Quasiperiodic Structures Research Articles

A Review of Ultrasound Tissue Characterization with Mean Scatterer Spacing.

Tissues exhibiting quasi-periodic structures can be modeled as a collection of diffuse scatterers and coherent scatterers. The mean scatterer spacing (MSS) of coherent and quasi-periodic components is directly related to tissue microstructure and has become an important quantitative ultrasound (QUS) parameter in the characterization of quasi-periodic tissues. In this paper, a review of the literature on the development of MSS as a QUS parameter was conducted. First, a unified theoretical background of MSS estimates was provided. Then, the application of MSS estimates was summarized with respect to liver, spleen, breast, bone, muscle, and other tissues. MSS estimation techniques were applied to (a) the diagnosis of hepatitis, liver fibrosis and cirrhosis, and lesions in tissues such as liver, breast, and spleen; (b) the differentiation between benign and malignant breast tumors, and the grading of breast cancer; (c) the detection of cancellous bone; and (d) the monitoring of the efficacy of treatments such as thermal ablation, with various levels of success. Future developments were also discussed in terms of real-time implementation of MSS estimates, local MSS estimation, relationship of MSS to other QUS parameters, combination of MSS with other QUS parameters, in vivo validation of MSS estimates, MSS parametric imaging, and three-dimensional ultrasound tissue characterization.

Tunable Multichannel Plasmonic Filter Based on a Single Graphene Sheet on a Fibonacci Quasiperiodic Structure

We propose a tunable multichannel plasmonic mid-infrared filter of a single graphene sheet depositing on a Fibonacci quasiperiodic structure. The transmission spectra are numerically analyzed by a finite-difference time-domain (FDTD) method, and the results show that the filtering properties of the proposed structure can be tuned by the chemical potentials of graphene, the width and depth of air grooves, and the refractive index of the substrate. The simulation results are discussed analytically by deducing the dispersion relation of surface plasmon polariton propagating on four layers structure of air/graphene/air/dielectric. The proposed structure may find potential applications in tunable filters, sensors, and integrated photonic circuits.

Quo Vadis Quasicrystals?

This Special Issue aims at gaining a deeper understanding on the relationship between the underlying structural order and the resulting physical properties in aperiodic systems, including quasicrystalline and related complex metallic alloys, photonic quasicrystals, and other structures exhibiting long-range aperiodic order. This Special Issue contains 12 papers which highlight recent developments in quasiperiodic crystal structure, photonic quasicrystals and related optical devices, the intrinsic electrical, thermal, and mechanical properties of icosahedral and decagonal metallic alloys, and the nature of chemical bonding in intermetallic compounds, from a multidisciplinary perspective. In light of the results presented in the contributions collected in this Special Issue, we can confidently expect that new insights into the interdisciplinary science of quasicrystals will be gained in the years to come, providing a sharper picture of their structures and related physical properties, and spurring further progress in practical issues related to both materials engineering science and nanotechnology.

Two‐scale cut‐and‐projection convergence; homogenization of quasiperiodic structures

We demonstrate how the problem of finding the effective property of quasiperiodic constitutive relations can be simplified to the periodic homogenization setting by transforming the original quasiperiodic material structure to a periodic heterogeneous material in a higher dimensional space. The characterization of two‐scale cut‐and‐projection convergence limits of partial differential operators is presented. Copyright © 2017 John Wiley & Sons, Ltd.

Graphene-based reconfigurable transmission filter near the wavelength of 1.55 μm

A reconfigurable transmission filter operating at the wavelength 1.55 μm and based on graphene is presented and discussed. The presented structure consists of Bragg mirrors and Fibonacci quasi-periodic structures where a graphene layer is intercalated at each interface. It is shown that the variation of the Fermi level in graphene allows the adjustment of the filter resonance wavelength. We show how this property makes it possible to compensate for the offsets of the resonance peak induced by an eventual error on the thickness of the dielectric layers composing the structure. The calculations made show that graphene act as a phase-shifter which can tune the wavelength of the resonance peak about 6 nm on both sides of the working wavelength, and also improve the transmission of the structure.

