Finite Array Research Articles

Lasing from Doubly Degenerate Bound States in the Continuum.

This paper reports dual-mode vortex lasing with a topological charge of -2 via doubly degenerate bound states in the continuum. We patterned a photonic crystal slab with hexagonal TiO2 nanoparticles arranged in a hexagonal lattice to support doubly degenerate bound states in the continuum at the Γ point, and the finite array was truncated to have a square boundary. Because emission from bound states in the continuum at the Γ point is forbidden, lasing emerges at off-Γ points, where the double degeneracy is lifted, resulting in two lasing peaks close in wavelength. The coherence time of vortex lasing is about 1.4 ps under pulsed pumping with a width of 75 fs. Polarization- and angle-resolved spectral measurements reveal that the two lasing peaks show orthogonal polarization states.

Scour around tripod/tripile foundations used in offshore wind turbines: use of a finite array of cylinders as tripod piles

Scour around tripod/tripile foundations used in offshore wind turbines: use of a finite array of cylinders as tripod piles

Water-tank metabarrier for seismic Rayleigh wave attenuation.

An innovative concept of metabarrier is presented for seismic Rayleigh wave attenuation, which consists of a periodic array of cylindrical water tanks acting as resonant units above the soil surface. A pertinent theoretical framework is developed and implemented in COMSOL Multiphysics. The framework treats the dynamics of the water tank by a well-established three-dimensional linear, pressure-based model for fluid-structure interaction under earthquake excitation, accounting for the flexibility of the tank wall; furthermore, the soil is idealized as a homogeneous and isotropic medium. Floquet-Bloch dispersion analysis of the unit cell demonstrates the presence of relevant band gaps in the low-frequency range below 20 Hz and in the higher frequency range as well. The dispersion analysis is validated by comparison with the frequency-domain analysis of a soil domain with a finite array of water tanks. The band gaps are of interest to attenuate seismic Rayleigh waves and, more generally, Rayleigh waves caused by other ground vibration sources such as road or railway traffic. The water-tank resonant units are readily tunable by varying the water level, which allows changing opening frequencies/widths of the wave attenuation zones. This is a remarkable advantage over alternative seismic metamaterials that, in general, are not designed to be tunable.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

A Study on a Compact Double Layer Sub-GHz Reflectarray Design Suitable for Wireless Power Transfer

The paper presents a novel small-footprint varactor diode-based reconfigurable reflectarray (RRA) design and investigates its power reflection efficiency theoretically and experimentally in a real-life indoor environment. The surface is designed to operate at 865.5 MHz and is intended for simultaneous use with other wireless power transfer (WPT) efficiency-improving techniques that have been recently reported in the literature. To the best of the authors’ knowledge, no RRA intended to improve the performance of antenna-based WPT systems operating in the sub-GHz range has been designed and studied both theoretically and experimentally so far. The proposed RRA is a two-layer structure. The top layer contains electronically tunable phase shifters for the local phase control of an incoming electromagnetic wave, while the other one is fully covered by metal to reduce the phase shifter size and RRA’s backscattering. Each phase shifter is a pair of diode-loaded 8-shaped metallic patches. Extensive numerical studies are conducted to ascertain a suitable set of RRA unit cell parameters that ensure both adequate phase agility and reflection uniformity for a given varactor parameter. The RRA design parameter finding procedure followed in this paper comprises several steps. First, the phase and amplitude responses of a virtual infinite double periodic RRA are computed using full-wave solver Ansys HFSS. Once the design parameters are found for a given set of physical constraints, the phase curve of the corresponding finite array is retrieved to estimate the side lobe level due to the finiteness of the RRA aperture. Then, a diode reactance combination is found for several different RRA reflection angles, and the corresponding RRA radiation pattern is computed. The numerical results show that the side lobe level and the deviation of the peak reflected power angles from the desired ones are more sensitive to the reflection coefficient magnitude uniformity than to the phase agility. Furthermore, it is found that for scanning angles less than 50°, satisfactory reflection efficiency can be achieved by using the classical reactance profile synthesis approach employing the generalized geometrical optics (GGO) approximation, which is in accord with the findings of other studies. Additionally, for large reflection angles, an alternative synthesis approach relying on the Floquet mode amplitude optimization is utilized to verify the maximum achievable efficiency of the proposed RRA at large angles. A prototype consisting of 36 elements is fabricated and measured to verify the proposed reflectarray design experimentally. The initial diode voltage combination is found by applying the GGO-based phase profile synthesis method to the experimentally obtained phase curve. Then, the voltage combination is optimized in real time based on power measurement. Finally, the radiation pattern of the prototype is acquired using a pair of identical 4-director printed Yagi antennas with a gain of 9.17 dBi and compared with the simulated. The calculated results are consistent with the measured ones. However, some discrepancies attributed to the adverse effects of biasing lines are observed.

