Light Localization in Local Isomorphism Classes of Quasicrystals

We study a continuum of photonic quasicrystal heterostructures derived from local isomorphism (LI) classes of pentagonal quasicrystal tilings. These tilings are obtained by direct projection from a five-dimensional hypercubic lattice. We demonstrate that, with the sole exception of the Penrose LI cl...

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Bibliographic Details
Published in:Physical review letters 2018-06, Vol.120 (24), p.247401-247401, Article 247401
Main Authors: Lin, Chaney, Steinhardt, Paul J, Torquato, Salvatore
Format: Article
Language:English
Subjects:
Heterostructures
Isomorphism
Localization
Photonics
Quasicrystals
Tiling
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Summary:We study a continuum of photonic quasicrystal heterostructures derived from local isomorphism (LI) classes of pentagonal quasicrystal tilings. These tilings are obtained by direct projection from a five-dimensional hypercubic lattice. We demonstrate that, with the sole exception of the Penrose LI class, all other LI classes result in degenerate, effectively localized states, with precisely predictable and tunable properties (frequencies, frequency splittings, and densities). We show that localization and tunability are related to a mathematical property of the pattern known as "restorability," i.e., whether the tiling can be uniquely specified given only a set of rules that fix all allowed clusters smaller than some bound.
ISSN:0031-9007
1079-7114
DOI:10.1103/physrevlett.120.247401