Quasiperiodic Structures Research Articles

Amplified spontaneous emission from a surface-modified GaN film fabricated under pulsed intense UV laser irradiation

We propose a simple method for fabricating random structures directly on Mg-doped GaN thin films. The process is relatively simple, involving only irradiation with strong UV pulses from a fabrication laser on the thin-film surface. After intense UV laser pulses (>400 MW/cm2) are irradiated on the flat GaN film, the surface is roughened and quasi-periodic structures form. When the roughened surface is excited with laser light of intensity about 10 times smaller than the fabrication laser intensity, emission increases around 367 nm, and spectral narrowing and threshold behavior are observed. Because such behaviors are not observed without the application of intense laser irradiation, we conclude that amplified spontaneous emission is induced in the modified GaN surface by the intense UV laser pulse irradiation. This method offers the possibility of easy and direct fabrication of microscale random-laser devices on semiconductor substrates.

Asymmetric topological edge states in a quasiperiodic Harper chain composed of split-ring resonators.

Quasiperiodic structures have recently been found to possess salient topological properties. In this Letter, we theoretically and experimentally demonstrate the topological edge states in a quasiperiodic Harper chain composed of split-ring resonators. In a finite-size Harper chain, we find that there is always a pair of edge states in the bandgaps, independent of the number of the resonators. Different from the topological edge states localized at both ends of a periodic chain, this pair of edge states is selectively localized at the left or right end of the quasiperiodic chain at different frequencies. These paired-edge states with asymmetric field distribution can be used for unidirectional propagation. Our results not only provide a versatile platform to study the topological physics beyond the periodic structures but also may be useful in some applications such as selective unidirectional power transfer.

Observation of Quasiperiodic Structures in the Hydroxyl Airglow on Scales Below 100 m

AbstractGravity waves are known to transport energy and momentum to the middle atmosphere. The breaking processes associated with divergence of fluxes of energy and momentum into the atmosphere occur on scales that cannot be resolved in models and therefore have to be parameterized. The question remains as to whether it is possible to use a turbulence model on scales below 100 m and what kind of turbulence model should that be. Here we use high spatial resolution observations of the OH nightglow located near 90‐km altitude from the Nordic Optical Telescope to observe quasiperiodic structures down to horizontal scales of 4.5 m. These results indicate that a Kolmogorov type of energy cascade model of turbulence with a −5/3 power law appears to be satisfied down to these short, 4.5‐m scales.

Effect of Uniaxial Strain on the Performance of One-Dimensional Graphene Fibonacci Photonic Crystal Biosensors

Many efforts have been made to improve efficiency of optical sensing devices to detect analyte and pathogens in highly diluted solutions. This paper reports on a study regarding the figure of merit of the optical sensors based on graphene quasi photonic crystals with Fibonacci sequences in different chemical potentials. We use transfer matrix method to find surface modes and calculate the sensitivity and full width at half-minimum of the resonance dip in the reflectance spectrum when graphene monolayers are under uniaxial strain. The strain not only changes the graphene electronic band structure, but also can be employed to tune the electrical properties of graphene monolayers. Results demonstrate that the performance of the proposed quasi periodic structures can be improved by adjusting the strain and the angle in which strain applied. In addition, our results show that the figure of merit enhances in Fibonacci structures with high sequences when chemical potential increases.

Tunable temperature-dependent THz photonic bandgaps and localization mode engineering in 1D periodic and quasi-periodic structures with graded-index materials and InSb.

We present the tunability of terahertz (THz) photonic bandgaps and localization modes in one-dimensional (1D) periodic and quasi-periodic structures based on alternating layers of graded-index materials and InSb. These configurations show that operation frequencies of photonic bands and localization modes can be tuned by controlling temperature, structural and grading parameters, grading profiles, and different quasi-periodic arrangements. The number of photonic bands and localization modes can also be modulated with layer thickness and quasi-periodic arrangements. Changes in the grouping of the materials considered also modulate the operation frequencies of photonic bands and localization modes in quasi-periodic structures. Results can be implemented to design thermo-tunable THz filters, reflectors, sensors, etc.

Study of the quasi – Periodic one dimensional domain structure near TC of TGS crystal by PFM and hybrid PFM methods

The phase transition of ferroelectric triglycine sulfate crystal (TGS) was studied in situ with the method of the piezoresponse force microscopy in the contact and hybrid modes. The formation of the metastable quasiperiodic domain structures was observed in narrow temperature range near phase transition. Two-dimensional correlation functions calculation allows to determine structure period and to analyze domain dynamics near Curie temperature TC.