13th International Conference on Quasicrystals

The 13th International Conference on Quasicrystals (ICQ13) was held in Kathmandu, Nepal, from 18th to 23rd September 2016. This episode of a series of conferences on quasicrystals followed twelve previous successful meetings. The first event, the “International Workshop on Aperiodic Crystals”, was held in Les Houches, France in 1986, which was followed by the “International Workshop on Quasicrystals” in Beijing, China in 1987 and the “International Meeting on Quasicrystals” in Vista-Hermosa, Mexico in 1989. Thereafter, a series of “International Conference on Quasicrystals” took place respectively in St. Louis, Missouri, USA in 1992 (ICQ4), Avignon, France in 1995 (ICQ5), Tokyo, Japan in 1997 (ICQ6), Stuttgart, Germany in 1999 (ICQ7), Bangalore, India in 2002 (ICQ8), Ames, Iowa, USA in 2005 (ICQ9), Zürich, Switzerland in 2008 (ICQ10), Sapporo, Japan in 2011 (ICQ11) and Cracow, Poland in 2013 (ICQ12).The conference covered a wide range of topics on quasicrystals: formation, growth, and phase stability; structure and modeling; mathematics of quasiperiodic and aperiodic structures; transport, mechanical and magnetic properties; and finally, surfaces and overlayer structures. In addition, other aspects of material science such as metamaterials, polymer science, metallic glasses, and metallic alloys were discussed. The conference also reviewed the state-of -art of quasicrystal research and its future direction.ICQ13 was attended by 98 researchers from 22 countries, including 26 PhD or master students. There were 13 invited talks (including a public lecture by the 2011 Nobel Laureate in Chemistry, Prof. Dan Shechtman), 3 tutorial lectures, 50 contributed talks and 36 poster presentations. The conference was truly interdisciplinary - comprising of theoretical and experimental physicists, chemists, material scientists, and mathematicians.The proceedings of the conference are published as open access in the Institute of Physics Conference Series. The papers have been reviewed in the regular refereeing process. Among 35 proceedings received, 30 have been accepted for the publication.The conference itself was held at the Dhulikhel Lodge Resort. The public lecture was organised at the central campus of Trubhuvan University in Kirtipur, hosted jointly by the Nepal Physical Society and the Central Department of Physics, while the tutorial lectures were held at Kathmandu University. These two events were open to local researchers and students. A special ceremony was organised for the inauguration of ICQ13, which was addressed and attended by the vice-chancellors of Tribhuvan University, Kathmandu University, Nepal Academy of Science and Technology (NAST), and representatives of various professional organisations, including the Nepal Government.The Jean-Marie Dubois Award for Excellence in Quasicrystals (2016) was presented to Dr. Marek Mihalkovič at ICQ13, for the theoretical work that has enabled and demonstrated the simulation of thermodynamic and dynamic properties of quasicrystals - based on realistic atomic-scale models and energetics. The Jean-Marie Dubois Award was established to recognize important, sustained research on any aspect of quasicrystals in the last 10-year period preceding the award. The prizes for best student presentation were awarded to Ito Natsu from Toyo University of Science, Japan for her paper titled “Synthesis and magnetic properties of the Au-Al-Yb approximant” and Nicolas Macé from Université Paris-Saclay, France for his paper titled “Gap structure and topological indices on the Fibonacci quasicrystal”.We gratefully acknowledge the generous financial support for ICQ13 from the International Union of Crystallography (IUCr), the European Integrated Center for the Development of New Metallic Alloys and Compounds (C-MAC), the International Centre for Diffraction Data (ICDD), Rigaku Oxford Diffraction, Embassy of Israel Kathmandu, Deutsch-Nepalische Gesellschaft, TBI Group, Phul Kumari Mahato Memorial Trust, Nepal Science Foundation Trust, Holy-Cow, officials of Non-Resident Nepali Association (NRNA) and NRNA-Australia.We would like to express our sincere thanks to the members of the Organising Committee, Program Committee and International Advisory Board, invited speakers, session chairs, editorial board members and reviewers of the conference proceedings and all others for their support and involvement in the conference.Last, but not least, we would like to thank the Local Organisation Committee of ICQ13 - chaired by Prof. Narayan Prasad Adhikari - for the efforts that made the conference so successful. We would also like to express our gratitude for the support we received from the University of Liverpool, UK, Tohoku University, Japan and Tribhuvan University, Nepal.We hope that the conference helped to promote the struggling tourism sector of Nepal, after the country was hit by devastating earthquakes in 2015. We thank the Nepal Tourism Board, Atithi Devo Bhava, Chandragiri Cable Car and Cultural Bands to help ICQ13 participants explore the culture, history and natural beauty of the Himalayan country Nepal during their stay.The 14th International Conference on Quasicrystals (ICQ14) will be held on 26 - 31 May 2019 in Bled, Slovenia.Thank you.Conference Chairs,Dr Hem Raj Sharma (the University of Liverpool, UK)Prof An Pang Tsai, Tohoku University, Japan31st January 2017

