Finite Array Research Articles

Localized waves in elastic plates with perturbed honeycomb arrays of constraints.

In this paper, we study wave propagation in elastic plates incorporating honeycomb arrays of rigid pins. In particular, we demonstrate that topologically non-trivial band-gaps are obtained by perturbing the honeycomb arrays of pins such that the ratio between the lattice spacing and the distance of pins is less than 3; conversely, a larger ratio would lead to the appearance of trivial stop-bands. For this purpose, we investigate band inversion of modes and calculate the valley Chern numbers associated with the dispersion surfaces near the band opening, since the present problem has analogies with the quantum valley Hall effect. In addition, we determine localized eigenmodes in strips, repeating periodically in one direction, that are subdivided into a topological and a trivial section. Finally, the outcomes of the dispersion analysis are corroborated by numerical simulations, where a time-harmonic point source is applied to a plate with finite arrays of rigid pins to create localized waves immune to backscattering.This article is part of the theme issue ‘Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)’.

Non-paraxial transformation of finite Airy Gaussian beam array in isotropic space

Based on vector Rayleigh-Sommerfeld diffraction integration, we investigate the non-paraxial transmission behavior of the finite Airy Gaussian beam array (FAGBA) in isotropic space. The intensity distribution of the x- component and longitudinal component of the FAGBA at different cross section of the free space are described numerically, respectively. The influences of truncation factor, distribution parameter, wavelength, beam waist radius and refractive index on the FAGBA evolution at several observation planes as well as its side transmission view in isotropic space are also discussed. Through the obtained analytical formulae and conclusions, the beam array transmission locus can be controlled more precisely in non-paraxial situation by altering these parameters to meet the practical usage, especially in area of optical trapping and optical tweezers.

Signature-based block diagram analysis. Calculating complex-structure signatures

Aim. The signature theory allows comparing the structural dependability of complex systems consisting of identical components using a numeric vector referred to as signature that is determined using a certain algorithm. The signature describes a system’s structure and is associated with the order statistics of the components’ times to failure. The paper aims to familiarize the Russian readers with the theory, as well as to build simple algorithms that would allow finding the signature of an arbitrary VooL system, including a series parallel system using the known signatures of its subsystems.Methods. Calculations and theorem proving primarily involve the use of combinatorics with various element selection patterns. Additionally, classical methods of the probability theory and mathematical theory of dependability are used.Conclusions. The paper introduces such concept of the mathematical dependability theory as technical system signature. The primary purpose of this characteristic consists in comparing the structural dependability of several, in particular, two systems. The algorithm is sufficiently simple and involves comparing two finite numeric arrays according to a certain rule. Structural dependability is understood as the dependability of connection circuits of components that are identical in terms of dependability. That significantly reduces the capabilities of the signature theory, as practically all technical systems consist of components with various dependability. However, with a certain conservatism, it can be considered that all of a system’s components have a dependability identical to that of the least dependable one. The degree of conservatism will be determined by the difference in the component dependability that will be a sufficiently low value for highly dependable components. Additionally, we should note the purely mathematical beauty of the signature theory that has recently been gaining significant momentum in foreign scientific publications. It must be noted that according to the classical laws of combinatorics, as the number n of system component elements grows, the construction of a technical system signature speeds up significantly. Therefore, it becomes necessary to develop sufficiently simple algorithms for calculating the signature of a random system. As part of the presented work, analytical approaches to signature acquisition were developed for both simple cases when a single component is, in series or parallely, added to a subsystem, and more complex situations when one or more subsystems are added to another subsystem. A number of cases of signature construction were considered using both the classical method, and the one suggested in this paper. An example was analysed of system dependability comparison using their respective signatures. The structural dependability of systems with various numbers of components was compared. The paper proves a number of theorems that allow calculating the signature of a random structure diagram consisting of components that are identical in terms of dependability.

