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arXiv · 1406.0257

Waves in almost-periodic particle chains

Yarden Mazor·Ben Z. Steinberg
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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.

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Yarden Mazor, Ben Z. Steinberg. 2014-06-02. Waves in almost-periodic particle chains. https://doi.org/10.1103/physrevb.90.045151

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