从慢传播到超光速传播：金属纳米球线性链中表面等离子体激元的色散特性
From Slow to Superluminal Propagation: Dispersive Properties of Surface Plasmon Polaritons in Linear Chains of Metallic Nanospheroids
摘要：
本文研究了表面等离子体激元在长球形和扁球形金属球线性周期链中的传播。我们发现，SPP群速度可以有效地控制通过改变的纵横比的球体。对于足够小的纵横比，间隙出现在链晶格的第一布里渊区中，其中不存在传播模式。取决于SPP偏振，间隙延伸到布洛赫波数q的特定间隔。因此，对于横向偏振，不存在波数q使得q_c^ \perp <|Q| < π/h，h为链周期。对于纵向极化SPP，间隙跨越间隔|q| <q_c^ \parallel。这里，q_c^ \perp和q_c^ \parallel是不同的常数，其取决于链参数、球体纵横比及其相对于链轴的取向。色散曲线对球体纵横比的依赖性导致了一些有趣的效果。特别地，可以通过利用长球体或扁球体来显著增加可以在LPC中传播的SPP的带宽。当q接近临界值时，|q - q_c^ \perp| <<π/h或|q - q_c^ \parallel| <<π/h时，SPP的衰变长度显著增加。此外，色散曲线获得非常大的正斜率或负斜率。这可以用来实现超光速群速度的现实链参数。我们在数值模拟中证明了高斯波包的超光速传播。理论和模拟都是基于考虑延迟的麦克斯韦方程组，因此是完全相对论的。
英文摘要：
We consider propagation of surface plasmon polaritons (SPPs) in linear periodic chains (LPCs) of prolate and oblate metallic spheroids. We show that the SPP group velocity can be efficiently controlled by varying the aspect ratio of the spheroids. For sufficiently small aspect ratios, a gap appears in the first Brillouin zone of the chain lattice in which propagating modes do not exist. depending on the SPP polarization, the gap extends to certain intervals of the Bloch wave number q. Thus, for transverse polarization, no propagating SPPs exist with wave numbers q such that q_c^\perp < | q | < π/h, h being the chain period. For longitudinally polarized SPPs, the gap spans the interval |q|<q_c^\parallel. Here q_c^\perp and q_c^\parallel are different constants which depend on the chain parameters, spheroid aspect ratio and its orientation with respect to the chain axis. The dependence of the dispersion curves on the spheroid aspect ratio leads to a number of interesting effects. In particular, bandwidth of SPPs that can propagate in an LPC can be substantially increased by utilizing prolate or oblate spheroids. When q is close to a critical value, so that |q - q_c^\perp|<<π/h or |q - q_c^\parallel|<<π/h, the decay length of the SPPs is dramatically increased. In addition, the dispersion curves acquire a very large positive or negative slope. This can be used to achieve superluminal group velocity for realistic chain parameters. We demonstrate superluminal propagation of Gaussian wave packets in numerical simulations. Both theory and simulations are based on Maxwell equations with account of retardation and, therefore, are fully relativistic.
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