Quasiperiodic Arrays Research Articles

Supermode analysis of seven-core photonic quasi-crystal fibers

We design custom-shaped modes for a sixfold symmetric photonic quasi-crystal fiber (PQF), an optical fiber with a sixfold symmetric quasi-periodic array of air holes in the cladding region. The supermodes of the PQF are calculated by the finite element method, and the coupling of an in-phase supermode for the quasi-periodic optical fiber is numerically optimized to obtain identical values. The optimization is guaranteed by the selection of appropriate PQF design parameters. The eigenvalue equation associated with a seven-core PQF is derived from a coupled mode equation. We realize mode shaping and provide the far-field distribution mode of PQFs. The results are beneficial for the structural design and uniform distribution of the in-phase supermodes of PQFs.

Quasiperiodic plasmonic concentrators for enhanced light absorption in ultra-thin film solar cells

ABSTRACTThis report will demonstrate broadband, wide-angle, and polarization-insensitive absorption enhancement in ultra-thin films resting on metal substrates that have been etched with arrays of shallow sub-wavelength cylindrical holes. Absorption enhancement will be studied as a function of array geometry, with particular emphasis given to quasiperiodic arrays (a class of deterministic aperiodic arrays that were originally developed to tessellate 2-D planes with regular polygons). Through simulations and experimental data, it was found that absorption enhancement is heavily dependent on the rotational symmetry of the pattern of holes, as well as the inter-hole distance.

Acoustic scattering from a finite quasi-periodic bulkhead cylindrical shell

Research on sound scattering from a finite quasi-periodic bulkhead cylindrical shell is conducted. The small deviation of bulkhead array exists. Firsts some applications are given to investigate the problem of backscattering from a periodic bulkhead cylindrical shell in order to verify the theory. Then the angle-frequency spectrum of the backscattering from quasi-periodic bulkhead cylindrical shell is calculated, and the angle-frequency spectrum shows that the quasi-periodic array of bulkhead results in the diffusion of Bloch-Floquet wave and background field. However, the resonance of bulkheads is covered by background field. Finally, the influences of the array random variable of bulkheads, the number of bulkheads and the spacing between bulkheads are discussed. The calculations show that the diffusion of Bragg waves is more evident with array random variable increasing; the power of Bragg waves is concentrated with the number of bulkheads increasing; with the spacing between bulkheads becoming broad, the number of Bragg waves increases and the diffusion of high modes Bragg waves becomes more serious. Based on the geometric characteristics of Bragg waves, the approximate calculation formula of the Bragg wave position on the angle-frequency spectrum is presented. The formula can forecast the position of Bragg wave on the angle-frequency spectrum exactly and the diffusion of Bragg waves roughly when the bulkheads array quasi-periodic.

S+C+L波段色散斜率补偿光子准晶体光纤

针对光纤通信中的色散补偿,尤其是密集波分复用系统的多信道同时补偿的需求,提出了一种用于宽带色散斜率补偿的光子准晶体光纤.该光纤结构包层空气孔为准晶体排列,并且在纤芯引入了中心缺陷.通过对光纤特性的数值分析表明,在1 460-1 625 nm的光通信波段,该结构光纤的相对色散斜率为0.004 4-0.002 9 nm^-1,相对色散斜率与标准单模光纤近似相等,且负色散值达-2 476 ps·nm^-1·km^-1.对标准单模光纤进行色散补偿后,在S＋C＋L波段色散值为（-0.5-0）ps·nm^-1·km^-1.该光纤可用于对当前光纤通信系统进行宽带色散补偿,实现多信道同时补偿,简化结构,并降低补偿成本.

Self-assembled nanostructured composites for solar absorber

Nanostructured composites designed for highly efficient solar energy absorption and conversion were studied. Self-assembled nanostructure was constructed on the Fe–Cr–Ni alloy surface directly through electrochemical treatment by applying potential of wave pulse in a mixed solution of sulfuric and chromic acid. The surface structure, featuring 2D quasi-periodic nano-needle array, was composed by a mixture of spinel oxides of the substrate elements. Film of this structure displays absorptivity of 99% over the solar spectrum (0.3–1.5μm), with low thermal emission in the IR region. The high selective absorption capability of nanostructured composites realizes efficient energy conversion and could be accepted in practice.

