Quasiperiodic Arrays Research Articles

Bridging Frontiers in Macromolecular and Supramolecular Sciences with Living Cationic Ring‐Opening Polymerization of Self‐Organizable Dendronized Cyclic‐Imino Ethers Generating Soft Frank–Kasper and Quasicrystal Arrays

AbstractLiving cationic ring‐opening polymerization accompanied by isomerization of cyclic imino ethers is performed at high temperatures that provide access to the synthesis of self‐organizable systems in their isotropic melt or solution state. This Perspective discusses fundamental mechanistic principles of this polymerization and bridges with the polymerization of dendronized cyclic iminoethers forming polymers that self‐organize soft Frank–Kasper and quasicrystal periodic and quasiperiodic arrays. These two fields represent frontiers in macromolecular and supramolecular science. A brief discussion of the impact of this polymerization on biomaterials and how it impacted contemporary mechanistic investigations is also made. Expected impacts via future synthetic developments and mechanistic investigations are discussed.

Engineering Anisotropy into Organized Nanoscale Matter.

Programming the organization of discrete building blocks into periodic and quasi-periodic arrays is challenging. Methods for organizing materials are particularly important at the nanoscale, where the time required for organization processes is practically manageable in experiments, and the resulting structures are of interest for applications spanning catalysis, optics, and plasmonics. While the assembly of isotropic nanoscale objects has been extensively studied and described by empirical design rules, recent synthetic advances have allowed anisotropy to be programmed into macroscopic assemblies made from nanoscale building blocks, opening new opportunities to engineer periodic materials and even quasicrystals with unnatural properties. In this review, we define guidelines for leveraging anisotropy of individual building blocks to direct the organization of nanoscale matter. First, the nature and spatial distribution of local interactions are considered and three design rules that guide particle organization are derived. Subsequently, recent examples from the literature are examined in the context of these design rules. Within the discussion of each rule, we delineate the examples according to the dimensionality (0D-3D) of the building blocks. Finally, we use geometric considerations to propose a general inverse design-based construction strategy that will enable the engineering of colloidal crystals with unprecedented structural control.

Superhydrophobic quasi-periodic concave microlens array on fused silica prepared by spatially modulated picosecond laser parallel processing

Fused-silica-based microlens array (MLA) has excellent stability in the harsh environment. However, it is still a challenge to efficiently prepare superhydrophobic quasi-periodic MLA and keep the optical performance of the microlens. In this paper, we proposed spatial modulated picosecond laser parallel processing method to prepare a superhydrophobic quasi-periodic MLA on fused silica. By using a spatial light modulator, the picosecond laser was shaped to multi-focal spots and line-shape beam, respectively, which improved the fabrication efficiency. The line-shape beam was the key to induce micro-nanostructures on the smooth MLA and keep the optical performance of the microlens. The results showed that the surface roughness of the microlens region was less than 100 nm. Combing with shaping picosecond laser processing and chemical treatment, the superhydrophobic MLAs showed the excellent anti-fogging and self-cleaning properties. The average contact angle of the superhydrophobic MLAs was 162.3°. The superhydrophobic MLA showed low adhesion to water droplet (<10 μN) and low contact angle hysteresis (2.1° ± 0.7°). We believe shaping picosecond laser parallel processing method is a flexible and low-cost approach to prepare superhydrophobic micro-optical elements on fused silica.

3D Surface-Enhanced Raman Scattering Substrate Based on an Array of Self-Assembled Au@SiO2 Microspheres

A quasi-periodic array of 3D gold-nanoparticle-capped SiO2 microspheres (Au@SiO2) was designed and prepared with a facile approach to enhance the Raman signal intensity of adsorbed biomolecules. Through adjusting the thickness and annealing of Au thin films initially deposited on arrays of self-assembled SiO2 microspheres, we were able to control the diameter of Au nanoparticles and their interparticle spacing to produce two types of plasmonic near-field hot spots, locating at the gaps of such densely arranged Au nanoparticles on individual SiO2 microspheres and in the gap regions of neighboring SiO2 microspheres, respectively. Such double near-field enhancement mechanism leads to a surface-enhanced Raman scattering (SERS) enhancement factor up to 3 × 106 for Rhodamine 6G molecules. The SERS signal intensity was highly uniform with a relative standard deviation of 4.5%. This 3D SERS substrate has significant potential for various applications in the field of SERS detection of analytes and wearable biosensing.

