Quasicrystal Patterns Research Articles

Exploring quantum quasicrystal patterns: A variational study

We study the emergence of quasicrystal configurations produced purely by quantum fluctuations in the ground-state phase diagram of interacting bosonic systems. By using a variational mean-field approach, we determine the relevant features of the pair interaction potential that stabilize such quasicrystalline states in two dimensions. Unlike their classical counterpart, in which the interplay between only two wave vectors determines the resulting symmetries of the solutions, the quantum picture relates in a more complex way to the instabilities of the excitation spectrum. Moreover, the quantum quasicrystal patterns are found to emerge as the ground state with no need of moderate thermal fluctuations. The study extends to the exploration of the excitation properties and the possible existence of super-quasicrystals, i.e. supersolid-like quasicrystalline states in which the long-range non-periodic density profile coexist with a non-zero superfluid fraction. Our calculations show that, in an intermediate region between the homogeneous superfluid and the normal quasicrystal phases, these exotic states indeed exist at zero temperature. Comparison with full numerical simulations provides a solid verification of the variational approach adopted in this work.

Multi-scale pattern with surface quasi crystal for wettability tuning

Transparent and stretchable structures with multi-scale patterns on PDMS surfaces for a tunable superhydrophobicity are presented. The samples result in the transfer of photoinduced quasi-crystal structures of azopolymer-based thin films onto an elastomer. The quasi-crystal surface patterns have different complexities generated with superimposed multiple exposures. The obtained samples can be stretched or compressed. Periodic circular nanocavities as small as 500 nm could be obtained with their shapes changed by stretching. The surface stretching or compressing induced on the elastomer surface allows the size manipulation of nanocavities. An application of these surfaces is presented for a large control of the super-hydrophobicity. The wetting of these patterns is compared to the same surface pattern modified with metal nanoparticles obtained by a metal dewetting process where the roughness is increased. We show that in this case the hydrophobicity is higher, and the droplet is sticky on these surfaces leading to a rose-petal effect.

Highly efficient surface-emitting semiconductor lasers exploiting quasi-crystalline distributed feedback photonic patterns

Quasi-crystal distributed feedback lasers do not require any form of mirror cavity to amplify and extract radiation. Once implemented on the top surface of a semiconductor laser, a quasi-crystal pattern can be used to tune both the radiation feedback and the extraction of highly radiative and high-quality-factor optical modes that do not have a defined symmetric or anti-symmetric nature. Therefore, this methodology offers the possibility to achieve efficient emission, combined with tailored spectra and controlled beam divergence. Here, we apply this concept to a one-dimensional quantum cascade wire laser. By lithographically patterning a series of air slits with different widths, following the Octonacci sequence, on the top metal layer of a double-metal quantum cascade laser operating at THz frequencies, we can vary the emission from single-frequency-mode to multimode over a 530-GHz bandwidth, achieving a maximum peak optical power of 240 mW (190 mW) in multimode (single-frequency-mode) lasers, with record slope efficiencies for multimode surface-emitting disordered THz lasers up to ≈570 mW/A at 78 K and ≈720 mW/A at 20 K and wall-plug efficiencies of η ≈ 1%.

Quasicrystal patterns in a neural field model

The authors show that a modulation of this connectivity structure can lead to the formation of quasicrystal patterns, thus expanding the repertoire of drug induced geometric hallucinations that can be explained by a Turing mechanism.

Effect of hierarchical surface relief grating on light extraction of polymer light-emitting diodes

We propose enhanced light extraction of polymer light-emitting diodes (PLEDs) with nano-sized diffractive grating patterns. Various diffractive gratings of hexagonal and quasicrystal patterns were fabricated with photo-addressable azopolymers by light interference lithography. Fabricated patterns were transferred to a glass substrate as a light extraction layer by an imprinting method. We prepared PLED cells having diffractive nano-gratings, and the performance of the PLED cells was systematically investigated in terms of luminous efficiency, external quantum efficiency, and electroluminescence spectrum. Compared to the reference PLED, the quasicrystal PLED cells showed improvements in external quantum efficiency, current efficiency, and power efficiency of 11.54%, 10.93%, and 19.43%, respectively.

