Array Beam Research Articles

An improved multiobjective evolutionary algorithm based on decomposition approach and its application in antenna array beam pattern synthesis

AbstractAntenna arrays can enhance the performance and reduce the overhead of the wireless communication systems. However, the beam pattern synthesis of antenna arrays are difficult problems since the optimization properties are usually trade‐offs that affect each other. In this paper, we formulate a multiobjective beam pattern optimization problem (MBPOP) to simultaneously reduce the maximum sidelobe level (SLL) and achieve the nulls of the antenna array beam pattern. The multiobjective evolutionary algorithm based on decomposition (MOEA/D) is a general and effective algorithm to solve the MOPs. However, it may be easy to lose population diversity and converge to local optimum. To overcome the issues above, we propose an improved MOEA/D (IMOEA/D) to deal with the formulated MBPOP. IMOEA/D introduces the normal distribution crossover operator (NDX), Lévy flight strategy and Euclidean distance‐based solution selection mechanism to enhance the performance of conventional MOEA/D to make it more suitable to solve the formulated MBPOP. Experiments are conducted and the results indicate that the proposed IMOEA/D has a better performance in terms of the convergence rate and population diversity compared to other algorithms for solving the formulated MBPOP.

Statistical properties of a controllable rotating elliptical Gaussian Schell-model vortex optical coherence lattice

A new source for a controllable rotating elliptical Gaussian Schell-model vortex optical coherence lattice with both spiral phase and rotation phase is introduced. It is shown that both the irradiance distribution of lattice and the degree of coherence (DOC) rotate synchronously in the same direction within a certain propagation, whose rotation velocity, direction and maximum angle all are controllable. Specifically, the rotation parameters broaden the transverse diffusion of the beam mean-squared width. Both the intensity lattice with solid or hollow beamlets and the splitting direction of the partially coherent vortex sub-beams can be controlled by adjusting the coherence widths in the source plane. Meanwhile, the lattice constant can flexibly control the distance and number of beamlets and the lattice periodicity of the source DOC profile. The effects of atmosphere turbulence parameters on the vortex beam array structure and the variation trend of the DOC are analyzed. Our results manifest such beam may be applied in particles trapping and rotating, and be beneficial for robust optical communications in turbulence.

Fluid dynamics investigation of a large array

The influence of surrounding fluid on a large array of oscillators is important to study for applications in fields such as medicine, biology, and atomic force microscopy. In the present study, we investigate a large array of cantilever beams oscillating in an unbounded fluid to better understand the fluid dynamic behavior. The two-dimensional boundary integral method is applied to analyze a large array of cantilever oscillators using an analytical solution approach for the unsteady Stokes and continuity equations. We analyze array sizes from 5 to 50 beams by comparing hydrodynamic transverse force and velocity profiles for two different velocity configurations. Including the interactions of neighbor and non-neighbor members leads to distinct array effects. With an increase in the number of oscillators in an array, the array effect influences the overall dynamics. Furthermore, to justify the influence of an array effect, the hydrodynamic loading is compared to the same and varying array surface area of different array sizes. Our analysis and new findings strengthen our hypothesis that the predictions of existing knowledge obtained from small-size arrays and coupled oscillators cannot readily inform dynamic predictions of large-size arrays. The underlying reason being the additional array effect(s) which are not present in a small-size array. The novelty of this paper is the ability to model such large arrays and investigate the array effect in an unbounded fluid.

Energy harvesting from a floor structure based on multiple piezoelectric transducer beams

In this paper, an energy harvesting floor based on piezoelectric transducers is studied. A structure with multiple layers of piezoelectric beams is designed. Different striking frequencies are studied. Fourier transform is applied to analyze the frequency characteristic of the output voltage. Experiments are explored to find out the optimal external load resistance for maximum output power. The experimental results show that, with three piezoelectric transducers in a beam array, and a stroke of 4 mm at the striking frequency of 1.263 Hz, the maximum output power is 733.5 µW.

Two-step maskless fabrication of compound fork-shaped gratings in nanomultilayer structures based on chalcogenide glasses.

We demonstrate an easy two-step maskless method for the fabrication of so-called compound fork-shaped gratings in nanomultilayer structures (NMLSs) based on chalcogenide glasses. Such elements allow one to generate different configurations of optical vortex (OV) beams with given topological charges (TCs). The used NMLS is particularly interesting because it enables one to realize the direct one-step writing of the surface relief without selective etching. We show that it is possible to control TCs of the generated OV beam arrays, their locations, and intensity. The proposed approach can easily be adapted to the fabrication of compound diffractive gratings performing the desired one- and two-dimensional generation and splitting of other structured laser beams.

