From slow to superluminal propagation: Dispersive properties of surface plasmon polaritons in linear chains of metallic nanospheroids

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^⊥<|q|<π/h, h being the chain period. For longitudinally polarized SPPs, the gap spans the interval |q|<q_c^∥. Here q_c^⊥ and q_c^∥ 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^⊥|⪡π/h or |q−q_c^∥|⪡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.