The theory of space-time varying metamaterials (Ref. 4659)

当我们第一次学习波的传播时，我们学到了折射率n。这首先是一个简单的数字;对于玻璃来说大约是1.5，对于金属来说是一个很大的复数。接下来，我们学习折射率可以取决于位置。折射率的空间依赖性导致反射，其中波矢量改变符号，这是最常见的波动现象之一。超材料的研究通常涉及设计亚波长尺度的结构，其有效折射率可以以受控的方式在空间中变化。但是折射率随时间变化呢？例如，n在整个空间中是相同的，但在某个时刻它的值会发生变化。同样存在反射，但与空间界面的反射不同，反射波在遇到时间“界面”后发生，正如因果关系所要求的那样[1]。在这种情况下，频率改变符号而不是波矢量。随着时间的推移改变折射率，我们就改变了波的频率（例如，在可见光的情况下，改变了波的颜色）。如果我们改变空间和时间的折射率，我们就有能力以一种不可能的方式改变波，改变它的频率和传播方向。时空变化的材料参数已经被证明可以在不需要增益的情况下导致极端的波放大[2]，以及霍金辐射等天体物理现象的实验室模拟[3]。然而，直到最近，制造参数随时间变化的材料一直具有挑战性。最近在光学[4]和声学[5]方面的实验已经使时变材料参数成为现实。然而，这些材料通常对入射波具有复杂的影响，这与上述简化的情况相去甚远。折射率不仅不会瞬间改变，而且还取决于频率。目前还没有一种公认的理论方法来计算这些材料中的场。本项目将在文献[6]的理论方法基础上发展时空变化超材料的理论，其中材料参数被算子取代。在本项目中，我们将：（1）研究时空变化超材料的物理，考虑各种实验平台，从声学，光学，和射频材料。(2)进一步发展[6]中的理论，处理非平面材料，非电磁波和更多的奇异材料参数，例如各向异性或双各向异性。尝试开发这些迄今为止仅进行数值处理的算子方程的解析解。(3)应用该理论来理解[1，2]中报告的效应在从理论理想化转向更现实的实验平台时如何变化。(4)利用该理论探索时空变化超材料中新的和不可预见的波动现象。加利菲河Tirole，S. Yin，H. Li，S. Vezzoli，P. A. Huidobro，M. G.锡尔韦里尼亚河Sapienza，A. Alu和J. B. Pendry“Photonics of Time-Variing Media”Adv. Phot. 4，014002（2022）。[2]J. B. Pendry，E. Galiffi和P.A. Huidobro，“Gain mechanism in time-dependent media”，Optica 8，636-637（2021）。[3]R. Anguero-Santacruz和D.霍金辐射在光学和超越“，菲尔。翻译罗伊。A 378，https://doi.org/10.1098/rsta.2019.0223（2020）。[4]J. Bohn，T. S.卢克角Tollerton，S. W.哈钦斯岛Brener，S. A. R.霍斯利，W. L.巴恩斯和E. Hendry，“氧化铟锡中ε-近零等离子体共振的全光开关”，Nat Commun。15 1017（2021）。[5]C.周，X。温氏N. Park等人，“用于声学超材料的数字虚拟化原子”，Nat. Commun. 11，251（2020）中所述。[6]S. A. R.霍斯利，E. Galiffi和Y. T. Wang，“Eigenpulses of dispersive time-varying media”arXiv：2208.11778（2022）。

When we first learn about wave propagation we are taught about the refractive index, n. This is first simply a number; about 1.5 for glass, and a large complex number for metals. Next we learn the refractive index can depend on position. The spatial dependence of the refractive index leads to reflection, where the wave vector changes sign, one of the most everyday of wave phenomena. Metamaterial research is commonly concerned with designing sub-wavelength scale structures with an effective refractive index that can be varied across space in a controlled way.But what about a refractive index that varies in time? An example could be where n is the same throughout space, but at some moment in time its value changes. Again there is reflection, but unlike reflection from a spatial interface, the reflected wave occurs after it encounters the temporal 'interface', as required by causality [1]. In this case the frequency changes sign rather than the wave vector. Varying the refractive index in time we thus alter the frequency (e.g. colour, in the case of visible light) of the wave. If we change the refractive index in both space and time we then have the ability to change the wave in a way that would be otherwise impossible, modifying both its frequency and direction of propagation. Space-time varying material parameters have been shown to lead to extreme wave amplification without requiring gain [2], and laboratory analogues of astrophysical phenomena such as Hawking radiation [3].However, until recently it has been challenging to make materials where the parameters vary in time. Recent experiment in optics [4] and acoustics [5] have made time varying material parameters a reality. Yet these materials typically have a complicated effect on an incident wave, that is a far cry from the simplified picture described above. Not only is the refractive index not changed instantaneously, but it also depends on frequency. At present there is no agreed theoretical approach to the calculation of fields within these materials. This project will develop the theory of space time varying metamaterials, building on the theoretical approach derived in [6] where the material parameters are replaced with operators.In this project we will:(1) Investigate the physics of space time varying metamaterials, considering a variety of experimental platforms, from acoustics, to optics, and radio frequency materials.(2) Further develop the theory in [6], treating non-planar materials, non-electromagnetic waves, and more exotic material parameters, e.g. anisotropy or bianisotropy. Attempt to develop analytical solutions to these operator equations that have so far been treated only numerically.(3) Apply the theory to understand how the effects reported in e.g. [1,2] change when moving from theoretical idealizations to more realistic experimental platforms.(4) Use the theory to explore new and unforeseen wave phenomena in space-time varying metamaterials.References:[1] E. Galiffi, R. Tirole, S. Yin, H. Li, S. Vezzoli, P. A. Huidobro, M. G. Silveirinha, R. Sapienza, A. Alu, and J. B. Pendry "Photonics of Time-Varying Media" Adv. Phot. 4, 014002 (2022).[2] J. B. Pendry, E. Galiffi, and P. A. Huidobro, "Gain mechanism in time-dependent media", Optica 8, 636-637 (2021).[3] R. Anguero-Santacruz and D. Bermudez, "Hawking radiation in optics and beyond", Phil. Trans. Roy. Soc. A 378, https://doi.org/10.1098/rsta.2019.0223 (2020).[4] J. Bohn, T. S. Luk, C. Tollerton, S. W. Hutchings, I. Brener, S. A. R. Horsley, W. L. Barnes, and E. Hendry, "All-optical switching of an epsilon-near-zero plasmon resonance in indium tin oxide", Nat Commun. 15 1017 (2021).[5] C. Cho, X. Wen, N. Park, et al. "Digitally virtualized atoms for acoustic metamaterials" Nat. Commun. 11, 251 (2020).[6] S. A. R. Horsley, E. Galiffi, and Y. T. Wang, "Eigenpulses of dispersive time-varying media" arXiv:2208.11778 (2022).