An improved biogeography‐based optimization approach for beam pattern optimizations of linear and circular antenna arrays

AbstractAntenna array makes an increasingly valuable contribution to various fields of communications. The beam pattern synthesis is one of the significant properties of antenna array. In this article, suppressing the maximum sidelobe levels (SLLs) of different antenna arrays is our main objective. Specifically, we first formulate the beam pattern optimization problems of the linear antenna array (LAA) and circular antenna array (CAA), respectively, and propose an improved biogeography‐based optimization (IBBO) approach to tackle the issue. IBBO introduces the hybrid migration and hybrid mutation operators by adopting several improved factors to strengthen the effect of conventional biogeography‐based optimization (BBO) algorithm. Emulate experiments are built to evaluate the performance of the IBBO for dealing with the formulated antenna array beam pattern optimization problems comprehensively.

Thermal blooming effect and the scaling laws of partial spatially coherent beam array propagating through the atmosphere

The thermal blooming effect and the scaling laws of partially coherent beam (PCB) array propagating in the atmosphere are studied. The four-dimensional (4D) computer code of time-dependent propagation to simulate PCB array through the turbulent atmosphere is designed. Based on numerical simulation, the propagation properties of PCB array are investigated in detail. It is shown that, as the spatial coherence parameter β decreases, the relative beam width increases and the thermal blooming effect becomes more severe. However, the change of the energy Strehl ratio (SRE) versus spatial coherence parameter β is not monotonic because the energy is concentrated on the main lobe for fully coherent beam array. Besides, the scaling laws to estimate the thermal blooming effects of PCB array are investigated. The modified expression of the distortion parameter Nd of a focused PCB array is derived, which is efficient to evaluate the strength of the thermal blooming effects.

Tuning of topological interface modes in an elastic beam array system with inerters

Topological phononic crystals in the mechanical setup became a topic of great interest owing to their applicability in various engineering systems such as waveguides or vibration isolation devices. If such systems are composed of elastic structures, they are usually characterized by a bulk-edge correspondence where the geometrical and material properties can play important role in the existence of stable surface and boundary modes. This work investigates the band transition and topological interface modes in a beam array system, where two sub-lattices of vertically aligned, parallel, and elastically coupled beams are connected at the chain center. To illustrate the existence of interface modes and understand their behavior, the corresponding eigenvalue problem is solved and frequency response function is sought for the system with a finite number of unit cells. Localization of the interface modes is demonstrated based on the steady-state responses of the beam array system to harmonic excitation. The effects of introduced defect masses and inerters on interface states are studied separately. It is revealed that the introduction of a small defect mass in the form of concentrated mass attached to some beam in the system does not affect the interface modes within the observed frequency range. On the other side, inerters produce frequency shifts towards lower values, which even in the case of small values of the inerter parameter causes the interface modes to vanish or even to appear inside another frequency band gap. The obtained results give an insight into the influence of inerter devices and their mass amplification effect on the interface states in complex periodic elastic systems. It also investigates the possibility to tune interface modes without significantly affecting the main band structure properties of the system.

Generation of Airy beam arrays in real and K spaces based on a dielectric metasurface.

Airy beams are widely used in various optical devices and optical experiments owing to their unique characteristics such as self-acceleration, self-recovery, and non-diffraction. Here we designed and demonstrated a metasurface capable of encoding two phase distributions independently in dual circular polarization channels. We experimentally observed the generated Airy beam arrays loaded on the metasurface in the real and K spaces. Compared with the traditional method, such method provides a more efficient solution to generate large capacity Airy beam arrays with switchable working modes in the broadband spectrum. The results may pave the way for the integration and miniaturization of micro-nano devices and provide a platform for information processing, particle manipulation, space-time optical wave packets, and Airy lasers.

Focal characteristics of partially coherent rectangular array beams focused by a bifocal lens system

The propagation characteristics of rectangular array beams through a bifocal lens system have been studied, including irradiance distribution and focal shift. By using Collins formula and diffraction integral, the analytical expressions for irradiance distributions of the array beams have been derived. The results show that the irradiance distributions exhibit diversified variations due to the different focal length in two directions, and the changes of the irradiance distributions for the correlated and uncorrelated superposition array beam are different. There are usually two maxima of the axial irradiance on propagation. The focal shifts demonstrate that the axial maximum irradiance near the larger focal distance is displaced toward the lens system when the Fresnel number is smaller. The focal shift results from the competition of the two irradiance maxima, which can lead to a permutation of the focal points. This work would be useful for the practical design and use of the bifocal lens in focusing array beams.