High rotational symmetry photonic structures fabricated with multiple exposure Displacement Talbot Lithography

Quasi-periodic structures with a high degree of rotational symmetry are desired for photonic applications because of their nearly isotropic optical response, in contrast to the highly directional behavior of periodic lattices. Here we introduce a method based on the superposition of periodic structures obtained by multiple exposure of a photomask with Displacement Talbot Lithography in which the photomask is rotated by a certain angle between exposures. The resulting structure can be considered as a Moiré pattern. High-quality patterns with 10 and 12-fold rotation symmetries and resolutions in the sub-micron to micron range are uniformly and reproducibly printed. The technique is suitable for the mass fabrication of wafer-scale quasi-periodic photonic patterns.

A High Quality Factor Filter Based on Quasi-Periodic Photonic Structure

A High Quality Factor Filter Based on Quasi-Periodic Photonic Structure

Intrinsic photonic wave localization in a three-dimensional icosahedral quasicrystal

Unlike the usual picture of Anderson localization, in three-dimensional quasicrystals light waves can localize without disorder, thanks to their short mean free path. Wave transport is one of the most interesting topics related to quasicrystals. This is due to the fact that the translational symmetry strongly governs the transport properties of every form of wave. Although quasiperiodic structures with1,2,3,4 or without1,5,6,7 disorder have been studied, a clear mechanism for wave transport in three-dimensional quasicrystals including localization is missing8,9. To study the intrinsic quasiperiodic effects on wave transport, the time invariance of the lattice structure and the loss-free condition must be controlled10,11. Here, using finite-difference methods, we study the diffusive-like transport and localization of photonic waves in a three-dimensional icosahedral quasicrystal without additional disorder. This result appears at odds with the well-known theory12 of wave localization (Anderson localization), but we found that in quasicrystals the short mean free path of the photonic waves makes localization possible.

The theoretical analysis of omnidirectional photonic band gaps in the one-dimensional ternary plasma photonic crystals based on Pell quasi-periodic structure

In this study, an omnidirectional photonic band gap (OPBG) in one-dimensional (1D) plasma photonic crystals (plasma-PCs) with Pell quasi-periodic structures, which are consisting of plasma and two isotropic dielectrics is theoretically calculated by the transfer matrix method. Compared to the Bragg gaps, the OPBG is not dependent on the angle of incidence and both transverse electric and transverse magnetic modes. The bandwidth and frequency region of the OPBG is not sensitive to Pell sequence order, but the bandwidth of the OPBG can be significantly enhanced, as the density and length of plasma layer are increased. The calculated results demonstrate that the 1D plasma-PCs with Pell quasi-periodic not only can obtain a larger bandwidth of OPBG but also have a shorter length in realizing devices, compared to the 1D Thue-Morse (Th-M) aperiodic or Fibonacci ones. It is clear that such 1D plasma-PCs with Pell quasi-periodic have advantages in realizing compact devices.