Kerr-type nonlinear response of a graphene-coated quasiperiodic structure composed of silicon dioxide and polystyrene layers in the THz region

In the terahertz frequency domain, we theoretically attempt to determine some properties of kerr-type nonlinear response of a graphene-coated one-dimensional quasiperiodic structure based on Fibonacci sequence. The supposed structure is constituted by silicon dioxide and nonlinear polystyrene dielectrics where graphene sheets are located between them. The calculations are accomplished by using standard transfer matrix method. Our numerical results demonstrate that the introduction of graphene sheets in the structure has an important role in reducing bistability thresholds. It is found that for both TE and TM waves the switching-up and switching-down thresholds of bistability are reduced in comparison to without graphene case. In addition, the threshold values of TM mode are less than those of TE one. Also, by manipulating parameters such as graphene chemical potential, graphene damping constant and sequence number of structure, some other interesting features are achieved. This paper provides a way to reduce bistability thresholds which are of optical switching issues.

A Brownian quasi-crystal of pre-assembled colloidal Penrose tiles

Penrose's pentagonal P2 quasi-crystal1-4 is a beautiful, hierarchically organized multiscale structure in which kite- and dart-shaped tiles are arranged into local motifs, such as pentagonal stars, which are in turn arranged into various close-packed superstructural patterns that become increasingly complex at larger length scales. Although certain types of quasi-periodic structure have been observed in hard and soft matter, such structures are difficult to engineer, especially over large areas, because generating the necessary, highly specific interactions between constituent building blocks is challenging. Previously reported soft-matter quasi-crystals of dendrimers5, triblock copolymers6, nanoparticles7 and polymeric micelles8 have been limited to 12- or 18-fold symmetries. Because routes for self-assembling complex colloidal building blocks9-11 into low-defect dynamic superstructures remain limited12, alternative methods, such as using optical and directed assembly, are being explored13,14. Holographic laser tweezers15 and optical standing waves16 have been used to hold microspheres in local quasi-crystalline arrangements, and magnetic microspheres of two different sizes have been assembled into local five-fold-symmetric quasi-crystalline arrangements in two dimensions17. But a Penrose quasi-crystal of mobile colloidal tiles has hitherto not been fabricated over large areas. Here we report such a quasi-crystal in two dimensions, created using a highly parallelizable method of lithographic printing and subsequent release of pre-assembled kite- and dart-shaped tiles into a solution-dispersion containing a depletion agent. After release, the positions and orientations of the tiles within the quasi-crystal can fluctuate, and these tiles undergo random, Brownian motion in the monolayer owing to frequent collisions between neighbouring tiles, even after the system reaches equilibrium. Using optical microscopy, we study both the equilibrium fluctuations of the system at high tile densities and alsothe 'melting' of the pattern as the tile density is lowered. At high tile densities we find signatures of a five-fold pentatic liquid quasi-crystalline phase, analogous to a six-fold hexatic liquid crystal. Our fabrication approach is applicable to tiles of different sizes and shapes, and with different initial positions and orientations, enabling the creation of two-dimensional quasi-crystalline systems (and other systems that possess multiscale complexity at high tile densities) beyond those of current self- or directed-assembly methods18-20. We anticipate that our approach for generating lithographically pre-assembled monolayers could be extended to create three-dimensional Brownian systems of fluctuating particles with custom-designed shapes through holographic lithography21,22 or stereolithography23.

Cover stories: Making the graphene quasicrystals cover.

Cover stories: Making the graphene quasicrystals cover.

Graphene-based tunable multichannel filter with arithmetic sequence quasiperiodic structure

A tunable multichannel mid-infrared filter based on monolayer graphene is proposed and investigated. The optical transmission spectra are numerically simulated by the method of finite-difference time-domain (FDTD). The numerical results denote that the filtering properties can be tuned by the chemical potentials of graphene, the depth of the air trench, the temperature, and the quasi-period number of the structure. The numerical results are discussed by deducing the effective refractive index of surface plasmon polaritons (SPPs) propagating on the multilayered structure of air/graphene/dielectric and air/graphene/air/dielectric. This work can provide a method to design tunable multichannel filter with a single layer of graphene. Due to its tunability and miniaturization, the proposed structure can be found application in high speed integrated photonic circuit.

