Quasicrystal Patterns Research Articles

FDTD analysis of out-of-plane propagation in 12-fold photonic quasi-crystals

The out-of-plane propagation characteristics of an infinitely extended 12-fold photonic quasi-crystal structure is modeled using the FDTD technique. The quasi-crystal pattern is designed using the dual beam multiple exposure holographic lithography system previously reported. Simulations indicate that two types of mode families are possible; “bandgap guided” and; “index guided”. Results are presented showing mode profiles; effective index versus propagation constant and wavelength plots; and modal attenuation due to power leakage. Potential applications include a new novel micro-structured optical fiber.

Isotropic photonic bandgap in Penrose textured metallic mircocavity

Photonic microcavity has modified photonic modes that have intense localized electric field, which can couple strongly with the embedded emission centers. In this work, we fabricated 2D photonic microcavities with Penrose quasicrystal pattern with 10-fold symmetry. Organic luminescence material tris(8-hydroxyquinoline) aluminum (Alq 3) was embedded into the microcavity and the angle resolved transmission (ART) and photoluminescence (ARPL) spectra of the microcavity were measured. The results showed that the normal Gaussian photoluminescence spectrum of Alq 3 has been strongly modified by the microcavity dispersion characteristic. In addition, omni-directional photonic band gap exists in the microcavity. The higher symmetry of Penrose quasicrystal pattern means that there was minimal difference in the directional dispersion characteristics.

FDTD analysis of 12-fold photonic quasi-crystal central pattern localized states

The TM bandgap features of the 2D 12-fold quasi-crystal are examined based on the width of the dielectric strip and pattern central symmetry location within the quasi-crystal. Results indicate that the bandgap properties observed for a particular fill factor is independent of the rotational symmetry center when the dielectric strip is wide, and still observable when the strip width is considerably reduced, confirming the general belief that the bandgap generating properties of the quasi-crystal are a local dielectric effect for the lower frequency band. Thin strips are shown to posses defect states in the bandgap region of the thicker equivalent strips, defect states analogous to intentionally introduced defect states of translational symmetric photonic crystals. We explore the mode profiles of the defect state when the defect is coincidental with the rotational symmetry central pivot point of the quasi-crystal pattern. In addition we show that the rotational center “defect” may be used to enhance the optical guidance of light around a 90° bend in a waveguide implanted in the quasi-crystal.

Photonic band gap properties of 12-fold quasi-crystal determined through FDTD analysis

The TM propagation properties of planar 12-fold photonic quasi-crystal patterns are theoretically examined using FDTD. The patterns examined can be produced using a dual beam multiple exposure technique. Simulated transmission plots are shown for various fill factors, dielectric contrast and propagation direction. It is shown that low index waveguides can be produced using the quasi-crystal photonic crystal pattern.

Production of quasi-crystal template patterns using a dual beam multiple exposure technique

We present a dual beam multiple exposure technique that can generate complex 2-D quasi-crystal template structures. The optical system is based on the interference of two laser beams producing a family of high intensity planes. Controlled reorientation of a photosensitive sample between exposures results in an exposure dose, when developed, returns a quasi-crystal pattern. Results are shown in which quasi-crystal patterns with 8, 10, and 12-fold rotation symmetry are produced in photoresist. The results of several test runs are shown in which the quasi-crystal patterns developed in photoresist are subsequently etched into silicon. Based on an extended application of the dual beam multiple exposure optical system, a potential technique for producing 3-D quasi-crystal patterns is presented.

2-D Photonic Quasicrystal in Metallic Microcavity

ABSTRACTPhotonic microcavity promises to be one of the photonic devices that can have immediate applications such as super bright LED and low threshold laser. Most photonic crystal structures currently used on microcavity are cubic or hexagonal, whose folding symmetry is no greater than 6. In this work, we fabricated 2-D photonic microcavity with Penrose quasicrystal pattern and measured the angular resolved transmission and photoluminescence spectra of the microcacity. From the experimental result it is found that isotropic photonic band gap exists in the microcavity with the Penrose quasicrystal pattern.

Deterministic and nondeterministic quasicrystal patterns with even symmetries

Quasicrystal patterns with symmetries found in diffraction experiments are studied. Nondeterministic models of quasicrystal structures can be obtained by composition of the inflation rules that generate the deterministic patterns.

