Dual-band left-handed metamaterials fabricated by using tree-shaped fractal

A method of fabricating dual-band left-handed metematerials （LHMs） is investigated numerically and experimen- tally by single-sided tree-like fractals. The resulting structure features multiband magnetic resonances and two electric resonances. By appropriately adjusting the dimensions, two left-handed （LH） bands with simultaneous negative per- mittivity and permeability are engineered and are validated by full-wave eigenmode analysis and measurement as well in the microwave frequency range. To study the multi-resonant mechanism in depth, the LHM is analysed from three different perspectives of field distribution analysis, circuit model analysis, and geometrical parameters evaluation. The derived formulae are consistent with all simulated results and resulting electromagnetic phenomena, indicating the ef- fectiveness of the established theory. The method provides an alternative to the design of multi-band LHM and has the advantage of not requiring two individual resonant particles and electrically continuous wires, which in turn facilitates planar design and considerably simplifies the fabrication.

From electromagnetic bandgap to left-handed metamaterials:modelling and applications

In this paper, numerical modelling of left-handed materials （LHMs） is presented using in-house and commercial software packages. Approaches used include the finite-difference time-domain （FDTD） method, finite element method （FEM） and method of moments （MoMs）. Numerical simulation includes verification of negative refraction and ＂perfect lenses＂ construction, investigation of evanescent wave behaviour in layered LHMs, reversed Shell＇s Law in electromagnetic band gap （EBG）-like structures and construction of LHMs using modified split ring resonators （SRRs）. Numerical results were verified to be in good agreement with theory, At the end of this paper, potential applications of LHMs in microwave engineering are discussed.

Double Negative Left-Handed Metamaterials for Miniaturization of Rectangular Microstrip Antenna

In this paper, I have explored a significant concept for the miniaturization of microstrip patch antenna configuration by using the double negative (DNG) left-handed Metamaterials, which have dielectric permittivity and magnetic permeability both negative, simultaneously. It is achieved through the concept of phase-compensation by thin slab consist of the double positive (DPS) material, which have dielectric permittivity and magnetic permeability both positive, simultaneously and DNG metamaterials as a substrate of the microstrip patch antenna. By combining the DNG metamaterial slab with the slab made of DPS materials form a cavity resonator whose dispersion relation is independent of the sum of thickness of the slabs filling this cavity but it depends on the ratio of their thicknesses. This cavity constitutes by DPS and DNG material is used as substrate of the microstrip antennas and the DNG material slab is behave as phase compensator.

Properties of single and multiple defect modes in one-dimensional photonic crystals containing left-handed metamaterials

Wave propagation is studied in structures consisting of alternate left- and right-handed layers. Bragg gap and zero-n gap appear in different frequency regions of the structure. The periodicity of the structure is broken by simply reversing the order of the layers in one half of the structure, resulting in defect modes located inside the zero-n gap and Bragg gap. These modes can be made very narrow by adding more layers in the structure. The defect mode located inside the zero-n gap is sensitive to the symmetry of the structure and insensitive to the angle of incidence of the incoming radiation. Multiple modes are also generated inside the gaps by repeating the structural pattern. Thus, a simple structure can be used for single and multiple modes that are imDortant for different applications.

Reflection and phase of left-handed metamaterials at microwave frequencies

We experimentally investigated the reflection and phase of the left-handed metamaterials (LHMs) in a rectangular waveguide for the normally incident microwave. The samples are constructed by periodically arraying the copper split ring resonators (SRRs) and wires. It is found that for the LHMs with one-layered SRRs, a reflection peak with a depth of -3.3 dB (i.e. with the reflectivity of 47%) occurs in the left-handed range. The dependence of reflection phase on the frequency is different from that of the transmission phase, and the reflection phase has an inflexion at the reflection peaks. For the LHMs with three-layered SRRs, the depth of reflection peak increases with the row number, i.e. reflection is weakened, and the reflection peak has a shift with respect to the left-handed transmission peak. It is thought that the interaction between different layers of SRRs is the reason of the shift.