Closed-Form Analysis of Reflection Losses in Microstrip Reflectarray Antennas

Microstrip reflectarray antennas consist of a grounded quasi-periodic array of printed elements able to compensate the phase displacement of a non-coherent electromagnetic excitation generated by a feeder. The design of reflectarray antennas is usually accomplished by tracing the reflection phase diagram of the periodic version of the printed surface, which is analogous to a high-impedance surface (HIS). Reflection losses of this periodic structure are here analyzed through a simple equivalent transmission line model. The analytical expressions of the surface impedance offered by a HIS (real and imaginary part) as a function of the imaginary part of the dielectric permittivity of the substrate are derived through well justified approximations. Some useful practical examples are then presented both for verifying the accuracy of the derived closed-form expressions and for studying the effect of the geometrical and electrical parameters of the periodic surface on the reflection losses. The dependence of the input impedance on the capacitance associated with the printed pattern is highlighted, demonstrating that highly capacitive elements (tightly coupled subwavelength elements) are preferable for minimizing reflection losses.

Local rotational symmetry effects on Fano resonances with constant non-resonant transmission channel

Three kinds of 12-fold quasi-periodic subwavelength hole arrays have been designed using the same dodecahedral supercell arranged with different local rotational symmetries. Fano resonances associated with spoof surface plasmons in these structures have been studied by far-infrared transmission measurements. The resonant transmission channels of the lowest-order Fano resonance mode have been compared directly between these structures, benefitting from constant non-resonant transmission channel. It is found that the higher is the local rotational symmetry of the supercell array, the higher the transmission intensity and the narrower the linewidth of the Fano resonance.

Formation of solar absorber surface on nickel with femtosecond laser irradiation

Through femtosecond (fs) laser pulse irradiation, we produce two-dimensional quasiperiodic arrays of nanostructure-covered conical microstructures (NC-CMs) on Ni. We also find that a significant amount of nickel oxide covers NC-CMs owing to the interaction of fs laser pulses with Ni in ambient air. We show that, by controlling the fluence of laser, the reflectance of the fs laser-treated Ni surface can change dramatically in the infrared but the surface still has a high absorptance at UV and visible wavelengths. Because of this unique spectral reflectance, the fs laser-treated Ni surface is well suited for use as a solar absorber surface.

Band Gaps of Lamb Waves Propagating in One-Dimensional Different Quasi-Periodic Composite Thin Plates

We present a comparative study on band-gap structures of Lamb waves propagating in one-dimensional quasi-periodic composite thin plates, which are composed of different quasi-periodic models such as Cantor, Fibonacci, Thue-Morse, and Double periodic sequences, respectively. The transmitted power spectra (TPS) of the transient Lamb waves propagating in composite plates is calculated numerically by employing the finite element method. By comparing among TPS in different plates with the different ratios of the plate thickness to the lattice spacing, it is found that different quasi-periodic models present different behavior of the split-up of band gaps. Our works are significant not only for understanding intrinsic physical property of the quasi-periodic sequences, but also for designing the special structures of quasi-periodic arrays to adjust the width of band gaps and the frequency ranges of phononic crystals in applications.

Quasi-Periodic Nanoripples in Graphene Grown by Chemical Vapor Deposition and Its Impact on Charge Transport

The technical breakthrough in synthesizing graphene by chemical vapor deposition methods (CVD) has opened up enormous opportunities for large-scale device applications. To improve the electrical properties of CVD graphene grown on copper (Cu-CVD graphene), recent efforts have focused on increasing the grain size of such polycrystalline graphene films to 100 μm and larger. While an increase in grain size and, hence, a decrease of grain boundary density is expected to greatly enhance the device performance, here we show that the charge mobility and sheet resistance of Cu-CVD graphene is already limited within a single grain. We find that the current high-temperature growth and wet transfer methods of CVD graphene result in quasi-periodic nanoripple arrays (NRAs). Electron-flexural phonon scattering in such partially suspended graphene devices introduces anisotropic charge transport and sets limits to both the highest possible charge mobility and lowest possible sheet resistance values. Our findings provide guidance for further improving the CVD graphene growth and transfer process.

