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Crystals 2017, 7(7), 183; doi:10.3390/cryst7070183

Lempel-Ziv Complexity of Photonic Quasicrystals

1
Departamento de Óptica, Facultad de Física, Universidad Complutense, 28040 Madrid, Spain
2
Departamento de Estadística e Investigación Operativa, Facultad de Matemáticas, Universidad Complutense, 28040 Madrid, Spain
3
Max Planck Institut für die Physik des Lichts, Staudtstraße 2, 91058 Erlangen, Germany
*
Author to whom correspondence should be addressed.
Academic Editor: Helmut Cölfen
Received: 27 April 2017 / Revised: 20 June 2017 / Accepted: 21 June 2017 / Published: 23 June 2017
(This article belongs to the Collection Structure and Properties of Quasicrystals)
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Abstract

The properties of one-dimensional photonic quasicrystals ultimately rely on their nontrivial long-range order, a hallmark that can be quantified in many ways depending on the specific aspects to be studied. Here, we assess the quasicrystal structural features in terms of the Lempel-Ziv complexity. This is an easily calculable quantity that has proven to be useful for describing patterns in a variety of systems. One feature of great practical relevance is that it provides a reliable measure of how hard it is to create the structure. Using the generalized Fibonacci quasicrystals as our thread, we give analytical fitting formulas for the dependence of the optical response with the complexity. View Full-Text
Keywords: quasicrystals; photonic crystals; photonic bandgap materials quasicrystals; photonic crystals; photonic bandgap materials
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Monzón, J.J.; Felipe, A.; Sánchez-Soto, L.L. Lempel-Ziv Complexity of Photonic Quasicrystals. Crystals 2017, 7, 183.

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