Collimated beam formation in 3D acoustic sonic crystals

We demonstrate strongly collimated beam formation, at audible frequencies, in a three-dimensional acoustic phononic crystal where the wavelength is commensurate with the crystal elements; the crystal is a seemingly simple rectangular cuboid constructed from closely-spaced spheres, and yet demonstrates rich wave phenomena acting as a canonical three-dimensional metamaterial. We employ theory, numerical simulation and experiments to design and interpret this collimated beam phenomenon and use a crystal consisting of a finite rectangular cuboid array of 4×10×10 polymer spheres 1.38 cm in diameter in air, arranged in a primitive cubic cell with the centre-to-centre spacing of the spheres, i.e. the pitch, as 1.5 cm. Collimation effects are observed in the time domain for chirps with central frequencies at 14.2 kHz and 18 kHz, and we deployed a laser feedback interferometer or Self-Mixing Interferometer – a recently proposed technique to observe complex acoustic fields—that enables experimental visualisation of the pressure field both within the crystal and outside of the crystal. Numerical exploration using a higher-order multi-scale finite element method designed for the rapid and detailed simulation of 3D wave physics further confirms these collimation effects and cross-validates with the experiments. Interpretation follows using High Frequency Homogenization and Bloch analysis whereby the different origin of the collimation at these two frequencies is revealed by markedly different isofrequency surfaces of the sonic crystal.

Experimental verification of nonreciprocal electromagnetic metasurface in a finite‐size array

AbstractThis paper presents experimental verification results for a finite‐sized array of a simple non‐reciprocal metasurface elements. The metasurface elements consists of ferrite loaded metal patches. Experimental results demonstrate nonreciprocity, achieving isolation exceeding 20 dB at 6.4 GHz in a 2×2 array. Additionally, these findings are compared with simulation results for a 4×4 array to validate its practicality in a finite array setting.

Interface states and optical coupling functionalities in the super-SSH lattices

We theoretically address the coupling between trimer lattices and reveal the existence of stable multiple edge and interface states. It is shown the superlattice can provides a tunable number of topologically protected edge and interface states depending on the coupling strength and topological phase of the connecting lattices. Dynamics and transport properties of interface states are also investigated, Due to the interference of linear modes with different propagation constants, stable oscillations resulted from the coupling of interface states in finite trimerized waveguide arrays are observed and can give rise to optical coupling functionalities, including directional coupling, beam splitting and beam oscillator.

A Wide-Band Low-Profile Antenna for a High-Integration Phased Array System.

In this paper, a wide-band, low-profile antenna is presented for a high-integration phased array system. The proposed antenna, implemented using a tightly coupled array, operates over roughly the X-K frequency band and is performant at 8 GHz-18.5 GHz. The antenna can scan to ±60 degrees in both the E- and H-planes. Compared to previous tightly coupled antennas with smaller element spacing, the antenna in this paper reaches 9.4 mm, which corresponds to 0.58 λ of high frequency, suitable for engineering application conditions in production. The antenna can be soldered to BGA T/R chips in this space. Additionally, to facilitate flexible assembly for large arrays, the antenna is manufactured modularly using four elements and its parasitic radiation is analyzed. Then, a method for repressing parasitic radiation is presented. Finally, the antenna is fabricated and measured in a microwave chamber, exhibiting an excellent pattern and scanning radiation. The measured performance agrees with the full-wave finite array simulations.