Large Single Crystal SnS2 Flakes Synthesized from Coevaporation of Sn and S

Remarkable properties of layered metal dichalcogenides and their potential applications in various fields have raised intense interest worldwide. We report tens of microns-sized ultrathin single crystal SnS2 flakes grown on amorphous substrates using a simple one-step thermal coevaporation process. X-ray pole figure analysis reveals that a majority of flakes are oriented with the (0001) plane parallel to the substrate and a preferred fiber texture. For few-layer-thick SnS2, Moire patterns of 6-fold and 12-fold symmetries are observed by transmission electron microscopy imaging and diffraction. These patterns result from the relative rotation between SnS2 layers in the ultrathin flake. The 12-fold symmetry is consistent with a known quasicrystal pattern. The photoluminescence spectrum supports that these ultrathin flakes possess a direct bandgap. Carrier lifetime measured by time-resolved photoluminescence of a single flake is a few nanoseconds. These results improve our understanding of the formation and ...

Lasing Characteristics of GaN-Based Photonic Quasi-Crystal Surface Emitting Lasers Operated at Higher Order Γ Mode

In this study, GaN-based photonic quasi-crystal surface emitting lasers (PQCSELs) operated at different Γ band-edge modes were fabricated and investigated. The photonic quasi-crystal patterns were defined by utilizing electron-beam lithography and inductively coupled plasma etching. Distinctive higher order Γ band-edge lasing modes were identified in the GaN PQCSELs. The threshold energy density and lasing wavelength for the S3 band-edge mode were 4.6 mJ/cm2 and 394.2 nm, respectively. The decreasing tendency of the threshold energy of PQCSEL was observed while the designed lasing mode moved from the higher Γ band to the lower Γ band. Numerical results showed that the S3 mode had the lower threshold and the threshold gain would be largely varied by tuning the ratio of air hole radius/lattice constant ( r / a ). Based on calculations and experiments, PQCSELs show the opportunity to realize lower threshold lasers than typical PC laser for specific value of r / a and appropriate higher order band-edge modes.

Plasmonic quasicrystals with broadband transmission enhancement.

Plasmonic quasicrystals (PlQCs), by integrating the properties of quasicrystals (rotational symmetry and long range ordering but lack translational symmetry) and surface plasmon polariton mediated effects, offer several advantages over plasmonic crystals (PlCs). For example, in PlQCs one could have broadband, polarization independent response. However, large area patterning by electron beam lithography requires precise lattice coordinates as well as a practical way to design the structures for specific spectral response. We demonstrate design and fabrication of large area quasicrystal air hole patterns of π/5 symmetry in metal film in which broadband, polarization and launch angle independent transmission enhancement is observed. We demonstrate bi-grating quasicrystals to show that designable transmission response is possible over visible to near infrared wavelength regions with about 15 times enhancement. These would be useful in many applications like energy harvesting, nonlinear optics and quantum plasmonics.

Fabrication of two kinds of eight-fold photonic quasi-crystals assisted by a specially designed prism

We demonstrate that two kinds of 2D eight-fold photonic quasi-crystals (PQCs) can be fabricated by a specially designed prism via single-exposure holographic lithography. The prism with five continuous side surfaces out of common eight symmetrical side surfaces, plus a top surface, is well designed for PQC fabrication. Compared with the traditional method of setting up eight free-space beams in the half-space for an eight-fold PQC fabrication, our specially designed prism reduces the number of beams, avoids the differences of beam-to-beam phases, and simplifies the fabrication process. The theory and computer simulation confirm the patterns of two kinds of PQCs by a single prism illumination recording. Further, these quasi-crystal patterns are successfully verified by experimental results under a scanning electron microscope. In addition, these samples show some good properties, such as uniformity over large area, the implementation of a single defect by underexposure, and symmetry break of the eight dots. Our special prism-assisted holographic lithography technique provides a base for further investigating the optical properties of these novel structures.

Observation of Robust FMR in Permalloy Quasiperiodic Arrays

We have used ferromagnetic resonance (FMR) at fixed frequency 9.7 GHz to investigate permalloy thin films patterned with antidots to form a five-fold quasicrystal pattern. For DC applied fields H below 3.5 kOe, we observed robust FMR spectra exhibiting two-fold rotational symmetry instead of the five-fold symmetry expected for quasicrystals. Dynamic micromagnetic simulations of the FMR spectra performed at <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\rm H}=1\ {\rm kOe}$</tex></formula> and 12 kOe exhibit two-fold and ten-fold rotational symmetry, respectively. The ten-fold symmetry observed in simulations is consistent with a saturated state of isolated write fields. We infer the two-fold rotational symmetry observed for <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\rm H}=1\ {\rm kOe}$</tex></formula> is due to an unsaturated state of five-fold write fields closely spaced on a square lattice.

