有限长纳米颗粒链中Rayleigh反常诱导的相矢量
Rayleigh Anomaly Induced Phase Gradients in Finite Nanoparticle Chains
摘要：
我们报告的理论研究，在有限的纳米颗粒链的瑞利异常引起的异常相梯度。相对于所施加的平面波的相位定义的这些相位梯度导致来自链的衍射方向相对于从用于无限链的光栅方程预期的方向的偏差。为了从理论上研究这种效应，我们使用基于离散偶极子近似的分析方法，该方法揭示了控制链动力学的多散射过程的组合性质。我们发现一个近似的封闭形式的解决方案，以粒子的偶极矩描述的单一互易系统与两个非互易的，单向系统的连续解决方案。在这个框架内，我们得到链激发不同的散射路径之间的干涉。此外，我们表明，沿链的偶极矩是由广义斐波那契级数所规定的递归关系。研究结果为理解纳米粒子阵列的动力学提供了一个新的视角。具体而言，独特的方法，分析空间激励的阵列夹杂物可能会出现新的光周期性行波天线的光学制度，如激光雷达，拓扑状态分析和任意波束成形方案的应用。
英文摘要：
We report on the theoretical study of anomalous phase gradients induced by Rayleigh anomalies in finite nanoparticle chains. These phase gradients, defined with respect to the phase of the applied plane wave, cause a deviation of the diffraction directions from the chain relative to the direction expected from the grating equation for infinite chains. To study the effect theoretically, we use an analytical approach based on the discrete dipole approximation, which reveals the combinatorial nature of the multi-scattering process that governs the chain dynamics. We find an approximate closed-form solution to the particles' dipole moments by describing the single reciprocal system with a successive solution of two non-reciprocal, one-way systems. Within this framework, we obtain the chain excitation by means of interference between different scattering paths. Moreover, we show that the dipole moments along the chain are governed by recursive relations dictated by the generalized Fibonacci series. The presented results provide a new perspective for understanding nanoparticle arrays' dynamics. Specifically, the unique approach for analytically analyzing the spatial excitations of the array inclusions may shed new light on emerging applications of periodic traveling wave antennas in the optical regime, such as LIDARs, topological states analysis and arbitrary beam shaping schemes.
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