Quasicrystal metasurface for dual functionality of holography and diffraction generation

Quasicrystal has attracted lots of attention since its discovery because of the mathematically non-periodic arrangement and physically unique diffraction patterns. By combining the quasi-periodic features of quasicrystal and the special rotational symmetry with metasurface, many novel phenomena and applications are proposed such as optical spin-Hall effect, non-linear far-field radiation control, and broadband polarization conversion. However, the additional functions and effects brought by phase and amplitude modulation on quasicrystal arrangement still lack research. Here, we design and fabricate a dielectric quasicrystal metasurface which can simultaneously reconstruct holographic images and exhibit diffraction patterns by assembling the nanostructures in a quasi-periodic array. Most importantly, we combine the global arrangement of metasurfaces with the local responses (phase and amplitude) of meta-atoms for achieving the dual functionality. Furthermore, we also suppress the zero diffraction order in the far-field based on the quasi-momentum matching rule. The proposed method has great mathematical importance and explores new possibilities for multifunctional meta-devices for holographic display, optical switching and anti-counterfeiting.

Design and optimization of dielectric metalens with quasi-periodic arrays

Metalenses have attracted a great deal of research interests due to the property of light controllability. How to enhance the focusing effect of metalens has always been a key problem that many researchers have been working on. In this paper, we propose a novel sub-dimensional resonance-based optimization method for dielectric metalens with golden angle spiral arrays. The waveguiding effect is first applied to the initial design of the quasi-periodic metalens through the defined equivalent period. Then the genetic algorithm is improved for adjusting the sub-dimensional structure of the initial metalens. The optimization results show that the peak intensity of central hot spot increases by 32 % while keeping the full width at half maximum (FWHM) almost unchanged. At the same time, the field intensity of side lobes around the hot spot decreases, which means that a potential way for high-contrast imaging is provided.

Bispectral optical cavity based on twin metamirrors

In this work, we introduce a new bispectral optical cavity concept for which we design twin pairs of highly reflective, ultra-low noise metamirrors. Metasurfaces, artificial structures composed of periodic or quasi-periodic arrays of nanostructures, offer unprecedented control over light properties, paving the way for new applications in areas from high-precision optical metrology to quantum science. Custom phase and an ultra-high reflection coefficient make these metasurfaces an ideal candidate to surpass traditional multilayer mirrors as metamirrors in precision interferometry, particularly by also minimizing thermal noise. The focusing metamirrors designed in this study expect to reflect 99.95% and 99.96% of the incoming light at both, 1064 nm and 1550 nm wavelength. Their planar counterparts even reach theoretical reflectivities of 99.9999% (1064 nm) and 99.9995% (1550 nm). These specialized metamirrors enable bispectral low-noise optical cavities, which would reduce the number of cavities in optical experiments or could be used as a versatile transfer cavity for frequency locking.

Fiber-Optic Hydraulic Sensor Based on an End-Face Fabry–Perot Interferometer with an Open Cavity

The paper describes the design and manufacturing process of a fiber optic microphone based on a macro cavity at the end face of an optical fiber. The study explores the step-by-step fabrication of a droplet-shaped macro cavity on the optical fiber’s end surface, derived from the formation of a quasi-periodic array of micro-cavities due to the fuse effect. Immersing the end face of an optical fiber with a macro cavity in liquid leads to the formation of a closed area of gas where interfacial surfaces act as Fabry–Perot mirrors. The study demonstrates that the macro cavity can act as a standard foundational element for diverse fiber optic sensors, using the droplet-shaped end-face cavity as a primary sensor element. An evaluation of the macro cavity interferometer’s sensitivity to length alterations is presented, highlighting its substantial promise for use in precise fiber optic measurements. However, potential limitations and further research directions include investigating the influence of external factors on microphone sensitivity and long-term stability. This approach not only significantly contributes to optical measurement techniques but also underscores the necessity for the continued exploration of the parameters influencing device performance.

All-dielectric terahertz metasurfaces for arbitrary linear polarization detection

The polarization state, an intrinsic property of electromagnetic waves, plays a key role in determining the mechanism of light–matter interactions. Recently, the bulky elements for evaluating polarization states have been miniaturized by using metasurfaces. However, determining arbitrary linear polarization (LP) states from vortex beams generated by metasurfaces is quite challenging. Here, a general design of all-silicon quasi-periodic arrays based on polarization multiplexing technology is proposed, which can be used for the detection of arbitrary incident LP state. By embedding independent helical phase profiles in two orthogonal LP channels, the generated interference spot at the predesigned focal plane is resolvable in a proper polarized direction. Benefiting from the establishment of a parametric theoretical model, the evolution of the incident polarization can be determined using key parameters defined on the pixelated focal plane. The proposed method can flexibly determine the polarization state of incident terahertz waves, which has great potential in remote sensing, high-resolution imaging, and data communication.