Folded Resonator for Glucose Solution Density Detection Based on Airy Beam Arrays

We presented an investigation on the evolution properties of the finite Airy beam array (FAiBA) in metamaterial’s slab system constituting of right-handed materials and double negative materials combining the generalized Huygens–Fresnel integral equation and the light transfer matrix. The beam intensity distribution on the receiver plane and its side transmission view on the (z, x) plane are demonstrated numerically with several array numbers. Moreover, we put forward a kind of folded resonator to detect glucose solution density based on the derived principle and conclusion; the influence of curvature radius on the emerging beam’s evolution characteristics is discussed, and the empirical formula between FAiBA’s received power and glucose solution density is derived by using the fit linear analysis. We hope that the present concept and the derived conclusions can be employed for monitoring in the environmental field, as well as the biomedical and food safety detection.

A portable non-invasive microwave based head imaging system using compact metamaterial loaded 3D unidirectional antenna for stroke detection

A metamaterial (MTM) loaded compact three-dimensional antenna is presented for the portable, low-cost, non-invasive microwave head imaging system. The antenna has two slotted dipole elements with finite arrays of MTM unit cell and a folded parasitic patch that attains directional radiation patterns with 80% of fractional bandwidth. The operating frequency of the antenna is 1.95–4.5 GHz. The optimization of MTM unit cell is performed to increase the operational bandwidth, realized gain, and efficiency of the antenna within the frequency regime. It is also explored to improve radiation efficiency and gain when placed to head proximity. One-dimensional mathematical modelling is analyzed to precisely estimate the power distribution that validates the performance of the proposed antenna. To verify the imaging capability of the proposed system, an array of 9 antennas and a realistic three-dimensional tissue-emulating experimental semi-solid head phantom are fabricated and measured. The backscattered signal is collected from different antenna positions and processed by the updated Iterative Correction of Coherence Factor Delay-Multiply-and-Sum beamforming algorithm to reconstruct the hemorrhage images. The reconstructed images in simulation and experimental environment demonstrate the feasibility of the proposed system as a portable platform to successfully detect and locate the hemorrhages inside the brain.

Experimental realization of tunable finite square optical arrays

Recently optical lattices containing optical vortices (OVs), which carry phase singularities and possess exotic optical properties, have attracted increasing attention due to their potential applications in optical trapping or light-matter interaction systems. Here, we propose a kind of arbitrary order alternated OV lattices with positive and negative topological charges ±n, which are named as the nth-order alternated OV lattices (NAOVLs), and we experimentally demonstrate their propagation properties. We find that such NAOVLs can generate finite square optical arrays with interesting patterns or defects near the focal plane or far-field Fraunhofer region. We further find a general law (although with some exceptions) about the number N of bright spots in finite optical arrays as the value n increases. The interference experiments confirm optical properties of such finite arrays close to the focal plane. Our results may have potential applications in particle trapping and experimental realizations of novel optical arrays for the interaction between special optical lattices and atoms (or molecules, ions, micro- or nano-particles).

A Multiband, Polarization-Controlled Metasurface Absorber for Electromagnetic Energy Harvesting and Wireless Power Transfer

A multiband, polarization-controlled energy harvesting metasurface is presented in this article for harvesting electromagnetic energy in the Wi-Fi bands. Inspired by the split-ring resonator (SRR), a metasurface of SRRs is designed by nesting multiple SRRs together. The novelty of the design lies in the controllable multiband polarization and adjustable absorption frequency, so as to achieve the active modulation of energy harvesting on the metasurface at different frequencies. The metasurface is composed of a periodic array of SRRs unit cells, an impedance-matched rectifier, and a load. Metasurface arrays and rectifier integration are proposed to reduce power losses, while the channels formed by the array enhance energy density and improve the ability to capture energy. Moreover, the design for the rectifier is capable of rectifying RF energy from multiple Wi-Fi bands simultaneously at low input RF power density. The finite array of <inline-formula> <tex-math notation="LaTeX">$5\times $ </tex-math></inline-formula> 5 SRRs absorber is fabricated and tested. Measurements in an anechoic chamber show that the fabricated prototype reaches the efficiency of 66.5&#x0025; at 2.4 GHz, 40.6&#x0025; at 5.2 GHz, 35.6&#x0025; at 5.8 GHz under transverse electric (TE) polarization, and 38.3&#x0025; at 5.3 GHz under transverse magnetic (TM) polarization when the incident power density is greater than 66 <inline-formula> <tex-math notation="LaTeX">$\mu \text{W}$ </tex-math></inline-formula>/cm².