Application of Rényi and Tsallis entropies to topic modeling optimization

This study proposes to minimize Rényi and Tsallis entropies for finding the optimal number of topics T in topic modeling (TM). A promising tool to obtain knowledge about large text collections, TM is a method whose properties are underresearched; in particular, parameter optimization in such models has been hindered by the use of monotonous quality functions with no clear thresholds. In this research, topic models obtained from large text collections are viewed as nonequilibrium complex systems where the number of topics is regarded as an equivalent of temperature. This allows calculating free energy of such systems—a value through which both Rényi and Tsallis entropies are easily expressed. Numerical experiments with four TM algorithms and two text collections show that both entropies as functions of the number of topics yield clear minima in the middle area of the range of T. On the marked-up dataset the minima of three algorithms correspond to the value of T detected by humans. It is concluded that Tsallis and especially Rényi entropy can be used for T optimization instead of Shannon entropy that decreases even when T becomes obviously excessive. Additionally, some algorithms are found to be better suited for revealing local entropy minima. Finally, we test whether the overall content of all topics taken together is resistant to the change of T and find out that this dependence has a quasi-periodic structure which demands further research.

On the failure resistance of quasi-periodic lattices

Quasi-periodic materials have been widely studied for their behavior regarding atomic dynamics, photonic, magnetic and electronic properties. They have unique properties inherited from their specific material symmetry. The recent development of additive manufacturing gives the opportunity to produce quasi-periodic structures to benefit from their unique capability. In this paper, quasi-periodic beam lattices are produced and failure experiments are performed. Then, a numerical model is proposed and validated. It is obtained that quasi-periodic Penrose lattices can outperform their periodic counterpart. These results open new ways to design architected materials with enhanced failure energy dissipation capabilities.

Neutron Reflectometry Studies of ZnO Films

Textured Al-doped ZnO films are studied using neutron reflectometry. The films are quasiperiodic structures with a period of several nanometers. The films are inhomogeneous in a surface layer with a thickness of 10–20 nm.

Manipulation of visible-light polarization with dendritic cell-cluster metasurfaces

Cross-polarization conversion plays an important role in visible light manipulation. Metasurface with asymmetric structure can be used to achieve polarization conversion of linearly polarized light. Based on this, we design a quasi-periodic dendritic metasurface model composed of asymmetric dendritic cells. The simulation indicates that the asymmetric dendritic structure can vertically rotate the polarization direction of the linear polarization wave in visible light. Silver dendritic cell-cluster metasurface samples were prepared by the bottom-up electrochemical deposition. It experimentally proved that they could realize the cross - polarization conversion in visible light. Cross-polarized propagating light is deflected into anomalous refraction channels. Dendritic cell-cluster metasurface with asymmetric quasi-periodic structure conveys significance in cross-polarization conversion research and features extensive practical application prospect and development potential.

Femtosecond laser-induced chemical vapor deposition of tungsten quasi-periodic structures on silicon substrates

A rapid, maskless deposition technique for writing conductive tracks via femtosecond laser-induced chemical vapor deposition has been developed. The technique can be used for a range of applications, one example being writing conductive tracks for the construction of microelectronic devices. The process uses pulsed ultrafast laser with 300 fs pulse length and 1030 nm wavelength for the direct deposition of tungsten tracks on silicon substrates from metal organic tungsten hexacarbonyl precursors. The written tracks consisted of wavy quasi-periodic walls with thickness of 200 nm and a periodicity of 500 nm, aligned perpendicular to the linear polarization of the laser beam. Fixed number of pulses spot dwell experiments revealed that a thin film formed before quasi-periodic structures grew on top of that thin film. The peak intensity threshold for the deposition process (8.64 × 1010 W/cm2) was lower than the threshold for surface modification on the silicon substrate (3.34 × 1011 W/cm2) at the same scanning speed of 10 μm/s and repetition rate of 502 kHz. Negligible damage to the underlying substrate was observed in the cross section. Scan speeds up to 100 μm s−1 were achieved in the process. The elemental composition of the deposits was measured to be 80% by weight tungsten in energy-dispersive x-ray spectroscopy methods and the resistivity of the deposit was measured to be 290 μΩ cm using the transfer length method.