Mechanical and damping performances of TPMS lattice metamaterials fabricated by laser powder bed fusion

Lattice metamaterials based on three-period minimum surface(TPMS)are an effective means to achieve lightweight and high-strength materials which are widely used in various fields such as aerospace and ships.However,its vibration and noise reduction,and damping properties have not been fully studied.Therefore,in this study,the TPMS structures with parameterization were designed by the method of surface migration,and the TPMS structures with high forming quality was manufactured by laser powder bed fusion(LPBF).The mechanical properties and energy absorption characteristics of the beam and TPMS structures were studied and compared by quasi-static compression.The modal shapes of the beam lattice structures and TPMS structures were obtained by the free modal analysis,and the damping properties of two structures were obtained by modal tests.For the two structures after heat treatment with the same porosity of 70%,the yield strength of the beam lattice structure reaches 40.76 MPa,elastic modulus is 20.38 GPa,the energy absorption value is 32.23 MJ·m^(-3),the damping ratio is 0.52%.The yield strength,elastic modulus,energy absorption value,and damping ratio of the TPMS structure are 50.74 MPa,25.37 GPa,47.34 MJ·m^(-3),and 0.99%,respectively.The results show that TPMS structures exhibit more excellent mechanical properties and energy absorption,better damping performance,and obvious advantages in structural load and vibration and noise reduction compared with the beam lattice structures under the same porosity.

A planar left-handed metamaterial based on electric resonators

A planar left-handed metamaterial（LHM） composed of electric resonator pairs is presented in this paper. Theoretical analysis, an equivalent circuit model and simulated results of a wedge sample show that this material exhibits a negative refraction pass-band around 9.6GHz under normal-incidence and is insensitive to a change in incidence angle. Furthermore, as the angle between the arm of the electric resonators and the strip connecting the arms increases, the frequency range of the pass-band shifts downwards. Consequently, this LHM guarantees a relatively stable torlerence of errors when it is practically fabricated. Moreover, it is a candidate for designing multi-band LHM through combining the resonator pairs with different angles.

Mass-spring model for elastic wave propagation in multilayered van der Waals metamaterials

Multilayered van der Waals(vdW)materials have attracted increasing interest because of the manipulability of their superior optical,electrical,thermal,and mechanical properties.A mass-spring model(MSM)for elastic wave propagation in multilayered vdW metamaterials is reported in this paper.Molecular dynamics(MD)simulations are adopted to simulate the propagation of elastic waves in multilayered vdW metamaterials.The results show that the graphene/MoS_(2)metamaterials have an elastic wave bandgap in the terahertz range.The MSM for the multilayered vdW metamaterials is proposed,and the numerical simulation results show that this model can well describe the dispersion and transmission characteristics of the multilayered vdW metamaterials.The MSM can predict elastic wave transmission characteristics in multilayered vdW metamaterials stacked with different two-dimensional(2D)materials.The results presented in this paper offer theoretical help for the vibration reduction of multilayered vdW semiconductors.

Nonreciprocal thermal metamaterials:Methods and applications

Nonreciprocity of thermal metamaterials has significant application prospects in isolation protection,unidirectional transmission,and energy harvesting.However,due to the inherent isotropic diffusion law of heat flow,it is extremely difficult to achieve nonreciprocity of heat transfer.This review presents the recent developments in thermal nonreciprocity and explores the fundamental theories,which underpin the design of nonreciprocal thermal metamaterials,i.e.,the Onsager reciprocity theorem.Next,three methods for achieving nonreciprocal metamaterials in the thermal field are elucidated,namely,nonlinearity,spatiotemporal modulation,and angular momentum bias,and the applications of nonreciprocal thermal metamaterials are outlined.We also discuss nonreciprocal thermal radiation.Moreover,the potential applications of nonreciprocity to other Laplacian physical fields are discussed.Finally,the prospects for advancing nonreciprocal thermal metamaterials are highlighted,including developments in device design and manufacturing techniques and machine learning-assisted material design.

General three-dimensional thermal illusion metamaterials

Thermal illusion aims to create fake thermal signals or hide the thermal target from the background thermal field to mislead infrared observers,and illusion thermotics was proposed to regulate heat flux with artificially structured metamaterials for thermal illusion.Most theoretical and experimental works on illusion thermotics focus on two-dimensional materials,while heat transfer in real three-dimensional(3D)objects remains elusive,so the general 3D illusion thermotics is urgently demanded.In this study,we propose a general method to design 3D thermal illusion metamaterials with varying illusions at different sizes and positions.To validate the generality of the 3D method for thermal illusion metamaterials,we realize thermal functionalities of thermal shifting,splitting,trapping,amplifying and compressing.In addition,we propose a special way to simplify the design method under the condition that the size of illusion target is equal to the size of original heat source.The 3D thermal illusion metamaterial paves a general way for illusion thermotics and triggers the exploration of illusion metamaterials for more functionalities and applications.