Comparison of CBFM-Enhanced Iterative Methods for MoM-Based Finite Antenna Array Analysis

In this article, we compare different iterative techniques enhanced by the CBFM, which are used to analyze finite arrays of disjoint antenna elements. These are based on the stationary-type methods (Jacobi, Gauss–Seidel, and macroblock Jacobi), the nonstationary GMRES, and the hybrid alternating GMRES-Jacobi (AGJ) method that combines these two types. In each iteration, the reduced CBFM system is constructed based on the previous iterates, the solution of which is used to update the solution vector in the next iteration with improved accuracy. In this way, the convergence of the classical iterative techniques can be greatly improved. The convergence rates and computational costs of the CBFM-enhanced iterative methods are analyzed by considering several MoM-based problems. The GMRES-based method, which employs the block-Jacobi preconditioner, outperforms the other methods when the MoM matrix is ill-conditioned. For well-conditioned MoM matrices with reduced diagonal dominance due to the increased presence of the interelement coupling effects, the AGJ method or the methods based on the stationary-type iterations may require smaller computational effort to converge to the desired solution accuracy in comparison to the GMRES-based approach.

Robust edge modes in dislocated systems of subwavelength resonators

Robustly manipulating waves on subwavelength scales can be achieved by, first, designing a structure with a subwavelength band gap and, second, introducing a defect so that eigenfrequencies fall within the band gap. Such frequencies are well known to correspond to localized modes. We study a one-dimensional array of subwavelength resonators, prove that there is a subwavelength band gap, and show that by introducing a dislocation we can place localized modes at any point within the band gap. We complement this analysis by studying the stability properties of the corresponding finite array of resonators, demonstrating the value of being able to customize the position of eigenvalues within the band gap.

Hysterical effects in flow structure behind a finite array of cylinders under gradually varying unsteady flow conditions

Hysterical effects in flow structure behind a finite array of cylinders under gradually varying unsteady flow conditions

Invertible neural networks for reconstructing acoustic fields

Sound field reconstruction from finite measurement arrays provides a means to interpolate and extrapolate acoustic quantities that describe the field. By assuming a linear projection on a basis that follows a principled source propagation, one can recover accurate estimates of the aforementioned sound fields. However, the recovery of the basis coefficients relies on explicit models of which measurement noise and data incompleteness can profoundly affect the uncertainty of the solution. This work aims to estimate the distribution of the underlying pressure conditioned on the observations of the measured pressure in a room. A framework for approximate inference is adapted for sound field reconstruction by applying generative flow-based models and invertible neural network architectures. In particular, we use conditional normalising flows for fast conditional posterior estimation and uncertainty quantification. The model's evaluation is carried out using experimental data measured with a spherical array and compared to hierarchical Bayes with Markov Chain Monte-Carlo sampling.

Synchrotron radiation transmission by two coupled flat microchannel plates: new opportunities to control the focal spot characteristics.

An improved theoretical model to calculate the focal spot properties of coherent synchrotron radiation (SR) soft X-ray beams by combining and aligning two microchannel plates (MCPs) is presented. The diffraction patterns of the radiation behind the MCP system are simulated in the framework of the electrodynamical model of the radiation emission from two-dimensional finite antenna arrays. Simulations show that this particular optical device focuses the soft X-ray radiation in a circular central spot with a radius of ∼4 µm. The study points out that such MCP-based devices may achieve micrometre and sub-micrometre spot sizes as required by many applications in the soft X-ray range. Finally, based on experimental and theoretical results of the radiation transmission by this MCP-based device, a new method to characterize the spatial properties of brilliant SR sources is discussed.