Dynamic programming with meta-reinforcement learning: a novel approach for multi-objective optimization

Multi-objective optimization (MOO) endeavors to identify optimal solutions from a finite array of possibilities. In recent years, deep reinforcement learning (RL) has exhibited promise through its well-crafted heuristics in tackling NP-hard combinatorial optimization (CO) problems. Nonetheless, current methodologies grapple with two key challenges: (1) They primarily concentrate on single-objective optimization quandaries, rendering them less adaptable to the more prevalent MOO scenarios encountered in real-world applications. (2) These approaches furnish an approximate solution by imbibing heuristics, lacking a systematic means to enhance or substantiate optimality. Given these challenges, this study introduces an overarching hybrid strategy, dynamic programming with meta-reinforcement learning (DPML), to resolve MOO predicaments. The approach melds meta-learning into an RL framework, addressing multiple subproblems inherent to MOO. Furthermore, the precision of solutions is elevated by endowing exact dynamic programming with the prowess of meta-graph neural networks. Empirical results substantiate the supremacy of our methodology over previous RL and heuristics approaches, bridging the chasm between theoretical underpinnings and real-world applicability within this domain.

Heat Bath in a Quantum Circuit.

We discuss the concept and realization of a heat bath in solid state quantum systems. We demonstrate that, unlike a true resistor, a finite one-dimensional Josephson junction array or analogously a transmission line with non-vanishing frequency spacing, commonly considered as a reservoir of a quantum circuit, does not strictly qualify as a Caldeira-Leggett type dissipative environment. We then consider a set of quantum two-level systems as a bath, which can be realized as a collection of qubits. We show that only a dense and wide distribution of energies of the two-level systems can secure long Poincare recurrence times characteristic of a proper heat bath. An alternative for this bath is a collection of harmonic oscillators, for instance, in the form of superconducting resonators.

Low-Profile Differentially-Fed Tightly-Coupled Dipole Array

Introduction. Tightly coupled dipoles currently belong to one of the most popular types of antenna arrays. Their main advantages include an electrically low-profile height, the ability to scan the beam across a wide sector of angles without the onset of scan blindness, and a low level of cross-polarization. In recent years, the number of publications on the topic of antenna arrays of this type has increased significantly. The authors have paid sufficient attention to baluns included in the antenna array elements. However, the possibility of implementing a differentially-fed scheme in antenna arrays of this type remains poorly studied. This makes the study of this subject especially relevant in the development of radio devices where such feed technique is preferable.Aim. Differentially-fed tightly-coupled dipole array design and study.Materials and methods. The following materials were used to create the prototype: copper sheet, ceramic glass substrate ST-50-1, dielectric RO3003. A numerical study of the characteristics was carried out in the ANSYS HFSS environment; an experimental study of the prototype was carried out in an anechoic chamber using an automated measuring complex and a vector network analyzer.Results. The results of designing a planar antenna array of tightly-coupled dipoles for the X-band are presented. In the antenna array, each of the dipole arms is fed using a separate coaxial cable, while the two arms of one dipole are fed out-of-phase. The results of a numerical study of the characteristics of an 8 × 8 antenna array made from the developed elements are presented. Across the range from 6.5 to 12.25 GHz, the average active VSWR does not exceed 3, while the gain varies from 21.5 to 25.7 dBi. The possibility of beam scanning in a sector of angles up to ±45° is shown. The results of an experimental study of the radiation characteristics and matching of the prototype of a single element are presented.Conclusion. The importance of taking into account the effects that arise at the edges of finite antenna arrays during simulations is shown. The feasibility of manufacturing and measuring antenna array prototypes with a large number of elements is experimentally confirmed. The proposed element design demonstrates the possibility of implementing the differentially-fed scheme in tightly coupled antenna arrays.

Quantitative Expression of the Modified Bragg's Law for Bragg resonances of water waves excited by five types of artificial bars

For Class I Bragg resonance excited by five types of finite periodic array of widely spaced bars (rectangular, parabolic, rectified cosinoidal, trapezoidal, and triangular bars), the average phase velocity between any two adjacent bars in each type of bar field has been specifically calculated by employing a mathematical transformation, and therefore, the excitation condition of Class I Bragg resonance excited by each bar field is clarified and the modified Bragg's law established by Xie and Liu becomes a quantitative form. On one hand, if the incident surface wavelength, L, is fixed in advance, then according to the excitation condition, we can directly obtain the critical bar spacing, d, at which Class I Bragg resonance occurs. On the other hand, if the bar spacing, d, is fixed, then according to the excitation condition, we can use an iteration scheme to find out the critical surface wavelength, L, at which Class I Bragg resonance will be excited. In comparison with existing experimental, numerical, and analytical results of Bragg resonance excited by the five types of bar fields, it is shown that the modified Bragg's law is much more accurate than the Bragg's law, and the phenomenon of phase downshift can be well explained. In the linear long-wave limit, owing to the simple dispersion relation, the modified Bragg's law becomes an explicit expression and coincides with Liu's approximate law very well, although the former is a straight line segment while the latter is a curved line segment. Finally, it is shown that the phase downshift of Bragg resonance becomes more significant as the cross-sectional area of bars increases.