Ionization and high harmonic generation of two-dimensional quasiperiodic structures in arbitrarily polarized strong laser fields

Motivated by collapsing of Riemannian manifolds and inhomogeneous scaling of left invariant Riemannian metrics on a real Lie group $G$ with a sub-group $H$, we introduce a family of interpolation equations on $G$ with a parameter $\epsilon>0$, interpolating hypo-elliptic diffusions on $H$ and translates of exponential maps on $G$ and examine the dynamics as $\epsilon\to 0$. When $H$ is compact, we use the reductive homogeneous structure of Nomizu to extract a converging family of stochastic processes (converging on the time scale $\frac 1 \epsilon$), proving the convergence of the stochastic dynamics on the orbit spaces $G/H$ and their parallel translations, providing also an estimate on the rate of the convergence in the Wasserstein distance. Their limits are not necessarily Brownian motions and are classified algebraically by a Peter Weyl's theorem for real Lie groups and geometrically using a weak notion of the naturally reductive property; the classifications allow to conclude the Markov property of the limit process. This can be considered as `taking the adiabatic limit' of the differential operators ${\mathcal L}^\epsilon=\frac 1 {\epsilon} \sum_k (A_k)^2+ \frac 1{\epsilon} A_0+ Y_0$ where $Y_0, A_k$ are left invariant vector fields and $\{A_k\}$ generate the Lie-algebra of $H$.

Ionization and high harmonic generation of two-dimensional quasiperiodic structures in arbitrarily polarized strong laser fields

The ionization and high harmonic generation from two-dimensional quasiperiodic structures in strong laser fields are studied by numerically solving the time-dependent Schrodinger equation, in which a two-dimensional Kronig–Penney potential has been adopted to mimic the target. The two-dimensional photoelectron momentum distribution is significantly governed by the two-dimensional quasiperiodic potential, and thus is distinct from the single atom case. The low order harmonics initiated by a circularly polarized driving laser field are also circularly polarized and present alternative helicities; however, the high order harmonics deviate from circular polarization due to the unstable phase variation between different components. This calculation shows that elliptically polarized harmonics can be effectively generated by a circularly polarized driving laser field, and it sheds light on laser–surface interaction.

Plasmon analysis and homogenization in plane layered photonic crystals and hyperbolic metamaterials

Dispersion equations are obtained and analysis and homogenization are carried out in periodic and quasiperiodic plane layered structures consisting of alternating dielectric layers, metal and dielectric layers, as well as graphene sheets and dielectric (SiO2) layers. Situations are considered when these structures acquire the properties of hyperbolic metamaterials (HMMs), i.e., materials the real parts of whose effective permittivity tensor have opposite signs. It is shown that the application of solely dielectric layers is more promising in the context of reducing losses.

A Topological Low-Pass Filter for Quasi-Periodic Signals

This article presents a two-stage topological algorithm for recovering an estimate of a quasiperiodic function from a set of noisy measurements. The first stage of the algorithm is a topological phase estimator, which detects the quasiperiodic structure of the function without placing additional restrictions on the function. By respecting this phase estimate, the algorithm avoids creating distortion even when it uses a large number of samples for the estimate of the function.

Second-order two-scale analysis and numerical algorithm for the damped wave equations of composite materials with quasi-periodic structures

In this paper, we perform a second-order two-scale analysis and introduce a numerical algorithm for the damped wave equations of composite materials with a quasi-periodic structure. Firstly, second-order two-scale asymptotic expansion solutions for these problems are constructed by a multiscale asymptotic analysis. In addition, we explain the importance of the second-order two-scale solutions by the error analysis in the pointwise sense. Moreover, explicit convergence rates of these second-order two-scale solutions are obtained in the integral sense. Then a second-order two-scale numerical method based on a Newmark scheme is presented to solve these multiscale problems. Finally, some numerical examples show the effectiveness and efficiency of the multiscale numerical method we proposed.