Surface solitons in quasiperiodic nonlinear photonic lattices

We study discrete surface solitons in semi-infinite, one-dimensional, nonlinear (Kerr), quasiperiodic waveguide arrays of the Fibonacci and Aubry-Andr\'e types, and explore different families of localized surface modes, as a function of optical power content (``nonlinearity'') and quasiperiodic strength (``disorder''). We find a strong asymmetry in the power content of the mode as a function of the propagation constant, between the cases of focusing and defocusing nonlinearity, in both models. We also examine the dynamical evolution of a completely localized initial excitation at the array surface. We find that, in general, for a given optical power, a smaller quasiperiodic strength is required to effect localization at the surface than in the bulk. Also, for fixed quasiperiodic strength, a smaller optical power is needed to localize the excitation at the edge than inside the bulk.

Bitter decoration of vortex patterns in superconducting Nb films with random, triangular, and Penrose arrays of antidots

We imaged Abrikosov vortex patterns in thin Nb films with random, periodic (triangular), and quasiperiodic (Penrose) arrays of antidots. Vortex positions were visualized by Bitter decoration for a range of applied fields $B$, antidot radii $r$, and densities ${n}_{p}$ after field-cooling through the transition temperature ${T}_{c}$ to a base temperature $T\ensuremath{\approx}2\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The observed vortex patterns correspond to snapshots of vortex positions at the time of decoration. The effectiveness of antidots as artificial pinning sites for vortices is found to be sensitive to several factors: array geometry, antidot size and density, and applied field. Overall, the triangular lattice provides the most effective pinning landscape, with antidots trapping the highest proportion of vortices, but for a wide range of parameters the Penrose lattice is equally effective. For a quantitative analysis, we determined the occupation number $n$ (average number of vortices trapped per antidot) from each image. This revealed a significantly more complicated dependence of antidot occupation on applied field and/or antidot density than that predicted by simple models considering pinning by an isolated antidot. In particular, upon increasing the antidot density ${n}_{p}$, we find a marked increase in $n$ for triangular arrays, which we attribute to the additional repulsion from interstitial vortices, pushing more vortices into antidots with decreasing antidot separation. This effect is also present but less pronounced for Penrose arrays, which can be explained by the variation of antidot spacing inherent to the Penrose geometry and accordingly more options for accommodating interstitial vortices.

Exploiting long-ranged order in quasiperiodic structures for broadband plasmonic excitation

A comparison of transmission spectra from periodic, quasiperiodic, and randomly spaced slit arrays in thick gold films reveals resonant plasmonic excitations that arise solely due to the long-range order of the quasiperiodic structures. Specifically, first-order plasmonic resonances at the air-gold interface of the quasiperiodic arrays are identified at a broader range of wavelengths than those observed from periodic structures with the same average slit distance. Thus, a quasiperiodic plasmonic coupler that couples both visible and near-infrared light to surface plasmon polaritons is designed and demonstrated.

Plasmonic concentrators for enhanced light absorption in ultrathin film organic photovoltaics

We report on experimental absorption enhancement in 24 and 150-nm-thick bulk heterojunctions of the conducting polymer poly(3-hexylthiophene) and the fullerene (6,6)-phenyl C61 butyric acid methyl ester. By using periodic and quasiperiodic hole arrays as nanoengineered plasmonic concentrators milled in a silver film, a spectrally broad, omnidirectional, and polarization-insensitive absorption enhancement is observed over that of a reference layer deposited on a flat film. As the result of increased absorption, an enhancement in the polymer fluorescence intensity is also observed. This demonstrates the potential of plasmonic concentrators for improved energy harvesting in ultrathin film solar cells.

Enhancing the critical current in quasiperiodic pinning arrays below and above the matching magnetic flux

Quasiperiodic pinning arrays, as recently demonstrated theoretically and experimentally using a five-fold Penrose tiling, can lead to a significant enhancement of the critical current Ic as compared to "traditional" regular pinning arrays. However, while regular arrays showed only a sharp peak in Ic(Phi) at the matching flux Phi1 and quasiperiodic arrays provided a much broader maximum at Phi<Phi1, both types of pinning arrays turned out to be inefficient for fluxes larger than Phi1. We demonstrate theoretically and experimentally the enhancement of Ic(Phi) for Phi>Phi1 by using non-Penrose quasiperiodic pinning arrays. This result is based on a qualitatively different mechanism of flux pinning by quasiperiodic pinning arrays and could be potentially useful for applications in superconducting micro-electronic devices operating in a broad range of magnetic fields.

