Parameters Of Metamaterials Research Articles

Extracting method of dynamic effective parameters for plate-type elastic metamaterials with decentralized resonant mass

In this paper, a method is presented to obtain both in-plane and out-plane dynamic effective parameters of plate-type elastic metamaterials with decentralized resonant mass. The method is derived by plate-type elastic metamaterials with concentrated resonant mass, and the effective material properties are obtained by averaging local physical field in each phase when prescribed displacements are applied on the boundaries of the unit cells. The accuracy of the method is verified, since the frequency ranges of negative mass density are the same with those of band gaps. In addition, the starting and ending of negative mass density are analyzed by eigenstates on the bandgap edges. Multi-negative parameters are produced by abundant resonances exhibited in the unit cells when synergetic motions are generated by the decentralized resonant mass. The proposed method is extended to determine the effective properties of the plate-type elastic metamaterials with decentralized resonant mass. Compared with the calculated effective properties of the model with concentrated resonant mass, more negative mass density regions are formed both in-plane and out-plane for the model with decentralized resonant mass. Moreover, negative moduli are also generated by monopolar and quadrupolar resonances, and the negative hybrid dispersion bands are produced by the combination of negative mass density and negative moduli. The calculated results show that the proposed method is convenient to determine both in-plane and out-plane dynamic effective parameters of plate-type elastic metamaterials with complex internal structures, and easier than the method based on the Mie scattering solution. Therefore, the proposed method will be helpful in designing plate-type elastic metamaterials with resonant micro-structures.

Maxwell Garnett theory limitations in the analysis of bi‐anisotropic composites

The constitutive parameters of metamaterials composed of asymmetrical inclusions are inaccurate when calculated using Maxwell Garnett theory. In this study, the authors discuss some particular cases of metamaterials composed of asymmetrical inclusions to demonstrate this statement. The unit cell single element dyadic is derived numerically using the induced currents by incident plane waves and is computed by point matching method of moments. The composite effective parameters approximated by Maxwell Garnett model were used to obtain the reflection and transmission coefficients from a bulk slab. The derived results were compared to the simulated numerical results with High Frequency Structure Simulator (HFSS) software. The scattering parameters from symmetrical and asymmetrical inclusions were compared and a parametric study was conducted. The scattering parameters are in good agreement when the material under consideration is composed of symmetrical inclusions and hold even for higher frequencies than Maxwell Garnett model theory limits. For asymmetrical inclusions the model provides inaccurate scattering parameters results. This discrepancy is especially pronounced when the illuminating field polarisation coincides with the inclusion asymmetry direction. These observations should be considered when Maxwell Garnett model is used for effective parameters analytical approximation.

Microstrip Patch Antennas Covered with Chiral Metamaterial Structures

In this working we present gain characteristic of microstrip patch antennas covered with chiral metamaterial. In order to determine gain of antennas covered with chiral metamaterial structure, S11 parameters and radiation pattern of antennas with chiral metamaterial and without chiral metamaterial are plotted and compared each other. The simulation results show that antennas covered with chiral metamaterial structure increase either gain or radiation pattern or both at operation frequency.

Surface Impedance of Isotropic Metamaterials

The Leontovich impedance condition is considered in relation to the boundary with an external isotropic medium characterized by the effective parameters of metamaterials. The surface impedance depends not only on the complex dielectric permittivity and complex magnetic permeability of the substance, but also on the type of the evanescent plane wave. Particular cases of transparent media and media with a balance of electrical and magnetic losses are considered. The conditions for the applicability of the impedance approximation are specified.