Bridging organic, molecular, macromolecular, supramolecular and biological sciences to create functions via fluorine chemistry and fluorinated reagents

After a brief introduction highlighting the challenges of fluorine chemistry and the latest developments in the field, this Perspective will discuss how a combination of fluorine and fluorous chemistry together with fluorinated reagents helped to bridge between organic, molecular, macromolecular, supramolecular and biological sciences to create functions in the laboratory of the corresponding author. The reactivity of fluoride as a leaving group is best illustrated by SNAr reactions when it helped to demonstrate single electron transfer-mediated side reactions and through molecular design replaced activated aryl fluorides with aryl chlorides in the synthesis of poly(etherketone)s. Subsequently it was demonstrated how Ni(II) sigma complexes provided an orthogonal approach to the Suzuki-type cross-coupling of arylfluorides, other halides and all aryl C–O based electrophiles. Fluorinated reagents facilitated cylotrimetrization vs cyclotetramerization of bis(methoxy)benzyl chloride and alcohol and the synthesis of the simplest molecular liquid crystals. Triflic acid, methyl triflate facilitated the most tolerant living polymerizations including of cyclic siloxanes, functional vinyl ethers and oxazolines to generate self-organizable dendronized polymers while fluorine, trifluoromethyl and trifluoromethoxy groups facilitated disassembly and reassembly of liquid crystal polyethers and poly(p-phenylenes). Fluorinated stereocenters accessed the first heterochiral recognition in side-chain liquid crystal poly(vinyl ether)s and their model compounds. Alkali metal triflates mediated self-organization of supramolecular nonfluorinated and fluorinated self-assembling minidendrons, dendrons, dendrimers and self-organizable dendronized polymers. The role of fluorinated alkyl groups and of alkali metal triflates in the self-assembly, disassembly and isomorphic replacement analysis, of supramolecular helical columns, of the assembly of helical cogwheel coat and of spherical supramolecular dendrimers forming Frank-Kasper periodic and quasiperiodic arrays was highlighted. A brief discussion of fluorinated amino acids, peptides and peptoids and their potential role in the self-assembly and functions resulted from dendritic dipeptides followed by a discussion of semifluorinated amphiphilic Janus dendrimers as models of biological membranes, including for cell fusion and fission, concludes this Perspective.

Ultrathin optically transparent and flexible wideband absorber based on ANN and DGCNN

Optically transparent and structurally flexible metamaterial absorbers (MMAs) are widely used in many practical applications. However, the realization of such MMAs requires both thickness reduction and bandwidth enhancement, which remains a challenge task. As a multi-objective optimization problem, it is a time-consuming and resource-demanding process. Guided by prior-knowledge, two degrees of freedom are taken into account in the design, namely the structure of unit-cells and their spatial arrangement. In this way, the multi-objective optimization problem is simplified into a two-step problem. A general procedure based on machine-learning (ML) method is proposed to solve this problem. First, an artificial neural network (ANN) is used to map the configuration parameters of a type of meta-atom onto its reflection coefficients; then, a dynamic graph convolutional neural network (DGCNN) is trained to realize the synthesis of quasi-periodic distributed MMA array; finally, combined with the differential evolution (DE) algorithm, the optimized configuration of the meta-atoms and their optimum distribution are obtained. Based on the proposed procedure, an ultrathin optically transparent and flexible MMA is designed, fabricated and further verified by experiments. The designed MMA realizes 87% absorption bandwidth covering 6.22 GHz–19.42 GHz (103% relative bandwidth) with the thickness only 3.3mm(0.068λL), which approaches the theoretical limit 1/17λL. And its averaged transparency is about 63% at the wavelength range 500–800mm. The whole design process is achieved 50 times faster than the conventional full-wave simulation, which convincingly demonstrates the superiority of the proposed method.

Nonreciprocal Electromagnetically Induced Unidirectional Absorption Based on the Quasi-Periodic Metastructure and Its Application for Permittivity Sensing

Nonreciprocal unidirectional absorption, as a critical feature in both applications of military and civilian, has always been a challenging research topic. Here, we introduce a linear incremental arrangement into the formation of the electromagnetically induced absorption (EIA) in a single metastructure unit, creating an asymmetry spatial modulation for the nonreciprocal electromagnetic responses. A unidirectional EIA peak with a high absorption reaching 87.87% is observed for the forward case, and nearly all the incident energy is reflected in the backward case. The maximum isolation ratio (IR) between the forward and backward absorptions is 10.79 dB. To obtain a higher forward absorption and enlarge the IR, an improved nonreciprocal metastructure array is proposed and experimentally demonstrated by applying a linear quasi-periodic array configuration. The forward electromagnetically induced unidirectional absorption is enhanced to 99.53% with an IR of 12.73 dB. The near-perfect absorption provides a promising platform for permittivity sensing, and the measurement of common microwave plates with different relative permittivity shows an excellent linear regression. Such an implementation innovatively combines the asymmetric spatial modulation with EIA to form unidirectional absorption, offering a new guideline for novel nonreciprocal devices, and possessing considerable practical applications in the wireless communication system, ultrasensitive sensing, one-way invisibility, and absorptive switching.