Swelling behaviour of PNIPAM-polyisoprene core-shell microgels at surface

Poly(N-isopropylacrylamide) (PNIPAM)-based microgels covered with hydrophobic but water-permeable shell were used for modification of a hydrophilic substrate with the aim to provide a ‘contraphilic’ wetting behaviour, namely, to make the surface more hydrophobic in water environment (polar medium) than in dry state in air (non-polar medium). Bottom-up approach has been applied for a stepwise preparation of a structured two-component surface. Loosely packed microgels self-organised into quasiperiodic arrays were chemically grafted to the hydrophilic, functionalised substrate. Afterwards, a surface-initiated polymerisation of isoprene was performed selectively from microgels making them hydrophobic. The surface was found to be water-sensitive, as observed by in situ AFM measurements. The surface fraction of the hydrophobic component increased from 13% in the dry state up to 25% in water due to swelling of the microgels. However, small contraphilic effect was recorded by water contact angle measurements because of a moderate lateral swelling of the core-shell microgels and due to a fast swelling of the microgels already upon the measurements.

Nanometrology optical ruler imaging system using diffraction from a quasiperiodic structure

This work demonstrates wafer-scale, path-independent, atomically-based long term-stable, position nanometrology. This nanometrology optical ruler imaging system uses the diffraction pattern of an atomically stabilized laser from a microfabricated quasiperiodic aperture array as a two-dimensional optical ruler. Nanometrology is accomplished by cross correlations of image samples of this optical ruler. The quasiperiodic structure generates spatially dense, sharp optical features. This work demonstrates new results showing positioning errors down to 17.2 nm over wafer scales and long term stability below 20 nm over six hours. This work also numerically demonstrates robustness of the optical ruler to variations in the microfabricated aperture array and discretization noise in imagers.

Nanometrology Using a Quasiperiodic Pattern Diffraction Optical Ruler

This paper presents a nanometrology optical ruler imaging system to enable rapid wafer-scale nanometrology, particularly for scanning probe microscopes. The ruler is generated by the diffraction of a 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-8</sup> stabilized laser by a metal thin-film pattern. Microfabrication techniques create a high-count quasiperiodic aperture array in the film which generates a translationally asymmetric feature-dense optical diffraction pattern well suited for the nanometrology application. An imager array samples the optical ruler and calculates its position by Fourier transform cross-correlation methods. Numerically, it is found that improving the imager by pixel count and size can reduce positioning errors down to 1/120th of the pixel size, after which further improvements yield no reduction in error. Experiments using a modest complementary metal-oxide-semiconductor imager demonstrate a positioning accuracy of 1/124th of the pixel size, or 29 nm. This system will enable high-precision high-throughput metrology and fabrication of nano- and microelectromechanical systems.

Formation of Stripe Domain Structures by Pulse Laser Irradiation of LiNbO3 Crystals

The formation of quasi-regular stripe nanodomain structure induced by ultraviolet pulse laser irradiation was studied in single crystalline congruent lithium niobate LiNbO3. It has been shown that the domain structure with average period about 4 μm consists of “straight” and “wave-like” nanodomain rays. The scanning electron microscopy allows us to reveal that the rays represent quasi-periodic arrays of individual nanodomains with average size 50–200 nm and period 100–500 nm. The spatial frequency multiplication of quasi-regular structures has been revealed.

Enhancement of the 1.54 μm Er3+ emission from quasiperiodic plasmonic arrays

Periodic and Fibonacci Au nanoparticle arrays of varying interparticle separations were fabricated on light emitting Er:SiNx films using electron beam lithography. A 3.6 times enhancement of the photoluminescence (PL) intensity accompanied by a reduction in the Er3+ emission lifetime at 1.54 μm has been observed in Fibonacci quasiperiodic arrays and explained with radiating plasmon theory. Our results are further supported by transmission measurements through the Fibonacci and periodic nanoparticle arrays with interparticle separation in the 25–500 nm range. This work demonstrates the potential of quasiperiodic nanoparticle arrays for the engineering of light emitting devices based on the silicon technology.