Theory of the Hall effect in three-dimensional metamaterials

We apply homogenization theory to calculate the effective electric conductivity and Hall coefficient tensor of passive three-dimensionally periodic metamaterials subject to a weak external static homogeneous magnetic field. We not only allow for variations of the conductivity and the Hall coefficient of the constituent material(s) within the metamaterial unit cells, but also for spatial variations of the magnetic permeability. We present four results. First, our findings are consistent with previous numerical calculations for finite-size structures as well as with recent experiments. This provides a sound theoretical justification for describing such metamaterials in terms of effective material parameters. Second, we visualize the cofactor fields appearing in the homogenization integrals. Thereby, we identify those parts of the metamaterial structures which are critical for the observed effective metamaterial parameters, providing a unified view onto various previously introduced single-constituent/multiple-constituent and isotropic/anisotropic architectures, respectively. Third, we suggest a novel three-dimensional non-magnetic metamaterial architecture exhibiting a sign reversal of the effective isotropic Hall coefficient. It is conceptually distinct from the original chainmail-like geometry, for which the sign reversal is based on interlinked rings. Fourth, we discuss two examples for metamaterial architectures comprising magnetic materials: yet another possibility to reverse the sign of the isotropic Hall coefficient and an approach to conceptually break previous bounds for the effective mobility.

The effect of geometric parameters of a single-gap SRR metamaterial on its electromagnetic properties as a unit cell of interior invisibility cloak in the microwave regime

Some geometric parameters of a metamaterial unit cell with single-gap Split Ring Resonator (SRR) are modified and the effect of these changes on its electromagnetic properties is examined. In particular, the relative magnetic permeability has been investigated. For unit cells with various geometric parameters the frequency fp in which the relative magnetic permeability is close to zero as well as the resonance frequency f0 are obtained. Finally, as an example, for each of the unit cells, the relative magnetic permeability at 9.5 GHz is obtained and by using these results an electromagnetic invisibility cloak is designed operating at 9.5 GHz which can has three different unit cells with different geometric parameters for each of its layers.

Simulation and analysis of light absorption in a new four-layered structure based on a metamaterial/graphene pair for solar cells

In this work, a new four-layer structure based on metamaterial/graphene pair is modeled as a solar cell. The proposed four-layer model consists of a silicon substrate, a metamaterial/graphene pair, and a semi-infinite glass cover. The absorption coefficient is derived and computed versus different layers’ parameters. The effect of the metamaterial refractive index and thickness on the absorption is highlighted as well as the effect of the graphene conductivity and thickness. The incidence angle impact on the absorption is also taken into consideration. Results show that the absorption can be totally controlled through changing the metamaterial parameters in visible and near-infrared radiation, as well as the incident angle. The absorption of the structure achieves values greater than 99% for incident electromagnetic waves of transverse electric (TE) and magnetic (TM) polarization.

Casimir repulsive-attractive transition between liquid-separated dielectric metamaterial and metal

We study the repulsive-attractive transition, regarded as stable equilibrium, between gold and dielectric metamaterial based on Mie resonance immersed in various fluids due to the interplay of gravity, buoyancy and Casimir force among different geometries consisting of parallel plates and spheres levitated over substrates. A wider range of separation distance of stable equilibrium is obtained with Mie metamaterial than natural materials. We investigate the relationship between separation distance of stable equilibrium and constructive parameters of Mie metamaterial and geometric parameters of the system, and provide simple rules to tune the equilibrium position by modifying constructive parameters of Mie metamaterial. Particularly, the effect of permeability of Mie metamaterial on equilibrium separation is also considered. Our work is promising for potential applications in frictionless suspension in micro/nanofabrication technologies.

Investigation on negative hybrid-resonant bands of elastic metamaterials by revised effective medium theory

In this paper, a revised effective medium theory is presented to investigate negative dispersion bands which are formed by the hybridization effect of multiple resonances. The negative hybrid-resonant bands are selective for propagation of compressional or shear waves. With a simplified model, a new negative dispersion band is firstly achieved by combinations of negative transverse modulus and negative mass density, thus three negative dispersion bands are formed by hybridization effect of a monopolar or quadrupolar resonance and a dipolar resonance. Secondly, transmission spectrums are also performed to demonstrate the negative behaviors of three hybrid resonant bands and illustrate their unusual transmission properties. Moreover, a revised effective medium theory based on numerical simulation is derived to obtain four effective parameters of the elastic metamaterials along two wave vectors when the long wavelength limitation is not fully satisfied, which perfectly explain the unusual transmissions of negative dispersion bands. Finally, the physical mechanisms of negative parameters are systematically investigated by three typical deformation states. The work has guiding significances for designing the elastic metamaterials structures with negative hybrid-resonant bands.