Active elastic metamaterials with equidistant solely resonant bandgaps

Elastic metamaterials are man-made structures with properties that transcend naturally occurring materials. One predominant feature of elastic metamaterials is locally resonant bandgaps, i.e., frequency ranges at which wave propagation is blocked. Locally resonant bandgaps appear at relatively low frequency and arise from the existence of periodically placed mechanical local resonators. Typically, elastic metamaterials exhibit both locally resonant and Bragg-scattering bandgaps, which can generally be different in width and frequency ranges. This paper proposes two designs of active elastic metamaterials that only exhibit locally resonant bandgaps, which are infinite in number, evenly spaced in the frequency spectrum, and identical in width. The mathematical model is established using the transfer matrix method and synthesis of locally resonant bandgaps is achieved via an active elastic support with carefully designed frequency-dependent stiffness. A single unit cell of each proposed metamaterials is thoroughly studied, and its dispersion relation is derived analytically, along with the periodically repeating bandgap limits and widths. Following the dispersion analysis and bandgap parametric studies, finite arrays of the proposed metamaterials are considered, and their frequency response is calculated to verify the analytical predictions from dispersion analyses.

A Multiobjective Array Beamforming Method for Arrays of Flexible Shape

High-performance beamforming incorporating multiple objectives for large-scale antenna arrays becomes increasingly important to improve the capacity and efficiency of wireless communication systems. The speed of synthesizing a desired beam pattern is critical in wireless communications systems to adapt to highly dynamic wireless channels. A modified particle swarm optimization (PSO) algorithm for synthesizing array beam patterns is proposed in this study. The initial positions of particles in PSO are designated following a Taylor distribution instead of being given uniformly distributed random values as in the classical PSO algorithm. The fitness functions are defined to include multiple objectives represented by producing multiple main lobes with customized deep and broadened nulls. Several scenarios have been established to examine the feasibility of the proposed algorithm. Moreover, the performance of the proposed algorithm is compared with those of the ones based on the classical PSO. A significant performance improvement for obtaining beamforming coefficients has been achieved. The robustness of the proposed algorithm is demonstrated further by applying it to a finite array on a curved surface for beamforming.

Inertia Modulated Meta-Structure With Time-Varying Inertia Amplification

Abstract In this work, a new inertia modulated meta-structure is proposed to enable time-dependent inertia parameters, and thereby realize non-reciprocal wave propagation via spatiotemporal modulation. The designed cell structure is composed of an oscillatory disk and a mass that slides in a guide embedded in the disk frictionlessly with prescribed motion. Effective moment of inertia and damping coefficients of the rocking motion of the cell structure are rendered time-dependent due to the inertia and Coriolis forces of the periodically sliding mass, which allows us to implement the expected spatiotemporal modulation upon a super-cell. Non-reciprocal propagation behavior of the proposed meta-structure is verified via the theoretical solution of the dispersion relation as well as the dynamic response of a finite array. Effects of modulation parameters, including the frequency, amplitude, and phase, on the unidirectional propagation characteristic are thoroughly investigated.

Bragg reflection of linear shallow-water waves by an array of widely spaced trapezoidal bars on a fringing reef flat

A closed-form solution to the linear shallow-water wave equation for wave reflection by a finite periodic array of widely spaced trapezoidal bars on a fringing reef flat is presented. It is shown that, when the total number, height, or top width of the trapezoidal bars increases, the strength of the Bragg resonance increases but the downward shift of the resonance phase becomes more pronounced. When the width of the reef face increases or when the reef face changes from a concave profile to a convex profile, the strength of the Bragg resonance decreases and the downward shift of the resonance phase also becomes more pronounced. Especially, it is found that the location of trapezoidal bars plays an important role in the strength and occurrence condition of the Bragg resonant reflection. Finally, the optimal collocation of the location and width of trapezoidal bars is investigated. Considering both construction cost and reflecting capacity, the relative width is recommended to be within 0.4≤wb/d≤0.6 and the distance from the reef edge to trapezoidal bars is suggested to be equal to the spacing of trapezoidal bars.