Bound States in the Continuum Help Shrimp Eyes to Catch More Light

Optical bound states in the continuum (BICs) have recently attracted a great deal of attention as an efficient way to localize and manipulate light at nanoscale. Traditionally, generation of BICs has relied on using artificial structures where suppression of radiative losses leads to very high Q factors. Here, we show that BICs may play an important biological role by boosting light–matter interactions in a biogenic nanostructure: tapetum reflector of a shrimp eye. Enveloping photosensitive units of the retina (rhabdoms), this system contains quasi-periodic arrays of spherical core–shell nanoparticles which include concentric lamellae of single-crystal isoxanthopterin nanoplates arranged around a hollow core. The radial alignment of the plates gives rise to the spherical anisotropy of the nanoparticles which provides access to quasi-BIC modes in a full visible domain. Thus, a tapetum reflector hosting BICs maximizes light interactions with rhabdoms, enhancing the eye’s sensitivity. Our findings suggest that BICs, previously associated with man-made structures only, can be generated in biogenic structures, performing crucial optical functionalities in living organisms.

OLEDs on planarized light outcoupling-enhancing structures in plastic

Light extraction from OLEDs remains a challenge. While consumer demand for OLEDs in display technology continues to grow as prices decline, commercial use of OLEDs in solid state lighting (SSL) applications is lagging due to low light extraction, which results in low efficiency. Previous studies have been directed toward increasing the light extraction factor η out , but cost-effective approaches that will enable high throughput and potential upscaling, as well as elucidation of the extraction process, are still lagging. One promising approach is the use of buried light extraction enhancing patterns that are planarized with a high refractive index (RI) layer. When adding substrate mode extracting means, the highest external quantum efficiencies (EQEs) were achieved using a complex approach of planarized vacuum nano holes. Here we present η out -enhancing planarized extraction structures (PES) in plastic. While plastic substrates currently present long-term stability issues and other drawbacks, as we show, they provide a tool for simple, inexpensive, and rapid generation of various enhancing structures that importantly can be transferred to the preferred rigid and flexible glass substrates. Moreover, plastic substrates are attractive for biomedical applications. The successful structures we present are easily scalable periodic corrugations, e.g., with pitch a ∼4.25 μm and pitch/depth ratio a/h ∼ 2.4 planarized by a layer of RI ∼1.9, resulting in maximal EQEs exceeding 60% for a green OLED and 48.5% for a white OLED. Comparable increased EQEs were achieved for structures with a ∼15 and 16 μm, and a/h ∼2.1 and 4, respectively. Enhanced extraction was also observed with a very simply fabricated quasiperiodic nanohole array, and surprisingly, with a random shallow design. The latter is at variance with simulations based on diffraction only. Results are discussed in terms of a , h , and structural parameters together with scattering matrix simulations to assess the effect of various PES parameters and the nanoparticle-embedded planarizing layer on η out . The experiments and simulations indicate contributions of diffraction, reflection, and scattering to EQE enhancement. • Light outcoupling-enhancing planarized extraction structures (PES) in plastic. • A tool for simple, inexpensive, & rapid generation of various enhancing structures. • Useful PES: periodic patterns, quasiperiodic nanohole array, random shallow design. • EQEs achieved: 61% - green OLED; 48.5% - white OLED. • Experiment & theory: enhanced EQEs due to diffractive & diffuse light scattering.

