The index of refraction governs the flow of light through materials. At visible and near-infrared wavelengths the real part of the refractive index is limited to less than 3 for naturally occurring transparent materials, fundamentally restricting applications. Here, we carried out experiments to study the upper limit of the effective refractive index of self-assembled metasurfaces at visible and near-infrared wavelengths. The centimeter-scale metasurfaces were made of a hexagonally close packed (HCP) monolayer of gold nanospheres coated with tunable alkanethiol ligand shells, controlling the interparticle gap from 2.8 to 0.45 nm. In contrast to isolated dimer studies, the macroscale areas allow for billions of gaps to be simultaneously probed and the HCP symmetry leads to large wavelength shifts in the resonance mode, enabling subnanometer length scale mechanisms to be reproducibly measured in the far-field. We demonstrate for subnanometer gaps that the optical response of the metasurfaces agrees well with a classical (local) model, with minor nonlocal effects and no clear evidence of ligand-mediated charge transfer at optical frequencies. We determine the effective real part of the refractive index for the metasurfaces has a minimum of 1.0 for green-yellow colors, then quickly reaches a maximum of 5.0 in the reds and remains larger than 3.5 far into the near-infrared. We further show changing the terminal group and conjugation of the ligands in the metasurfaces has little effect on the optical properties. These results establish a pragmatic upper bound on the confinement of visible and near-infrared light, potentially leading to unique dispersion engineered coatings.

中文翻译：

---

可调谐的亚纳米间隙等离子后表面

折射率控制光通过材料的流动。在可见光和近红外波长处，对于自然存在的透明材料，折射率的实部限制为小于3，从根本上限制了应用。在这里，我们进行了实验，以研究可见光和近红外波长下自组装超颖表面的有效折射率的上限。厘米级的超表面由涂覆有可调链烷硫醇配体壳的金纳米球的六方密堆积（HCP）单层制成，将颗粒间的间隙控制在2.8至0.45 nm之间。与孤立的二聚体研究相比，宏观区域允许同时探测数十亿个缺口，并且HCP对称性导致共振模式下的大波长偏移，能够在远场中重复测量亚纳米长度标度机制。对于亚纳米间隙，我们证明了超表面的光学响应与经典（局部）模型非常吻合，具有较小的非局部效应，并且在光学频率上没有清晰的配体介导的电荷转移证据。我们确定，对于超黄色表面，折射率的有效实数部分对于绿黄色至少为1.0，然后在红色中迅速达到最大为5.0，并在远红外区域保持大于3.5。我们进一步表明，改变端基和亚表面配体的共轭对光学性能的影响很小。这些结果为可见光和近红外光的局限性建立了务实的上限，