Frequency Tunable Graphene Metamaterial Reflectarray

In this paper, the radiation characteristics of frequency tunable graphene based metamaterial reflectarray have been investigated. The unit-cell consists of graphene two gaps split-ring-resonator (SRR) printed on a thick SiO2 substrate. The metamaterial parameters of the unit-cell have been calculated at different graphene chemical potentials and different SRR gaps. Using waveguide simulator, the reflection coefficient phase of the graphene metamaterial reflectarray unit-cell has been investigated. A 13 × 13 graphene metamaterial reflectarray antenna fed by a circular horn antenna is designed and analyzed at different graphene chemical potentials. Full-wave analysis for the graphene metamaterial reflectarray antenna has been applied using the finite integration technique.

Revealing the physical insight of a length-scale parameter in metamaterials by exploiting the variational formulation

For micro-architectured materials with a substructure, called metamaterials, we can realize a direct numerical simulation in the microscale by using classical mechanics. This method is accurate, however, computationally costly. Instead, a solution of the same problem in the macroscale is possible by means of the generalized mechanics. In this case, no detailed modeling of the substructure is necessary; however, new parameters emerge. A physical interpretation of these metamaterial parameters is challenging leading to a lack of experimental strategies for their determination. In this work, we exploit the variational formulation based on action principles and obtain a direct relation between a parameter used in the kinetic energy and a metamaterial parameter in the case of a viscoelastic model.

A compact wideband and high gain GRIN metamaterial lens antenna system suitable for C, X, Ku band application

In this paper, a rectangular split ring resonator (RSRR) based gradient refractive index (GRIN) metamaterial structure arranged in 30 × 10 array of size 4 cm × 4 cm for lens antenna is addressed. The novelty in the design lies in the introduction of the splits in the rectangular rings in order to enhance the coupling of the currents between the rings. This ultimately results in the collimation of the field in the desired direction and improves the gain and bandwidth of the antenna system. The multilayer metamaterial structure is proposed to design a low loss, broadband, highly focusing thin lens. The metamaterial lens array is combined with a horn antenna system to achieve a gain improvement of 3–11 dB and cross polarization level below −23 dB in the frequency range of 3.5–19.5 GHz with a −3 dB gain bandwidth efficiency of 113%. The metamaterial medium parameters such as permittivity(ε), permeability(μ) and refractive index(η) variation of the proposed design is found to reveal its near zero values in the operating range, depicting it as a near zero metamaterial (NZMTM). The variation in the refractive index of the metamaterial lens is due to parasitic coupling between the metamaterial layers and that facilitates to design thin broadband lens antenna system. This broadband high gain lens antenna is found suitable for C, X, Ku band application.

Anisotropic metamaterial waveguide driven by a cold and relativistic electron beam

We study the interaction of a cold and relativistic electron beam with a cylindrical waveguide loaded by an anisotropic and dispersive metamaterial layer. The general dispersion relation for the transverse magnetic (TM) mode, through the linear fluid model and Maxwell equations decomposition method, is derived. The effects of some metamaterial parameters on dispersion relation are presented. A qualitative discussion shows the possibility of monomodal propagation band widening and obtaining more control on dispersion relation behavior. Especially for epsilon negative near zero metamaterials, these effects are considerable. Finally, the anisotropy and metamaterial layer thickness impacts on wave growth rate for different metamaterials are considered. The results demonstrate that we can control both wave growth rate and voltage of saturation peak by metamaterial parameters.

Chirped dark solitons in optical metamaterials

The ultrashort pulse propagation in metamaterials that is governed by the generalized nonlinear Schrödinger equation with pseudoquintic nonlinearity and self-steepening effect is investigated. By adopting a nonlinear chirp anstaz, we obtain an elliptic differential equation with a fifth-degree nonlinear term describing the evolution of the wave amplitude in the metamaterial. We present a variety of exact chirped dark soliton solutions for the model in the presence of the self-steepening term. The obtained results show that the corresponding chirp is proportional to the field intensity and depends on the self-steepening parameter. Parametric conditions on the metamaterial parameters for the existence of the dark structures as well as the nonlinear chirp associated with each of these optical pulses are also presented.