Bragg Resonance and Phase Upshift of Linear Water Waves Excited by a Finite Periodic Array of Parabolic Trenches

The Bragg resonant reflection excited by a finite periodic array of parabolic trenches was analytically studied. First, the modified mild-slope equation (MMSE) with implicit coefficients was transformed into an ordinary differential equation with explicit coefficients through variable substitution. Second, an analytical solution to the MMSE was established in terms of the Frobenius series, and the convergence condition for the series solution was given. Finally, by means of the mass-conservation matching conditions, an analytical formula for the reflection coefficient was built. With the analytical formula, the effects of the number, the depth and the width of trenches on the peak value, the phase and the band width of the resonance, were investigated. The results show that, when the depth and width of trenches keep constant, and the number of trenches increases, the Bragg resonance peak value will increase up to 1, while the resonance bandwidth will narrow down and approach a fixed value. When the number and width of trenches keep constant, the Bragg resonance peak value will increase with the depth of trenches. When the number and depth of trenches keep constant, the Bragg resonance peak value will increase at first and then decrease with the width of trenches, which implies that there exists a certain width of trenches to make the Bragg resonance peak value reach the maximum, laying a theoretical base for the optimization of Bragg resonance vs. the trench width. Particularly, the phase upshift of the Bragg resonance wave reflection peak value recently observed over finite periodically arranged cycloidal trenches, was confirmed again over the parabolic trenches. That implies that, the phase upshift of the Bragg resonance reflection peak value is a common phenomenon excited by finite periodic trenches with arbitrary cross sections. Consequently, for sinusoidal ripples and periodic artificial bars, the phase of the Bragg resonance reflection will shift downward, while for an array of periodic trenches, regardless of the shape of the trench cross section, the phase of the Bragg resonance reflection will shift upward. In addition, starting from the initial definition of the Bragg resonance, the mathematical mechanism of the phenomenon of phase upshift is well explained.

On Subclasses of Recognizable ωω−Partial Array Languages

In this paper, the concepts of infinite partial array languages (ωω−partial array languages) and the classes of ωω−partial array languages, namely, local ωω−partial array languages, Buchi local ωω−partial array languages, and Muller local ωω−partial array languages are defined, and their related properties are studied. Furthermore, we introduce nondeterministic finite online tessellation h‐automata on ωω−partial array languages. In addition, we prove that the class of all adherences of finite local partial array languages is equal to the class of all local ωω−partial array languages and also prove that every ωω−regular partial array language is a projection of Buchi local ωω−partial array language.

Area efficient and high-speed Galois field multiplier for mobile edge computing devices

Mobile Edge Computing is one of the prominent technologies in 5G communication to improve throughput, scalability and reliability. In this work, area efficient and high-speed multipliers are implemented using finite field (Galois field) arithmetic which are widely utilised by edge computing devices. The performance of finite field multiplication operation is closely related to finite field elements representation. The proposed polynomial-based finite field bit parallel systolic array multiplier is able to achieve almost double the speed of existing multipliers. There is a considerable reduction in area and power for the proposed word-level normal basis finite field multiplier compared to the existing multipliers. The results clearly indicate that the proposed method improves the efficiency of finite field multipliers in terms of area, delay or power consumption. In order to process the real-time data efficiently, both the local computing and data offloading are carried out in developing a joint computation algorithm. The trade-off analysis between local computing and data offloading shows that local computing plays a more important role when the data size is small, but data offloading is preferred when the data size increases.

Optimization of Coupled Periodic Antenna Using Genetic Algorithm with Floquet Modal Analysis and MoM-GEC

In this paper Genetic Algorithm has been integrated with Fouquet modal analysis to optimize radiation pattern of coupled periodic antenna. Floquet analysis is used with MoM-GEC (Moment-Generalized Equivalent Circuit) method to study a finite periodic array with uniform amplitude and linear phase distribution. This method is very advantageous for studying large antenna array since it considerably reduces the computation time and the number of operations. In this way, Genetic algorithm is introduced and combined with Floquet analysis to optimize the radiation pattern distribution of this coupled periodic antenna. The goal of the optimization is to provide a better radiation characteristic for the coupled periodic antenna with maximum side lobe level reduction.

