Brazilian Synchrotron Light Laboratory (LNLS), Brazilian Center for Research in Energy and Materials (CNPEM), Zip Code 13083-970, Campinas, Sao Paulo, Brazil.
Department of Physics, Department of Chemistry, and JILA, University of Colorado, Boulder, Colorado 80309, USA.
Nanoscale. 2019 Nov 28;11(44):21218-21226. doi: 10.1039/c9nr07387f. Epub 2019 Oct 30.
The nanophotonics of van der Waals (vdW) materials relies critically on the electromagnetic properties of polaritons defined on sub-diffraction length scales. Here, we use a full electromagnetic Hertzian dipole antenna (HDA) model to describe the hyperbolic phonon polaritons (HPs) in vdW crystals of hexagonal boron nitride (hBN) on a gold surface. The HP waves are investigated by broadband synchrotron infrared nanospectroscopy (SINS) which covers the type I and type II hyperbolic bands simultaneously. Basically, polariton waves, observed by SINS, are assigned to the resultant electric field from the summation over the irradiated electric fields of dipoles distributed along the crystal edge and at the tip location and a non-propagating field. The values of polariton momenta and damping extracted from the HDA model present excellent agreement with theoretical predictions. Our analysis shows that the confinement factor of type I HPs exceeds that of the type II ones by up to a factor of 3. We extract anti-parallel group velocities (v) for type I (v = -0.005c, c is the light velocity in a vacuum) in relation to type II (v = 0.05c) polaritonic pulses, with lifetimes of ∼0.6 ps and ∼0.3 ps, respectively. Furthermore, by incorporating consolidated optical-near field theory into the HDA model, we simulate real-space images of polaritonic standing waves for hBN crystals of different shapes. This approach reproduces the experiments with a minimal computational cost. Thus, it is demonstrated that the HDA modelling self-consistently explains the measured complex-valued polariton near-field, while being a general approach applicable to other polariton types, like plasmon- and exciton-polaritons, active in the wide range of vdW materials.
范德瓦尔斯（vdW）材料的纳米光子学依赖于在亚衍射长度尺度上定义的极化激元的电磁特性。在这里，我们使用全电磁赫兹偶极天线（HDA）模型来描述在金表面上的六方氮化硼（hBN）vdW 晶体中的双曲声子极化激元（HP）。通过同时覆盖 I 型和 II 型双曲带的宽带同步辐射红外纳米光谱（SINS）研究 HP 波。基本上，由 SINS 观察到的极化激元波被分配到沿晶体边缘和尖端位置分布的偶极子辐照电场的总和以及非传播场的总和的合成电场。从 HDA 模型提取的极化激元动量和阻尼值与理论预测非常吻合。我们的分析表明，I 型 HP 的约束因子比 II 型的约束因子高出高达 3 倍。我们提取了 I 型（v = -0.005c，c 是真空中的光速）与 II 型（v = 0.05c）极化激元脉冲的反平行群速度（v），寿命分别为∼0.6 ps 和∼0.3 ps。此外，通过将综合光学近场理论纳入 HDA 模型，我们模拟了不同形状的 hBN 晶体的极化激子驻波的实空间图像。这种方法以最小的计算成本再现了实验。因此，证明 HDA 建模自洽地解释了所测量的复值极化近场，同时也是一种适用于其他极化激元类型（如等离子激元和激子极化激元）的通用方法，这些类型在广泛的 vdW 材料中活跃。