Velocity Structure of Density Currents Propagating over Rough Beds

In most practical cases, density-driven currents flow over surfaces that are not smooth; however, the effects of bottom roughness on these currents have not been fully understood yet. Hence, this study aims to examine the velocity structure of density currents while propagating over rough beds. To this end, alterations in the vertical velocity profiles within the body of these currents were investigated in the presence of different bottom roughness configurations. Initially, laboratory experiments were carried out for density currents flowing over a smooth surface to provide a baseline for comparison. Thereafter, seven bottom roughness configurations were tested, encompassing both dense and sparse bottom roughness. The bottom roughness consisted of repeated arrays of square cross-section beams covering the full channel width and perpendicular to the flow direction. The primary results indicate that the bottom roughness decelerated the currents and modified the shape of velocity profiles, particularly in the region close to the bed. Additionally, a critical spacing of the roughness elements was detected for which the currents demonstrated the lowest velocities. For the spacings above the critical value, increasing the distance between the roughness elements had little impact on controlling the velocity of these currents. Moreover, using dimensional analysis, equations were developed for estimating the mean velocities of the currents flowing over various configurations of the bottom roughness. The findings of this research could contribute towards better parameterization and improved knowledge of density currents flowing over rough beds. This can lead to a better prediction of the evolution of these currents in many practical cases as well as improved planning and design measures for the control of such currents.

Compact solid-state optical phased array beam scanners based on polymeric photonic integrated circuits

Optical phased array (OPA) devices are being actively investigated to develop compact solid-state beam scanners, which are essential in fields such as LiDAR, free-space optical links, biophotonics, etc. Based on the unique nature of perfluorinated polymers, we propose a polymer waveguide OPA with the advantages of low driving power and high optical throughput. Unlike silicon photonic OPAs, the polymer OPAs enable sustainable phase distribution control during beam scanning, which reduces the burden of beamforming. Moreover, by incorporating a tunable wavelength laser comprising a polymer waveguide Bragg reflector, two-dimensional beam scanning is demonstrated, which facilitates the development of laser-integrated polymeric OPA beam scanners.

Propagation properties of phase-locked radially-polarized vector fields array in turbulent atmosphere.

Owing to the increasing demand for information transmission, the information capacity of free-space optical communications must be increased without being significantly affected by turbulence. Herein, based on a radially-polarized vector field array, analytical formulae for three parameters are derived: average intensity, degree of polarization, and local states of polarization (SoPs). Propagation properties varying with propagation distance, strength of turbulence, beam waist, and beamlet number are investigated. In particular, the results show that the sign of local SoPs on different receiver planes is consistent with that of the source field, and that the SoPs remain constant at specific locations as the propagation distance increases; hence, the effect of turbulence on local SoPs is slight. Meanwhile, three different SoPs, i.e., linear, right-handed, and left-handed rotation polarizations, appear at corresponding locations, thereby enabling the channel capacity to be increased. This study may not only provide a theoretical basis for vector beam array propagation in a turbulent environment, but also propose a feasible solution for increasing the channel capacity and reliability to overcome challenges in a free-space link. Additionally, this study may benefit potential applications in laser lidar and remote sensing.

Средняя диаграмма направленности и способ снижения среднего уровня боковых лепестков цифровой антенной решетки.

n the development of the existing statistical theory of antennas, new analytical relations are obtained for estimating the average radiation pattern of a digital antenna array. These ratios take into account the variance of rounding errors of the weight coefficients, errors in the amplitude and phase calibration of the antenna, jitter noise and rounding errors of the signal at the output of the analog-to-digital converter. It is shown that most of the factors affect the average level of the side lobes, as in analog antenna arrays. However, the variances of the phase calibration errors and the jitter noise determine the contribution of the new term, which has symmetry in the angular coordinate and has an extremums in the direction of the main beam of the antenna array and in the direction that is mirrored relative to the main beam. It is established that the variances of rounding errors depend on the signal-to-noise ratio and, when performing numerical studies, should be estimated based on the results of experimental studies. It is shown that digital processing in a sliding window reduces the average level of the side lobes by separating the spectral components of the signal and noise.

Beam Tracking Using Least Mean Squares Algorithm for single-cell Massive MIMO Communication System

Millimetres wave (mm-wave) is an attractive option for high data rate applications in the 5G wireless communication systems that require proper beamforming and channel tracking. In this paper, we study, analyse and compare the performance of two closely related stochastic gradient descent-based approaches, namely the least mean square (LMS) algorithm, and the normalized least mean square (NLMS) algorithm, for tracking the transmit array beam in addition to the channel status. These adaptive filters usually result in a trade-off between convergence and accuracy. We found that the quality of the tracking results, measured in mean squared error (MSE) sense, are heavily dependent on the present step-the size of the gradient descent.

Fast compressive beamforming with a modified fast iterative shrinkage-thresholding algorithm.

