Kolakoski sequences – an example of aperiodic order

Sing, Bernd

doi:10.1016/j.jnoncrysol.2003.11.021

Cited by 20 publications

(24 citation statements)

References 5 publications

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“…In this paper we pay attention to aperiodic systems which are constructed according to the classical and generalized Kolakoski schemes [6][7][8]. A Kolakoski self-generation sequence is defined by the property that it equals the sequence of its run-lengths, where a run is a maximal subword consisting of identical letters [8].…”

Section: Kolakoski Sequence Generation Rulesmentioning

confidence: 99%

“…A Kolakoski self-generation sequence is defined by the property that it equals the sequence of its run-lengths, where a run is a maximal subword consisting of identical letters [8]. A one-sided infinite sequence…”

Section: Kolakoski Sequence Generation Rulesmentioning

confidence: 99%

“…By analogy with [8] the sequence w which is started from digit 2 is named K(2, 1), while another one w which is started from 1 is called…”

Section: Kolakoski Sequence Generation Rulesmentioning

confidence: 99%

“…Besides, all these structures exhibit properties of self-similarity. This class of structures can be divided into two major groups, namely [5]: quasicrystals based on Fibonacci substitutional rule and aperiodic photonic structures based on Thue-Morse, Rudin-Shapiro, period-doubling and Kolakoski [6][7][8] inflation rules.…”

Section: Introductionmentioning

confidence: 99%

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Omnidirectional Reflection From Generalized Kolakoski Multilayers

Fesenko¹

2015

PIER M

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Abstract-The origin of omnidirectional band gaps in one-dimensional layered photonic structures which are aligned according to the generalized Kolakoski inflation rule are studied using the transfer matrix formalism. On their basis some particular designs of cascaded aperiodic heterostructures are proposed. It is found that the proposed cascaded structures stand out by the omnidirectional reflection bands which cover whole near-infrared spectral region.

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Section: Kolakoski Sequence Generation Rulesmentioning

confidence: 99%

Section: Kolakoski Sequence Generation Rulesmentioning

confidence: 99%

“…By analogy with [8] the sequence w which is started from digit 2 is named K(2, 1), while another one w which is started from 1 is called…”

Section: Kolakoski Sequence Generation Rulesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Omnidirectional Reflection From Generalized Kolakoski Multilayers

Fesenko¹

2015

PIER M

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“…Extra information about generation rules of the Kolakoski sequence, its general properties and configuration of different multilayers based on the Kolakoski generation scheme, can be found in Refs. [30,31] and Refs. [24][25][26], respectively.…”

Section: Aperiodic Bragg Reflection Waveguide Configurationmentioning

confidence: 99%

Dispersion properties of Kolakoski-cladding hollow-core nanophotonic Bragg waveguide

et al. 2016

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A comprehensive analysis of guided modes of a novel type of a planar Bragg reflection waveguide that consists of a low refractive index guiding layer sandwiched between two finite aperiodic mirrors is presented. The layers in the mirrors are aperiodically arranged according to the Kolakoski substitution rule. In such a waveguide, light is confined inside the core by Bragg reflection, while dispersion characteristics of guided modes strongly depend on aperiodicity of the cladding. Using the transfer matrix formalism bandgap conditions, dispersion characteristics and mode profiles of the guided modes of such a waveguide are studied on the GaAs/AlAs and Si/SiO 2 epitaxial platforms, which are compatible with hybrid and heteroepitaxial frameworks of silicon photonics.

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