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

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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).