Generative design of graded metamaterial arrays for dynamic response modulation

Mechanical metamaterials (MMs) are micro-structured systems that have long attracted research as well as application interests due to their exotic dynamic functionalities and properties not seen in ordinary materials. Graded MM arrays further enrich the scope of achievable dynamic behavior by employing non-periodic media. Designing such systems is particularly challenging due to the unclear design-performance relationship as well as the heavy computational burden. In this work, we aim to control the time domain response patterns of finite MM arrays and introduce a data-driven design approach that addresses the current challenges. A high-fidelity reduced order modeling (ROM) method is incorporated with statistical learning approaches to realize data generation and physics validation with minimal effort. A variational autoencoder (VAE) is trained to learn the design-performance relation and is used to retrieve classes of design configurations associated with a desired performance. An example application for impact mitigation is shown, and the designed MM arrays exhibit superior protection performance. The combined ROM-VAE approach presents a systematic toolset for designing graded MM arrays with modulated responses, capable of a broad spectrum of tasks such as fast prototyping, inverse generation, and design principle identification.

ON THE FEATURES OF THE WORK OF A FINITE ACOUSTIC ANTENNA FORMED BY FREE-FLOODING CYLINDRICAL TRANSDUCERS

The problem of sound radiation by a finite antenna array formed by free-flooding cylindrical transducers with flanges is considered. Two variants for the antenna array are considered: the same electrical voltage is supplied to the electrodes of all transducers and a different voltage is applied to them in order to equalize the oscillatory speeds of the transducers. Numerical data for the basic electrical, mechanical and acoustic characteristics of the antenna array are analyzed, taking into account the acoustic interaction of the transducers.

On the Hybrid Modelling of Rigid Sonic Crystal Embedded in Plenum Chamber at Low Frequencies Using the Effective Medium Approach and Finite Element Method

This study explores the application of homogenization schemes in modelling acoustic wave propagation in a finite array of circular scatterers embedded into a 2D cavity. The cavity is integrated into the 2D waveguide attached to the cavity inlet and outlet. Square-lattice sonic crystal (SC), composed of rigid and radially symmetric circular cylinders, is used to represent the finite array in this study. The model is aimed at informing the novel designs of plenum windows with superior soundproofing performance. The sound transmission performance is analysed with hybrid numerical simulation using the Finite Element Method (FEM) and homogenization scheme. A theoretical homogenization method based on the Effective Medium Approach (EMA) is reviewed and implemented on the modelling of the SC array inside the cavity at low frequencies and then implemented in FEM. Comparison of the transmission loss (TL) reveals a high degree of matching between settings with and without homogenization at low-frequency range. It is observed that performance of the hybrid model maintains a high degree of matching provided the cavity modes are dominated by a single characteristic scale in the low frequency. This includes the case of a narrow plenum chamber with only a single cylinder placed inside the cavity with a width of one lattice constant. This homogenization method is proven to be more computationally efficient in FEM compared to the modelling of exact geometry of the problem.

Analysis of geometric defects in square locally resonant phononic crystals: A comparative study of modeling approachesa).

Phononic crystals can develop defects during manufacturing that alter the desired dynamic response and bandgap behavior. This frequency behavior change can enable successful defect inspection if the characteristic defect response is known. In this study, the behavior of a defective square unit cell comprising a freed and shortened leg is studied using a wave finite element method and an approximate continuous-lumped model to elucidate the defect induced qualitative dynamical features. These metrics are a computationally inexpensive alternative to modeling a defective unit cell within a large pristine array entirely in finite elements. The accuracy of these models is validated by comparing the result to a full finite element model. The impact of a shortened unit cell leg on the behaviors of an infinite array of defective cells and a finite array with a single defect are successfully predicted through dispersion curves and frequency response functions, respectively. These methods reveal defect-induced modes that split the local resonance bandgap of the pristine cell, as well as new anti-resonances resulting from the shortened leg. The study uses both approaches to evaluate the effect of defects in complex phononic crystal geometries and provides a comparative evaluation of the results of each model.