Waves in almost-periodic particle chains

Abstract

Almost periodic particle chains exhibit peculiar propagation properties that are not observed in perfectly periodic ones. Furthermore, since they inherently support non-negligible long-range interactions and radiation through the surrounding free-space, nearest-neighbor approximations cannot be invoked. Hence the governing operator is fundamentally different than that used in traditional analysis of almost periodic structures, e.g. Harper's model and Almost-Mathieu difference equations. We present a mathematical framework for the analysis of almost periodic particle chains, and study their electrodynamic properties. We show that they support guided modes that exhibit a complex interaction mechanism with the light-cone. These modes possess a two-dimensional fractal-like structure in the frequency-wavenumber space, such that a modal phase-velocity cannot be uniquely defined. However, a well defined \emph{group velocity} is revealed due to the fractal's inner-structure.

10 pages, 9 figures

References in corpus (4)

• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Theory of Linear Chains of Metamaterial/Plasmonic Particles as Sub-Diffraction Optical Nanotransmission Lines
• Propagation of Surface Plasmons in Ordered and Disordered Chains of Metal Nanospheres
• From Slow to Superluminal Propagation: Dispersive Properties of Surface Plasmon Polaritons in Linear Chains of Metallic Nanospheroids