Stochastic L-systems and quasicrystal patterns

Bracketed stochastic Lindenmayer systems (L-systems) are used for the description of certain species of non-deterministic quasicrystal patterns. Several classes of substitution tilings with eight-fold symmetry are introduced. They form the basis for non-deterministic octagonal structures which can be described with stochastic DT0L-systems. Heptagonal structures can also be described with stochastic DT0L-systems, whereas the appropriate scheme for structures with nine-fold symmetry is a stochastic ET0L-system.

Student Activities: Symmetries and Quasicrystal Patterns

School Science and MathematicsVolume 94, Issue 7 p. 385-386 Student Activities: Symmetries and Quasicrystal Patterns First published: November 1994 https://doi.org/10.1111/j.1949-8594.1994.tb15700.xAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume94, Issue7November 1994Pages 385-386 RelatedInformation

Some remarks on quasi-crystal structure

The Fourier transform of a skeletal delta function that characterizes the most striking features of experimental quasicrystal diffraction patterns is evaluated. The result plays a role analogous to the Poisson summation formula for periodic delta functions that underlie classical crystallography. The real-space distribution can be interpreted in terms of a backbone comprising a system of intersecting equiangular spirals into which are inscribed (self-similar) gnomons of isosceles triangles with length-to-base ratio the golden mean τ. In addition to the vertices of these triangles, there is an infinite number of other points that may tile space in two or three dimensions. Other mathematical formulae of relevance are briefly discussed.

Ion channeling in T-phase quasicrystals: an investigation by Rutherford backscattering and particle induced X-ray emission

The channeling properties of a T-phase A1 62Cu 20Co 15Si 3 quasicrystal are investigated in a Rutherford backscattering study employing 2 MeV He-ions. Besides axial channeling along the decagonal axis, also planar channeling is observed in planes having the decagonal axis in common and showing the decagonal symmetry of the quasicrystal. Besides a system of main planes, various planes exhibiting only weak channeling properties are observed; they correspond to linear arrangements of vertices in a two-dimensional Penrose grid, demonstrating the close relationship between T-phase quasicrystal and Penrose pattern. Rutherford backscattering (RBS) has also been used to study the decoration of the T-phase structure by Co/Cu- and Al/Si-atoms; in addition, particle induced X-ray emission PIXE served to distinguish between Co- and Cu-atoms. The experimental data are compared with channeling computer simulations on a model T-phase quasicrystal proposed by Steurer and Kuo [6].

Hierarchical structure in quasicrystal diffraction patterns: X-ray scattering on periodic approximants of Fibonacci superlattices.

We report an x-ray scattering study of a series of periodic Fibonacci superlattices, which are converging rational approximants of ideal quasiperiodic Fibonacci superlattices. An analytic expression of the structure factor is derived that agrees well with experiments. This expression, which generalizes the standard formula used for classical crystals, reflects two multiplicative contributions: a sampling function which depends only on the stacking geometry, and a form factor involving only the structure factors of the tiling blocks. In the quasicrystal limit each line of the dense, countable spectrum can be associated with the order of the first approximant in which it appears, thus providing a hierarchical structure for the spectrum. Furthermore, the experimental partial breaking of selection rules gives evidence for the existence of interface defects.

Generation and experimental measurement of a one-dimensional quasi-crystal diffraction pattern

A microcomputer-generated one-dimensional quasi-crystal grating is produced on a high-resolution monitor. Photographic reproduction of the grating with about a 30× reduction in size produces an acceptable optical grating. The location of diffraction maxima and the relative intensity pattern produced by passing HeNe laser light through the grating is compared to the theoretical prediction with mixed results. The comparison of two types of film that can be used for this experiment is also discussed.

Distortion and peak broadening in quasicrystal diffraction patterns.

In this paper, we discuss how quenched strains in phonon and phason variables and/or quenched dislocations can lead to peak broadening and distortion in quasicrystal diffraction patterns. We argue that high-resolution electron micrographs and observations of distortions in electron diffraction patterns indicate the presence of anisotropic strains in the phason variable in the icosahedral phase of Al-Mn and related alloys. Such strains also contribute to the x-ray peak widths and line shapes.

Indexing problems in quasicrystal diffraction.

Various features of quasicrystal diffraction patterns are discussed. The projection scheme is used throughout and applied in some detail to the pattern formed by icosahedral Al-Mn. Comparison with the diffraction pattern formed by the vertices of a three-dimensional Penrose tiling leads to the value 4.60 A\r{} for the rhombohedron edge length.