Dual-Slot Cavity Antenna for mm-Wave Beamforming Array

A cavity-fed, dual-slot element and its 4-element linear array configurations for beam-steering applications at 28 GHz are described. The element cavity is formed from rectangular substrate integrated waveguide (SIW), perturbed at one of its corners to excite dual slots for increasing the impedance bandwidth. With a mobile terminal in mind, we look to both classical array principles and to the available theories for finite arrays with mutual coupling, to help guide the design. The impact of the finite ground-plane required to support the slot elements and array is investigated by simulation, including the impact on the patterns of using a cellphone chassis as a platform. A chassis-born 4-element (8 slots) configuration, suitable for beamforming in 28 GHz 5G networks is demonstrated for both linear polarizations. The simulation results are supported by pattern measurements of prototypes, a challenging task at 28 GHz.

Packable and Readily Deployable Tightly Coupled Dipole Array (TCDA) With Integrated Planar Balun

To overcome the limited payload dedicated to onboard antennas for CubeSat/SmallSat applications, this paper presents a novel, foldable, dual-polarized Tightly Coupled Dipole Array (TCDA). In comparison to previous vertical feeds used for TCDAs, this array integrates a planar microstrip balun feed to enable foldability. The proposed array attains 5.4:1 (0.6-3.20 GHz) impedance bandwidth with VSWR < 3 at broadside and scans down to 45∘ at all azimuth planes. Notably, a substrate-integrated in-plane folding mechanism based on Lamina Emergent Torsion (LET) joints is employed to achieve foldability coupled with a simple fabrication process. The average simulated radiation efficiency was 95% across the band. A 5 × 8 prototype array was fabricated and tested to verify the finite array’s foldability, bandwidth, and gain performance. This prototype achieves 80% one-dimensional size reduction, yielding 60% overall volume reduction. Consequently, the array prototype can be folded and stowed in a compact volume of 1.4U ( 25 cm× 7.2 cm× 9 cm ).

Low-RCS Broadband Phased Array Using Polarization Selective Metamaterial Surface

In this letter, a broadband wide-scanning phased array with radar cross-section (RCS) reduction performance is presented. The proposed phased array is composed of two types of antenna elements: Ant-0 and Ant-1. Ant-0 and Ant-1 are the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</i> -polarized dipole antennas that have almost the same radiation performance over the frequency range of 6.5–12 GHz. Ant-1 is obtained by codesigning Ant-0 with a polarization selective metamaterial surface (PSMS), and the PSMS has little effect on the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</i> -polarized radiation performance. As of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i> -polarized incident waves, the phase difference of the reflected waves on Ant-0 and Ant-1 is around 180° over the frequency range of 3.74–15.1 GHz; thus, a broadband scattering cancelation is achieved. A 5×16 finite array is fabricated and measured, and the measured results show great agreement with the simulated results. The fabricated phased array antenna has the ability to scan to ±60° with active VSWR < 3 over the frequency range of 6.5–12 GHz and over the frequency range of 3.9–15.1 GHz, and ultrabroadband monostatic RCS reduction is achieved.

Floquet Spectral Almost-Periodic Modulation of Massive Finite and Infinite Strongly Coupled Arrays: Dense-Massive-MIMO, Intelligent-Surfaces, 5G, and 6G Applications

In this study, we introduce a new formulation based on Floquet (Fourier) spectral analysis combined with a spectral modulation technique (and its spatial form) to study strongly coupled sublattices predefined in the infinite and large finite extent of almost-periodic antenna arrays (e.g., metasurfaces). This analysis is very relevant for dense-massive-MIMO, intelligent-surfaces, 5G, and 6G applications (used for very small areas with a large number of elements such as millimeter and terahertz waves applications). The numerical method that is adopted to model the structure is the method of moments simplified by equivalent circuits MoM GEC. Other numerical methods (such as the ASM-array scanning method and the windowing Fourier method) used this analysis in their kernel to treat periodic and pseudo-periodic (or quasi-periodic) arrays.