependent). The permittivity functions are sketched (not drawn in scale) in (a) and the schematic of the structure in (b). The calculated spectrum of the electric field distribution using the space-time medium (black line) and the effective space-time metamaterial (red dashed line) is shown in (c).    ACKNOWLEDGEMENT  V.P-P. would like to thank the support of the Leverhulme Trust under the Leverhulme Trust Research Project Grant scheme (RPG-2020-316). V.P.-P. also acknowledges support from Newcastle University (Newcastle University Research Fellowship). N.E. acknowledges partial support from the Simons Foundation/Collaboration on Symmetry-Driven Extreme Wave Phenomena award number 733684.  REFERENCES  [1] N. Engheta and R. W. Ziolkowski, Metamaterials: Physics and Engineering Explorations. 2006. [2] E. Lier, D. H. Werner, C. P. Scarborough, Q. Wu, and J. A. Bossard, “An octave-bandwidth negligible-loss radiofrequency metamaterial,” Nat. Mater., vol. 10, no. 3, pp. 216–222, Mar. 2011. [3] S. Legaria, J. Teniente, S. Kuznetsov, V. Pacheco-Peña, and M. 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Lett., vol. 118, no. 10, p. 101901, Mar. 2021. [25] V. Pacheco-Peña and N. Engheta, “Antireflection temporal coatings,” Optica, vol. 7, no. 4, p. 323, Apr. 2020. [26] V. Pacheco-Peña and N. Engheta, “Temporal aiming,” Light Sci. Appl., vol. 9, no. 129, pp. 1–12, Dec. 2020. [27] E. Galiffi et al., “Photonics of time-varying media,” Adv. Photonics, vol. 4, no. 01, pp. 1–32, Feb. 2022. [28] V. Pacheco-Peña and N. Engheta, “Effective medium concept in temporal metamaterials,” Nanophotonics, vol. 9, no. 2, pp. 379–391, 2020. [29] V. Pacheco‐Peña and N. Engheta, “Merging effective medium concepts of spatial and temporal media,” Accepted, IEEE Antennas and Propagation magazine, 2023. DOI 10.1109/MAP.2023.3254480  

Space-time effective media enabled by spatial interfaces and temporal boundaries: a four-dimensional approach

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Space-time effective media enabled by spatial interfaces and temporal boundaries: a four-dimensional approach

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