Suppression of low-frequency ultrasound broadband vibration using star-shaped single-phase metamaterials

In order to suppress the low-frequency ultrasound vibration in the broadband range of 20 k Hz—100 k Hz,this paper proposes and discusses an acoustic metamaterial with low-frequency ultrasound vibration attenuation properties,which is configured by hybrid arc and sharp-angle convergent star-shaped lattices.The effect of the dispersion relation and the bandgap characteristic for the scatterers in star-shaped are simulated and analyzed.The target bandgap width is extended by optimizing the geometry parameters of arc and sharp-angle convergent lattices.The proposed metamaterial configured by optimized hybrid lattices exhibits remarkable broad bandgap characteristics by bandgap complementarity,and the simulation results verify a 99%vibration attenuation amplitude can be obtained in the frequency of20 k Hz—100 k Hz.After the fabrication of the proposed hybrid configurational star-shaped metamaterial by 3D printing technique,the transmission loss experiments are performed,and the experimental results indicate that the fabricated metamaterial has the characteristics of broadband vibration attenuation and an amplitude greater than 85%attenuation for the target frequency.These results demonstrate that the hybrid configurational star-shaped metamaterials can effectively widen the bandgap and realize high efficiency attenuation,which has capability for the vibration attenuation in the application of highprecise equipment.

Reconfigurable mechanism-based metamaterials for ternary-coded elastic wave polarizers and programmable refraction control

Elastic metamaterials with unusual elastic properties offer unprecedented ways to modulate the polarization and propagation of elastic waves.However,most of them rely on the resonant structural components,and thus are frequency-dependent and unchangeable.Here,we present a reconfigurable 2D mechanism-based metamaterial which possesses transformable and frequency-independent elastic properties.Based on the proposed mechanism-based metamaterial,interesting functionalities,such as ternarycoded elastic wave polarizer and programmable refraction,are demonstrated.Particularly,unique ternary-coded polarizers,with 1-trit polarization filtering and 2-trit polarization separating of longitudinal and transverse waves,are first achieved.Then,the strong anisotropy of the proposed metamaterial is harnessed to realize positive-negative bi-refraction,only-positive refraction,and only-negative refraction.Finally,the wave functions with detailed microstructures are numerically verified.

Modeling and analysis of gradient metamaterials for broad fusion bandgaps

A gradient metamaterial with varying-stiffness local resonators is proposed to open the multiple bandgaps and further form a broad fusion bandgap.First,three local resonators with linearly increasing stiffness are periodically attached to the spring-mass chain to construct the gradient metamaterial.The dispersion relation is then derived based on Bloch's theorem to reveal the fusion bandgap theoretically.The dynamic characteristic of the finite spring-mass chain is investigated to validate the fusion of multiple bandgaps.Finally,the effects of the design parameters on multiple bandgaps are discussed.The results show that the metamaterial with a non-uniform stiffness gradient pattern is capable of opening a broad fusion bandgap and effectively attenuating the longitudinal waves within a broad frequency region.

3D Printing of Periodic Porous Metamaterials for Tunable Electromagnetic Shielding Across Broad Frequencies

The new-generation electronic components require a balance between electromagnetic interference shielding efficiency and open structure factors such as ventilation and heat dissipation.In addition,realizing the tunable shielding of porous shields over a wide range of wavelengths is even more challenging.In this study,the well-prepared thermoplastic polyurethane/carbon nanotubes composites were used to fabricate the novel periodic porous flexible metamaterials using fused deposition modeling 3D printing.Particularly,the investigation focuses on optimization of pore geometry,size,dislocation configuration and material thickness,thus establishing a clear correlation between structural parameters and shielding property.Both experimental and simulation results have validated the superior shielding performance of hexagon derived honeycomb structure over other designs,and proposed the failure shielding size(D_(f)≈λ/8-λ/5)and critical inclined angle(θf≈43°-48°),which could be used as new benchmarks for tunable electromagnetic shielding.In addition,the proper regulation of the material thickness could remarkably enhance the maximum shielding capability(85-95 dB)and absorption coefficient A(over 0.83).The final innovative design of the porous shielding box also exhibits good shielding effectiveness across a broad frequency range(over 2.4 GHz),opening up novel pathways for individualized and diversified shielding solutions.

Topology optimization of chiral metamaterials with application to underwater sound insulation

Chiral metamaterials have been proven to possess many appealing mechanical phenomena,such as negative Poisson's ratio,high-impact resistance,and energy absorption.This work extends the applications of chiral metamaterials to underwater sound insulation.Various chiral metamaterials with low acoustic impedance and proper stiffness are inversely designed using the topology optimization scheme.Low acoustic impedance enables the metamaterials to have a high and broadband sound transmission loss(STL),while proper stiffness guarantees its robust acoustic performance under a hydrostatic pressure.As proof-of-concept demonstrations,two specimens are fabricated and tested in a water-filled impedance tube.Experimental results show that,on average,over 95%incident sound energy can be isolated by the specimens in a broad frequency range from 1 k Hz to 5 k Hz,while the sound insulation performance keeps stable under a certain hydrostatic pressure.This work may provide new insights for chiral metamaterials into the underwater applications with sound insulation.