Revealing natural fluorescence in transparent insect wings by linear and nonlinear optical techniques

For most natural organisms, the physical, chemical and biological aspects of fluorescence emission are poorly understood. For example, to the best of our knowledge, fluorescence from the transparent wings of any of the 3000 known species of cicadas has never been reported in the literature. These wings are known to exhibit anti-reflective properties arising from quasi-periodic arrays of nipples. Our study, using linear and nonlinear optical techniques, including spectrofluorimetry, two-photon fluorescence spectroscopy and Second Harmonic Generation (SHG), reveals the fluorescence properties in the wings the grey and the common cicadas (Cicada orni and Lyristes (Tibicen) plebejus, respectively), as well as the broad-bordered bee hawk-moth (Hemaris fuciformis). The study suggests that fluorescence would be more widespread in transparent insect wings than what was previously believed. Comparing this result to the fluorescence emission from the wings of the Bornean damselfly (Vestalis amabilis), we inferred that this emission probably arises from resilin, a protein reported to enhance wing flexibility. Moreover, the nonlinear optical investigation of the insects’ wings provided further insight into wing structure, indicating that multiphoton techniques add valuable information for the analysis of insect integuments. The strong SHG signal detected from the wing veins implies that these veins are materially organised in a non-centrosymmetric and hence non-random fashion.

Subwavelength Quasi-Periodic Array for Infrared Antireflection.

Infrared antireflection of a zinc sulfide (ZnS) surface is important to improve performance of infrared detector systems. In this paper, double-pulse femtosecond laser micro-machining is proposed to fabricate a subwavelength quasi-periodic array (SQA) on ZnS substrate for infrared antireflection. The SQA consisting of approximately 30 million holes within a 2 × 2 cm2 area is uniformly formed in a short time. The double-pulse beam can effectively suppress the surface plasma shielding effect, resulting in obtaining a larger array depth. Further, the SQA depth is tunable by changing pulse energy and pulse delay, and can be used to readily regulate the infrared transmittance spectra as well as hydrophobicity. Additionally, the optical field intensity distributions of the SQA simulated by the rigorous coupled-wave analysis method indicate the modulation effect by the array depth. Finally, the infrared imaging quality captured through an infrared window embedded SQA is evaluated by a self-built infrared detection system.

Hofstadter butterfly and topological edge states in a quasiperiodic photonic crystal cavity array.

Quasiperiodic structures with additional synthetic degrees of freedom have recently been recognized as a promising way for investigating high-dimensional topological phases with lower physical dimensions. Here, we investigated the well-known Harper-Aubry-André model on an integrated photonic platform by proposing a new design of a quasiperiodic photonic crystal (PhC) cavity array. This array is composed of closely coupled H1 PhC cavities with their cavity lengths being periodically modulated in the real space. The frequency spectrum of the structure shows the main features of the Hofstadter butterfly, which is one of the most important phenomena in the Harper-Aubry-André model. By varying the modulation phase, this structure exhibits nontrivial topology, which supports strongly localized topological edge states. These results have shown that quasiperiodic PhC cavity arrays can serve as the testbed for studying topological phases and new topological phenomena on an integrated platform.

Electrode Cooling and Microwave Absorption by Phase Change Fluid Discharge Plasma

It is hard to realize the high microwave absorption property and the low operating temperature in a gas discharge plasma simultaneously, due to the electron number density, and electron neutral collision frequency physically needed for the former is a typical severe heating scenario for the latter. In this article, the phase change process is proposed to be introduced into the controlled area of the discharge plasma system to increase collision frequency and decrease the discharging electrode temperature at the same time. An ac high-voltage power-driven quasi-periodic array of the phase change fluid discharge (PCFD) device is investigated. The most apparent tendency of the PCFD plasma is the improved diffusivity and uniformity. At the same time, the temperature of the electrode and its vicinity, where the phase change material is reserved, is lower than the ambient temperature. Compared with the controlled discharge state of the low gaseous pressure dielectric barrier discharge (L-DBD) plasma without phase change process, the absorption attenuation in the <inline-formula> <tex-math notation="LaTeX">$X$ </tex-math></inline-formula>-band is enhanced in all tested polarization angles, which driving strategy could control. Analyses show that the increased microwave absorption, frequency shift, and bandwidth broadening mainly result from the phase change process and its influences on the plasma discharge.

Method for Calculation of the Interaction of Elements in a Large Convex Quasi-Periodic Phased Antenna Array

Method for Calculation of the Interaction of Elements in a Large Convex Quasi-Periodic Phased Antenna Array

Fast Prediction of Quasi-Periodic Array Using Dynamical Graph Convolutional Neural Networks

In this letter, a novel approach based on dynamic graph convolutional neural networks (DGCNNs) is proposed to analyze the quasi-periodic array consisting of the cells with different geometric parameters. Each vertex node in a graph represents a cell in quasi-periodic array and the features of each vertex node are determined by the geometric parameters of the corresponding cell. The connections in graph are initialized and dynamically updated to learn the mutual coupling among cells. DGCNNs are constructed and trained such that the neural networks can obtain the relationships among cells. The trained DGCNNs can predict the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> -parameters of a quasi-periodic array and the numerical experiments demonstrate the accuracy and efficiency of our method.