Toroidal moment is an electromagnetic excitation that lies outside the familiar picture of electric and magnetic multipoles. It has recently been a topic of intense research in the fields of nanophotonics and metamaterials due to its weakly radiating nature and its ability to confine electromagnetic energy. Among extensive studies on toroidal moments and their applications, high quality factor (Q) toroidal resonances have been experimentally realized only in a very limited set of geometries and wavelengths. In this study, we demonstrate that a metasurface consisting of arrays of hollow dielectric cuboids supports a high Q-factor resonances at near-infrared and visible wavelengths due to the destructive interference between toroidal dipoles and magnetic quadrupoles. Using silicon as the high index dielectric, an experimental Q-factor of 728 is realized at a wavelength of 1505 nm, which is one of the highest values reported in the near-infrared using a dielectric metasurface. Importantly, our resonator geometry enables very efficient coupling of the toroidal resonance to the environment. This makes our metasurface design useful for refractometric sensing, where we measure a sensitivity of 161 nm per refractive index unit with a line width of 2.01 nm, efficiently distinguishing an index change of less than 0.02. We also find that a metasurface made of a relatively low-index dielectric, titanium dioxide (n < 2.4), is also capable of supporting the same toroidal mode with an observed Q-factor of 160 at visible wavelengths. With the versatility and robustness that dielectric metasurfaces provide, toroidal resonances are expected to be a powerful tool for investigating strong light–matter interaction and nonlinear phenomena at the nanoscale.

中文翻译：

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介电超表面中的高品质因数环形共振

环形力矩是一种电磁激励，它位于电和磁多极子的熟悉画面之外。由于其弱的辐射性质和限制电磁能的能力，近来它已成为纳米光子学和超材料领域中的一项深入研究的主题。在关于环形矩及其应用的广泛研究中，仅在非常有限的一组几何形状和波长范围内通过实验实现了高品质因数（Q）环形共振。在这项研究中，我们证明了由空心电介质长方体阵列组成的超表面支持高Q由于环形偶极子和磁性四极子之间的相消干涉，在近红外和可见光波长处的高因子共振。使用硅作为高折射率电介质，在1505 nm的波长下实现了728的实验Q因子，这是使用电介质超表面在近红外中报道的最高值之​​一。重要的是，我们的谐振器的几何形状可以使环形谐振非常有效地耦合到环境。这使得我们的超表面设计可用于折光检测，在折光检测中，我们测量的每个折光指数单位的灵敏度为161 nm，线宽为2.01 nm，可有效区分小于0.02的折射率变化。我们还发现一个超颖做了一个比较低折射率电介质，二氧化钛（的ñ<2.4），还能够在可见光波长下以160的Q因子支持相同的环形模式。借助介电超表面所提供的多功能性和鲁棒性，环形共振有望成为研究纳米级强光物质相互作用和非线性现象的有力工具。