Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.
Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA.
Phys Rev Lett. 2018 Jun 15;120(24):247401. doi: 10.1103/PhysRevLett.120.247401.
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.
我们研究了一类由五边形准晶平铺的局域同构（LI）类衍生而来的光子准晶异质结构。这些平铺是通过从五维超立方晶格的直接投影得到的。我们证明，除了彭罗斯 LI 类之外，所有其他的 LI 类都会导致简并的、有效的局域态，具有精确可预测和可调谐的性质（频率、频率分裂和密度）。我们表明，局域化和可调谐性与图案的一个数学性质有关，这个性质被称为“可修复性”，即给定一组只固定所有允许的小于某个界限的较小簇的规则，能否唯一地确定平铺。
