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

当我们第一次学习波传播时，我们学到了折射率n。这首先是一个简单的数字；对于玻璃，大约是1.5，对于金属，是一个很大的复数。接下来，我们了解到折射率可以依赖于位置。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。超材料研究通常关注的是设计具有有效折射率的亚波长尺度结构，该结构可以以可控的方式在空间中变化。但折射率随时间变化的情况又如何呢？例如，n在整个空间中都是相同的，但在某个时刻它的值发生了变化。同样也有反射，但与空间界面的反射不同，按照因果关系的要求，反射波在遇到时间‘界面’后发生。在这种情况下，频率改变的是符号而不是波矢。随着时间改变折射率，我们因此改变了波的频率(例如，在可见光的情况下是颜色)。如果我们同时改变空间和时间的折射率，那么我们就有能力以一种否则不可能改变的方式改变波，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产生极值波放大[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是一个挑战。最近在光学[4]和声学[5]方面的实验使时变材料参数成为现实。然而，这些材料通常对入射波有复杂的影响，这与上面描述的简化图像相去甚远。折射率不仅不是瞬时变化的，而且还取决于频率。目前，对于这些材料中的场的计算，还没有达成一致的理论方法。这个项目将发展时空变化的超材料理论，建立在[6]中用算符代替材料参数的理论方法上。在这个项目中，我们将：(1)研究时空变化的超材料的物理，考虑从声学到光学和射频材料的各种实验平台。(2)进一步发展[6]中的理论，处理非平面材料、非电磁波和更多奇异的材料参数，例如各向异性或双各向异性。(3)应用该理论来理解[1，2]中所报道的效应是如何从理论理想化转移到更现实的实验平台上的。(4)使用该理论来探索时空变化的超材料中新的和不可预见的波动现象。参考文献：[1]E.Galiffi，R.Tiole，S.Yen，H.Li，S.Vezzoli，P.A.Huidobro，M.G.Silveirinha，R.Sapienza，A.Alu，和J.B.Pendry《时变媒体的光子学》Adv.Phot.4,014002(2022年).[2]J.B.Pendry，E.Galiffi，和P.A.Huidobro，“依赖时间的介质中的增益机制”，Optica 8,636-637(2021年).[3]R.Anguero-Santacruz和D.Bermudez，“光学和其他领域的霍金辐射”，菲尔.翻译过来的。罗伊SoC。A 378，https://doi.org/10.1098/rsta.2019.0223(2020年)。[4]J.Bohn，T.S.Luk，C.Tollerton，S.W.Hutchings，I.Brener，S.A.R.Horsley，W.L.Barnes，和E.Hendry，“在铟锡氧化物中epsilon-近零等离激元共振的全光学开关”，NAT Commun。15 1017(2021).[5]Cho，X.wen，N.Park，等.《声学超材料的数字化虚拟原子》NAT。交警。11,251(2020年)。[6]S.A.R.Horsley，E.Galiffi，和Y.T.Wang，《色散时变介质的本征脉冲》arxiv：2208.11778(2022年)。

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).