High quality factor polychromatic filters based on hybrid photonic structures

In this work, we have investigated theoretically the transmission properties of a hybrid quasi-periodic photonic system, which is a combination of a periodic H(LH)5 and a quasi-periodic multilayer structure(QPMS)P: H(LH)5(QPMS)PH(LH)5, where P is the repetitive number of QPMS. Simulation results showed that the number, position and the quality factor of the transmission peaks depend on the repetitive number (P) and the incident angle for both the (TE) and (TM) polarizations. Furthermore, we have studied the influence of two air layers (A) inside the previous structures at the 12th and 29th positions:H(LH)5A (QPMS)2A H(LH)5. The results illustrate that the introducing of the defect layers in our system provides a possible mechanism for optimizing the parameters of the transmission peaks, thus the obtaining of polychromatic filters with a high quality factor (Q) and with a minimum of layers and thickness.

Tunable multiband directional electromagnetic scattering from spoof Mie resonant structure

We demonstrate that directional electromagnetic scattering can be realized in an artificial Mie resonant structure that supports electric and magnetic dipole modes simultaneously. The directivity of the far-field radiation pattern can be switched by changing wavelength of the incident light as well as tailoring the geometric parameters of the structure. In addition, we further design a quasiperiodic spoof Mie resonant structure by alternately inserting two materials into the slits. The results show that multi-band directional light scattering is realized by exciting multiple electric and magnetic dipole modes with different frequencies in the quasiperiodic structure. The presented design concept is suitable for microwave to terahertz region and can be applied to various advanced optical devices, such as antenna, metamaterial and metasurface.

Self-Similar Transformation and Vertex Configurations of the Octagonal Ammann–Beenker Tiling**Supported by the National Natural Science Foundation of China under Grant No 11674102.

Based on the matching rules for squares and rhombuses, we study the self-similar transformation and the vertex configurations of the Ammann–Beenker tiling. The structural properties of the configurations and their relations during the self-similar transformation are obtained. Our results reveal the distribution correlations of the configurations, which provide an intuitive understanding of the octagonal quasi-periodic structure and also give implications for growing perfect quasi-periodic tiling according to the local rules.

Deforming black hole and cosmological solutions by quasiperiodic and/or pattern forming structures in modified and Einstein gravity

We elaborate on the anholonomic frame deformation method, AFDM, for constructing exact solutions with quasiperiodic structure in modified gravity theories, MGTs, and general relativity, GR. Such solutions are described by generic off-diagonal metrics, nonlinear and linear connections and (effective) matter sources with coefficients depending on all spacetime coordinates via corresponding classes of generation and integration functions and (effective) matter sources. There are studied effective free energy functionals and nonlinear evolution equations for generating off-diagonal quasiperiodic deformations of black hole and/or homogeneous cosmological metrics. The physical data for such functionals are stated by different values of constants and prescribed symmetries for defining quasiperiodic structures at cosmological scales, or astrophysical objects in nontrivial gravitational backgrounds some similar forms as in condensed matter physics. It is shown how quasiperiodic structures determined by general nonlinear, or additive, functionals for generating functions and (effective) sources may transform black hole like configurations into cosmological metrics and inversely. We speculate on possible implications of quasiperiodic solutions in dark energy and dark matter physics. Finally, it is concluded that geometric methods for constructing exact solutions consist an important alternative tool to numerical relativity for investigating nonlinear effects in astrophysics and cosmology.

Quasiperiodic Quantum Ising Transitions in 1D.

Unlike random potentials, quasiperiodic modulation can induce localization-delocalization transitions in one dimension. In this Letter, we analyze the implications of this for symmetry breaking in the quasiperiodically modulated quantum Ising chain. Although weak modulation is irrelevant, strong modulation induces new ferromagnetic and paramagnetic phases which are fully localized and gapless. The quasiperiodic potential and localized excitations lead to quantum criticality that is intermediate to that of the clean and randomly disordered models with exponents of ν=1^{+} (exact) and z≈1.9, Δ_{σ}≈0.16, and Δ_{γ}≈0.63 (up to logarithmic corrections). Technically, the clean Ising transition is destabilized by logarithmic wandering of the local reduced couplings. We conjecture that the wandering coefficient w controls the universality class of the quasiperiodic transition and show its stability to smooth perturbations that preserve the quasiperiodic structure of the model.