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Journal ArticleDOI

Quasiperiodic GaAs-AlAs Heterostructures

21 Oct 1985-Physical Review Letters (American Physical Society)-Vol. 55, Iss: 17, pp 1768-1770
TL;DR: The first realization of a quasiperiodic (incommensurate) superlattice is reported, which consists of alternating layers of GaAs and AlAs to form a Fibonacci sequence in which the ratio of incommensurate periods is equal to the golden mean.
Abstract: We report the first realization of a quasiperiodic (incommensurate) superlattice. The sample, grown by molecular-beam epitaxy, consists of alternating layers of GaAs and AlAs to form a Fibonacci sequence in which the ratio of incommensurate periods is equal to the golden mean $\ensuremath{\tau}$. X-ray and Raman scattering measurements are presented that reveal some of the unique properties of these novel structures.
Citations
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Journal ArticleDOI
31 Oct 1997-Science
TL;DR: In this article, quasi-periodic structure was introduced into nonlinear optical materials such as LiTaO3 crystals for quasi-phase-matching second-harmonic generation and sum-frequency generation.
Abstract: Quasi-periodic structure can be introduced into nonlinear optical materials such as LiTaO3 crystals. Such structures were used for quasi–phase-matching second-harmonic generation. These materials are now shown to be able to couple second-harmonic generation and sum-frequency generation through quasi–phase-matching. The approach led to a direct third-harmonic generation with high efficiency through a coupled parametric process. The result verifies that high-order harmonics may be generated in a quadric nonlinear medium by a number of quasi–phase-matching processes, and therefore, exhibits a possible important application of quasi-periodic structure materials in nonlinear optics.

638 citations

Journal ArticleDOI
TL;DR: In this paper, wave transmission properties in one dimensional nonlinear lattices are discussed and the results from the theory of dynamical systems are used to investigate various aspects of wave transmission and wave localization.

362 citations

Journal ArticleDOI
TL;DR: The role of aperiodic order in different domains of science and technology from an interdisciplinary approach is discussed in this paper, where several conceptual links between quasiperiodic crystals and the hierarchical structure of biopolymers are discussed.
Abstract: In this work we consider the role of aperiodic order in different domains of science and technology from an interdisciplinary approach. To start with, we introduce some general classification schemes for aperiodic arrangements of matter. Afterwards, we review the main physical properties and possible applications of quasiperiodic crystals. Several conceptual links between quasiperiodic crystals and the hierarchical structure of biopolymers are then discussed in connection with the charge transfer properties of both biological and synthetic DNA chains. The widespread presence of Fibonacci numbers and the golden mean in different physical contexts is also discussed. Promising technological applications of aperiodic systems are finally reviewed by considering both current and potential applications. In particular, we analyse the capability of exploiting aperiodic order in the design of novel devices based on semiconductor heterostructures and dielectric multilayers.

308 citations

Journal ArticleDOI
TL;DR: A comprehensive and up-to-date review of the main physical properties (such as energy profiles, localization, scale laws, multifractal analysis, transmission spectra, transmission fingerprints, electronic structures, magnetization curves and thermodynamic properties) of the elementary excitations that can propagate in multilayered structures with constituents arranged in a quasiperiodic fashion is presented in this article.

254 citations

Journal ArticleDOI
TL;DR: In this paper, the peculiarities of quasiperiodic order for the properties of photonic and phononic (sonic) heterostructures are discussed, and a review of the relationship between 1D and 2D structures based on one-dimensional substitutional sequences such as the Fibonacci, Thue-Morse, period-doubling, Rudin-Shapiro and Cantor sequence is presented.
Abstract: This review focuses on the peculiarities of quasiperiodic order for the properties of photonic and phononic (sonic) heterostructures. The most beneficial feature of quasiperiodicity is that it can combine perfectly ordered structures with purely point-diffractive spectra of arbitrarily high rotational symmetry. Both are prerequisites for the construction of isotropic band gap composites, in particular from materials with low index contrast, which are required for numerous applications. Another interesting property of quasiperiodic structures is their scaling symmetry, which may be exploited to create spectral gaps in the sub-wavelength regime. This review covers structure/property relationships of heterostructures based on one-dimensional (1D) substitutional sequences such as the Fibonacci, Thue–Morse, period-doubling, Rudin–Shapiro and Cantor sequence as well as on 1D modulated structures, further on 2D tilings with 8-, 10-, 12- and 14-fold symmetry as well as on the pinwheel tiling, the Sierpinski gasket and on curvilinear tilings and, finally, on the 3D icosahedral Penrose tiling.

251 citations