Waves in almost-periodic particle chains release_rev_7f84d4d7-4593-41b3-9063-545c4e56f250

by Yarden Mazor, Ben Z. Steinberg

Released as a article .

2014  

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 group velocity is revealed due to the fractal's inner-structure.
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Type  article
Stage   submitted
Date   2014-06-02
Version   v1
Language   en ?
arXiv  1406.0257v1
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