Actively tunable sandwich acoustic metamaterials with magnetorheological elastomers

Sandwich structures are widespread in engineering applications because of their advantageous mechanical properties.Recently,their acoustic performance has also been improved to enable attenuation of low-frequency vibrations induced by noisy environments.Here,we propose a new design of sandwich plates(SPs)featuring a metamaterial core with an actively tunable low-frequency bandgap.The core contains magnetorheological elastomer(MRE)resonators which are arranged periodically and enable controlling wave attenuation by an external magnetic field.We analytically estimate the sound transmission loss(STL)of the plate using the space harmonic expansion method.The low frequency sound insulation performance is also analyzed by the equivalent dynamic density method,and the accuracy of the obtained results is verified by finite-element simulations.Our results demonstrate that the STL of the proposed plate is enhanced compared with a typical SP analog,and the induced bandgap can be effectively tuned to desired frequencies.This study further advances the field of actively controlled acoustic metamaterials,and paves the way to their practical applications.

All-dielectric left-handed metamaterial based on dielectric resonator:design,simulation and experiment

Dipoles with Lorentz-type resonant electromagnetic responses can realise negative effective parameters in their negative resonant region. The electric dipole and magnetic dipole can realise, respectively, negative permittivity and negative permeability, so both the field distribution forms of electric and magnetic dipoles are fundamentals in designing left-handed metamaterial. Based on this principle, this paper studies the field distribution in high-permittivity dielectric materials. The field distributions at different resonant modes are analysed based on the dielectric resonator theory. The origination and influence factors of the electric and magnetic dipoles are confirmed. Numerical simulations indicate that by combining dielectric cubes with different sizes, the electric resonance frequency and magnetic resonance frequency can be superposed. Finally, experiments are carried out to verify the feasibility of all-dielectric left-handed metamaterial composed by this means.

Propagation of Gaussian beams family through a Kerr-type left-handed metamaterial

In this paper the propagation of elegant Hermite-cosh-Gaussian, elegant Laguerre Gaussian, and Bessel Gaussian beams through a Kerr left-handed metamaterial （LHM） slab have been studied. A split-step Fourier method is used to investigate the propagation of laser beams through this media. Numerical simulation shows that Gaussian beams have different focusing behaviors in a Kerr LHM slab with positive or negative nonlinearity. Beam focusing happens in slabs with positive nonlinearity and not in slabs with negative nonlinearity; however, negative nonlinearity is required for a Kerr LHM slab to act like a lens. Additionally, the focusing properties of beams can be controlled by controlling the thickness of the slab or the input power of the incident beam. A multilayer structure is also proposed to have beam focusing by thinner slabs and passing longer distances.

A novel structure for a broadband left-handed metamaterial

A low absorptivity broadband negative refractive index metamaterial with a multi-gap split-ring and metallic cross （MSMC） structure is proposed and investigated numerically and experimentally in the microwave frequency range. The effective media parameters were retrieved from the numerical and experimental results, which clearly show that there exists a very wide frequency band where the permittivity and permeability are negative. The influence of the structure parameters on the magnetic response and the cut-off frequency of the negative permittivity are studied in detail. This metamaterial would have potential application in designing broadband microwave devices.

Left-Handed Characteristics Tunable C-Shaped Varactor Loaded Textile Metamaterial for Microwave Applications

This paper presents a textile-based C-shaped split-ring resonators(SRR)metamaterial(MTM)unit cells with an electrical tunability function.The proposed MTM was composed of two symmetrical C-shaped SRR combined with a central diagonal metal bar,whereas the RF varactor diode is placed on the backside of the splitted ground plane.Stopband behavior of single and array MTM unit cells were analyzed while the achieved negative index physical characteristics were widely studies.Though four different MTM arrays(i.e.,1×1,1×2,2×1,and 2×2)were analyzed in simulation,a 2×2-unit cell array was chosen to fabricate,and it was further undergone experimental validation.This proposed tunable MTM exhibits double negative(DNG)/left-handed properties with an average bandwidth of more than 2.8 GHz.Furthermore,attainable negative permittivity and negative permeability are within 2.66 to 9.59 GHz and within 2.77 to 15 GHz,respectively,at the frequency of interest(between 1 and 15 GHz).Moreover,the proposed tunable MTM also showed tunable transmission coefficient characteristics.The proposed electrically tunable textile MTM might function in a dynamic mode,making it suitable for a variety of microwave-wearable applications.A satisfactory agreement between simulations and experiments were achieved,demonstrating that the proposed MTM can operate over a wide bandwidth.