Fabrication of diffractive microlens array by femtosecond laser-assisted etching process

Graphical abstractDisplay Omitted Highlights? The diffractive microlens array is fabricated by the femtosecond laser and chemical etching process. ? The effect of micro-grating forming is studied upon laser power and etching ratio. ? The quasi-crystal diffraction patterns with the types of cross and octagon can be achieved. The study presents the fabrication of diffractive microlens array on glass substrate by using the femtosecond laser (FS-laser) and chemical etching process. Here, the laser is based on an all-in-one FS-laser system with the central wavelength of 517?2.5nm for fabricating the embedded grating structures inside glass substrate. The laser beam focused distance between the surface and sample is 25µm. The repetition rate and pulse duration of FS-laser are 100kHz and 350fs, respectively. The attenuated laser beam is directly into objective lens (20i?) with the numerical apertures (NA=0.4). Hence, the microstructures can be patterned by the routes of X-Y motion stage. The glass sample is then etched by hydrofluoric acid (HF) in an ultrasonic bath for 15min for developing structures. Finally, the results show a successful process for forming the microlens array of the diffractive patterns, in which two types of cross and octagon are obtained from the single and double diffraction, respectively.

Lasing action in gallium nitride quasicrystal nanorod arrays

We report the observation of lasing action from an optically pumped gallium nitride quasicrystal nanorod arrays. The nanorods were fabricated from a GaN substrate by patterned etching, followed by epitaxial regrowth. The nanorods were arranged in a 12-fold symmetric quasicrystal pattern. The regrowth grew hexagonal crystalline facets and core-shell multiple quantum wells (MQWs) on nanorods. Under optical pumping, multiple lasing peaks resembling random lasing were observed. The lasing was identified to be from the emission of MQWs on the nanorod sidewalls. The resonant spectrum and mode field of the 12-fold symmetric photonic quasicrystal nanorod arrays is discussed.

Light Extraction Efficiency Enhancement of GaN-Based Light Emitting Diodes on n-GaN Layer Using a SiO2 Photonic Quasi-Crystal Overgrowth

In this paper, GaN-based LEDs with a SiO2 photonic quasi-crystal (PQC) pattern on an n-GaN layer by nano-imprint lithography (NIL) are fabricated and investigated. At a driving current of 20 mA on Transistor Outline (TO)-can package, the better light output power of LED III (d = 1.2 microm) was enhanced by a factor of 1.20. After 1000 h life test (55 degrees C/50 mA) condition, Normalized output power of LED with a SiO2 PQC pattern (LED III (d = 1.2 microm)) on an n-GaN layer only decreased by 5%. This results offer promising potential to enhance the light output power of commercial light-emitting devices using the technique of nano-imprint lithography.

Fabrication of Si-based two-dimensional photonic quasicrystals by using multiple-exposure holographic lithography

Two-dimensional (2D) photonic quasicrystal (PQC) template patterns have been fabricated by using multiple-exposure holographic lithography (MHL). The MHL technique is based on Lloyd’s mirror setup using interference of two equivalent beams, which is an excellent method for fabricating periodic structures of a large area. The 2D PQC array shows various sizes and shapes with a change in the incident angle (θ) and rotation angle (γ) of the multiple-exposure beams. In addition, the filling factor (η), which is a very important factor for optical characteristic of 2D PQCs, was controlled by the exposure time (τ). The fabricated PQCs showed eight-, ten-, and 12-fold patterns with high-order rotational symmetries. Diffraction patterns using 632.8 nm HeNe laser were also observed with n-rotation symmetry for the corresponding n-fold PQCs. After fabricating the PQCs, reactive-ion etching of the silicon wafer was performed with 50-nm-thick chromium (Cr) as a mask in CF4/O2 plasma to a 1.3 μm depth. The authors confirmed that fabrication of n-fold 2D PQCs in a large area with suitable optical characteristics could be controlled by some parameters of MHL.