Compressive beamforming has been successfully applied to direction-of-arrival estimation with sensor arrays. The results demonstrated that this technique achieves superior performance when compared with traditional high-resolution beamforming methods. The existing compressive beamforming methods use classical iterative optimization algorithms in their compressive sensing theories. However, the computational complexity of the existing compressive beamforming methods tend to be excessively high, which has limited the use of compressive beamforming in applications with limited computing resources. To address this issue, this paper proposes a fast compressive beamforming method which combines the shift-invariance of the array beam patterns with a fast iterative shrinkage-thresholding algorithm. The evaluation shows that the proposed fast compressive beamforming method successfully reduces the number of floating-point operations by 3 orders of magnitude when compared with the existing methods. In addition, both the simulations and experiments demonstrate that the resolution limit for discerning closely spaced sources of the introduced fast method is comparable to those of the existing compressive beamforming methods, which use classical iterative optimization algorithms.

Design, Simulation, Fabrication, and Characterization of an Electrothermal Tip-Tilt-Piston Large Angle Micromirror for High Fill Factor Segmented Optical Arrays.

Micro-electromechanical system (MEMS) micromirrors have been in development for many years, but the ability to steer beams to angles larger than 20° remains a challenging endeavor. This paper details a MEMS micromirror device capable of achieving large motion for both tip/tilt angles and piston motion. The device consists of an electrothermal actuation assembly fabricated from a carefully patterned multilayer thin-film stack (SiO2/Al/SiO2) that is epoxy bonded to a 1 mm2 Au coated micromirror fabricated from an SOI wafer. The actuation assembly consists of four identical actuators, each comprised of a series of beams that use the inherent residual stresses and coefficient of thermal expansion (CTE) mismatches of the selected thin films to enable the large, upward, out-of-plane deflections necessary for large-angle beamsteering. Finite element simulations were performed (COMSOL v5.5) to capture initial elevations and tip/tilt motion displacements and achieved <10% variance in comparison to the experiment. The measured performance metrics of the micromirror include tip/tilt angles of ±23°, piston motion of 127 µm at sub-resonance, and dynamics characterization with observed resonant frequencies at ~145 Hz and ~226 Hz, for tip/tilt and piston motion, respectively. This unique single element design can readily be scaled into a full segmented micromirror array exhibiting an optical fill-factor >85%, making it suitable for optical phased array beam control applications.

Experimental phase control of a 100 laser beam array with quasi-reinforcement learning of a neural network in an error reduction loop.

An innovative scheme is proposed for the dynamic phase control of a laser beam array. It is based on a simple neural network included in a phase correction loop that predicts the complex field array from the intensity of the induced scattered pattern through a phase intensity transformer made of a diffuser. A crucial feature is the use of a kind of reinforcement learning approach for the neural network training which takes account of the iterated corrections. Experiments on a proof-of-concept system demonstrated the high performance and scalability of the scheme with an array of up to 100 laser beams and a phase setting at λ/30.

The LOFAR Two-meter Sky Survey: Deep Fields Data Release 1

The Low Frequency Array (LOFAR) is an ideal instrument to conduct deep extragalactic surveys. It has a large field of view and is sensitive to large-scale and compact emission. It is, however, very challenging to synthesize thermal noise limited maps at full resolution, mainly because of the complexity of the low-frequency sky and the direction dependent effects (phased array beams and ionosphere). In this first paper of a series, we present a new calibration and imaging pipeline that aims at producing high fidelity, high dynamic range images with LOFAR High Band Antenna data, while being computationally efficient and robust against the absorption of unmodeled radio emission. We apply this calibration and imaging strategy to synthesize deep images of the Boötes and Lockman Hole fields at ~150 MHz, totaling ~80 and ~100 h of integration, respectively, and reaching unprecedented noise levels at these low frequencies of ≲30 and ≲23μJy beam−1in the inner ~3 deg2. This approach is also being used to reduce the LOTSS-wide data for the second data release.

Small footprint phase locking system for a large tiled aperture laser array.

A phase sensing system fitted to the control of coherent laser beam array of large cross section is experimented. It is based on the use of a fiber bundle that collects a weak part of the synthetic wavefront, that scales it down (1/40) and that reshapes it in a more compact arrangement (2D to 1D array). Then, the reconfigured beam array can be analyzed by a small footprint system making the large laser beam array easier to phase-lock. The discrete laser array wavefront transmitted by the meter long fiber bundle was stabilized thanks to a multiple arm servo loop. Laser array phase locking was further ensured by random scattering through a diffuser, associated to an alternating projection algorithm. Six fiber laser beams constituting a 110 mm diameter synthetic aperture, were phase-locked with λ/16 accuracy.