Octonacci photonic crystals with negative refraction index materials

We investigate the optical transmission spectra for s-polarized (TE) and p-polarized (TM) waves in one-dimensional photonic quasicrystals on a quasiperiodic multilayer structure made up by alternate layers of SiO2 and metamaterials, organized by following the Octonacci sequence. Maxwell's equations and the transfer-matrix technique are used to derive the transmission spectra for the propagation of normally and obliquely incident optical fields. We assume Drude-Lorentz-type dispersive response for the dielectric permittivity and magnetic permeability of the metamaterials. For normally incident waves, we observe that the spectra does not have self-similar behavior or mirror symmetry and it also features the absence of optical band gap. Also for normally incident waves, we show regions of full transmittance when the incident angle θC = 0° in a particular frequency range.

Magnetic Response and Valence Fluctuations in the Extended Anderson Lattice Model with Quasiperiodicity

We study valence fluctuations in the extended Anderson model on two-dimensional Penrose lattice, using the real-space dynamical mean-field theory combined with the continuous-time Monte Carlo method. Calculating $f$-electron number, $c$-$f$ spin correlations, and magnetic susceptibility at each site, we find site-dependent formations of the singlet state and valence distribution at low temperatures, which are reflected by the quasiperiodic lattice structure. The bulk magnetic susceptibility is also addressed.

Additional external electromagnetic fields for laser microprocessing of metals.

Ultra-short pulsed laser processing is a potent tool for microstructuring of a lot of materials. At certain laser parameters, particular periodical and/or quasi-periodical µm-size surface structures evolve apparently during processing. With extended plasmonics theory, it is possible to predict the structure formation, and a systematic technology can be derived to alter the surface for laser processing. In this work, we have demonstrated the modification of the laser processing with applying tailored dynamic surface electro-magnetic fields. Possible improvement in applications is seen in the fields of process efficiency of laser ablation and a superior control of the surface topography.

Simultaneous localization of photons and phonons within the transparency bands of LiNbO3 phoxonic quasicrystals.

We report the properties of dual phononic-photonic band gaps and localized modes of eightfold lithium niobate (LiNbO3) phoxonic quasicrystals (PhXQCs). Complete and large phoxonic band gaps are easily achieved despite the low refractive index of LiNbO3 substrate. Point defect intentionally introduced can form localized modes within both forbidden and transparency bands over a wide range of geometric parameters. Further analysis indicates that the localized modes within transparency bands originate from the intrinsic high-order rotational symmetry of quasiperiodic structures, which resemble whispering gallery modes. LiNbO3 PhXQCs provide a good candidate to enhance phononic-photonic interaction and show considerable advantage over the periodic counterparts.

Quasiperiodic Frank–Kasper phases derived from the square–triangle dodecagonal tiling

Frank–Kasper (F-K) phases form an important set of large-cell crystalline structures describing many intermetallic alloys. They are usually described in term of their atomic environments, with atoms having 12, 14, 15 and 16 neighbours, coded into the canonical $$Z_p$$ cells (with p the coordination number), the case $$p=12$$ corresponding to a local icosahedral environment. In addition, the long-range structure is captured by the geometry of a network (called either “major skeleton” or “disclination network”) connecting only the non-icosahedral sites (with $$p\ne 12$$ ). Another interesting description, valid for the so-called layered F-K phases, amounts to give simple rules to decorate specific periodic 2d tilings made of triangles and squares and eventually get the 3d periodic F-K phases. Quasicrystalline phases can sometime be found in the vicinity, in the phase diagram , of the F-K crystalline alloys; it is therefore of interest to understand whether and how the standard F-K construction rules can be generalized on top of an underlying quasiperiodic structure. It is in particular natural to investigate how well square–triangle quasiperiodic tilings with dodecagonal symmetry, made of square and (equilateral) triangles, can be used as building frames to generate some F-K-like quasicrystalline structures . We show here how to produce two types of such structures, which are quasiperiodic in a plane and periodic in the third direction, and containing (or not) $$Z_{16}$$ sites.