다중-노출 홀로그라피 방법을 이용한 광자준결정 제작

Two-dimensional photonic quasicrystal (PQCs) template patterns have been fabricated on a 1.1 -thick DMI-150 photoresist using a multiple-exposure holographic method. A 442-nm HeCd laser was utilized as a light source and the holographic exposure was carried out at a fixed angle of

Hexagonal array photonic crystal with photonic quasi-crystal defect inclusion

The central region of a hexagonal array photonic crystal is replaced with the central region of a higher rotational order photonic quasi-crystal pattern. The quasi-crystal, with band gaps and defect states now acts as the defect region of the hexagonal array. For the model system examined, different types of “defect” states are identified, and the modal properties examined. The higher degree of defect state control provided by the mixing of photonic crystal types can find applications in resonator design for laser cavities and WDM as well as assist in the formation of non-conventional photonic crystal waveguide designs. Results are presented specifically for the hexagonal array and 12-fold quasi-crystal and can be extended to other photonic crystal combinations.

Photofabrication of Two-Dimensional Quasi-Crystal Patterns on UV-Curable Molecular Azo Glass Films

In this work, two-dimensional surface quasi-crystal patterns were developed by using a novel azobenzene-containing amorphous material (IAC-4), which was newly synthesized for the application. IAC-4 contains a core of isosorbide moiety and two push-pull type azo chromophores as the inner part. The periphery of IAC-4 is functionalized with four cinnamate groups, which can undergo [2+2] photocycloaddition reaction upon UV light irradiation. The molecular design can allow IAC-4 to readily form surface relief structures upon Ar+ laser irradiation, and the formed structures can be further stabilized through a photo-cross-linking reaction induced by UV light irradiation. On the basis of the material, two-dimensional (2D) quasi-crystal structures with different rotation symmetries were successfully fabricated on the IAC-4 films by using the dual-beam multiple exposure technique. In contrast to the approach using photoresist, the quasi-crystal structures were fabricated through the photoinduced mass migration, and no subsequent wet-etch or dry-etch step was required in the process. The quasi-crystal structures with rotation symmetry as high as 60-fold could be feasibly fabricated through this approach. The surface patterns and fabrication method can be potentially applied in areas such as optics, communications, and security inspection.

Aperiodic Polymer Tiles

MATERIALS SCIENCE Quasicrystals have sufficient long-range order to produce a diffraction pattern, but do not show the three-dimensional translational periodicity found in normal crystals. They have been observed in metallic and small molecular systems, often through small compositional changes in the materials, although in many cases the quasicrystals are of poor quality and stability. Hayashida et al. show this sort of patterning over a much larger length scale in three-arm block copolymers made of polyisoprene (I), polystyrene (S), and poly(2-vinylpyridine) (P) mixed with a polystyrene homopolymer. Previously this system has been shown to form the (3.3.4.3.4) Archimedean tiling structure, with every vertex surrounded by a pattern of triangle (3) and square (4) cells. Upon changing the I:S:P ratio, the ratio of triangles to squares shifted from the Archimedian value of 2 to 2.305, and a dodecagonal quasicrystal pattern emerged. The tiling, however, was not perfect: Transition regions led to sections showing sixfold symmetry and a triangle-to-square ratio of 8:3. When the composition of the blend was changed further, the overall quasiperiodicity of the triangles and squares was lost. Thus, it may be possible to tune the tiling patterns through small changes in the polymer composition. MSL Phys. Rev. Lett. 98 , 195502 (2007).

Spatial mapping on surface light extraction from 2D photonic quasicrystals patterned GaN‐based light emitters

We report the observations of surface light extraction enhancement from two-dimensional (2D) photonic crystal (PC) and Photonic Quasicrystal (PQC) patterns on electrical current injected GaN-based light emitters. Spatial mapping of the surface extraction was acquired by a microscopic electrical luminescence setup and a scanning near-field optical microscope (SNOM). Slight difference of mapping profile between twelve-fold PQC and regular triangular PC was obtained. It is shown that 12PQC was more efficient for light extraction. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Mode localization and band-gap formation in defect-free photonic quasicrystals

Defects in photonic crystals are local regions in which the translational symmetry is broken. The same definition can be applied to photonic quasicrystals except in this case the symmetry is the 2pi/n rotational symmetry, where n is the rotational fold number. In this context, if no such defects are present, the structure is called "defect-free". Even though photonic quasicrystal patterns can be defect-free, localized modes can still exist in such structures. These modes resemble those of a central potential that suggests that localization in photonic quasicrystals are actually "extended" modes of the rotational symmetry. A possible connection is suggested between these localized modes and short-range dependence of the photonic band gap (PBG). Such a connection implies a tight-binding description of PBG formation of photonic quasicrystals - making them more similar to electronic semiconductors than regular photonic crystals.