Adaptive manifold interpolation techniques for acoustic metamaterial characterization in HPC environments

Functionally graded acoustic metamaterials (FGAMs) can be designed to have specific waveguide properties dictated by a theory relevant to the application. Frequently, these material properties do not exist naturally, and must be fabricated by gradually layering manufactured unit cell microstructures, resulting in a (usually smooth) variation of properties. Tailoring these microstructures to the demands of the relevant theory requires assembling microstructures with very specific material properties—a process that often requires haphazardly searching a large domain space of unit cells for desirable parameter combinations. Moreover, the process of determining the material tensor of interest for a specific set of metamaterial cell design parameters typically involves solving a costly high dimensional finite element problem for each new microstructure cell of interest. This work presents a gradient-based, manifold interpolation technique to characterize acoustic metamaterial homogenized elastic tensors. An adaptive refinement method is used to seed the interpolation data allowing the method to reliably recover unit cell stiffness tensors within predefined error bounds—allowing for interpolation of a cell with desired properties within specified error tolerances while minimizing the number of unit cells that require high-fidelity, computationally-expensive simulation. Finally, an implementation of the process is presented in a massively parallel computing environment.

Nonlocal response of tunable photonic metamaterials with semiconductor inclusions

Effective parameters of homogenized photonic crystals with a semiconductor bar in the unit cell are calculated and analyzed. The applied homogenization theory is based on the Fourier formalism within the form-factor division approach. The calculated effective parameters, namely, the components of the effective permittivity tensor, are nonlocal since they depend on not only frequency but also the wave vector. Using the nonlocal effective parameters, the complex dispersion relation for photonics modes propagating in a periodic semiconductor–dielectric array can be described even beyond the long-wavelength limit. We have analyzed the temperature dependence of the nonlocal effective parameters for photonic metamaterials composed of InSb square bars in a silica–glass host matrix. In the case of continuous (infinitely long) bars, the metamaterial shows plasma-like behavior with a temperature-dependent effective plasma frequency in the THz range. For the case of cut semiconductor bars, the metamaterial behaves as a dielectric in the lowest frequency band, whose width can also be tuned by varying the temperature. Using the nonlocal effective permittivity, the optical spectra (reflectivity and transmittance) for a slab of InSb square bars in a glass matrix were calculated and analyzed.

Closed-form formulae of effective parameters of hyperbolic metamaterial made by stacked hole-array layers working at terahertz or microwave radiation

A metamaterial made by stacked hole-array layers known as a fishnet metamaterial behaves as a hyperbolic metamaterial at wavelength much longer than hole-array period. However, the analytical formulae of effective parameters of a fishnet metamaterial have not been reported hindering the design of deep-subwavelength imaging devices using this structure. We report the new closed-form formulae of effective parameters comprising anisotropic dispersion relation of a fishnet metamaterial working at terahertz or microwave frequency. These effective parameters of a fishnet metamaterial are consistent with those obtained by quasi-full solutions using known effective parameters of a hole-array layer working at frequency below its spoof plasma frequency with the superlattice period much smaller than the hole-array period. We also theoretically demonstrate the deep-subwavelength focusing at {\lambda}/83 using the composite structure of a slit-array layer and a fishnet metamaterial. It is found that the focused intensity inside a fishnet metamaterial is several times larger than that without the fishnet metamaterial, but the transmitted intensity is still restricted by large-wavevector difference in air and a fishnet metamaterial. Our effective parameters may aid the next-generation deep-subwavelength imaging devices working at terahertz or microwave radiation.

Origin of Negative Imaginary Part of Effective Permittivity of Passive Materials**Supported by the National Natural Science Foundation of China under Grant No 51102007, and the Fund for Discipline Construction of Beijing University of Chemical Technology under Grant No XK1702.

The anti-resonant phenomenon of effective electromagnetic parameters of metamaterials has aroused controversy due to negative imaginary permittivity or permeability. It is experimentally found that the negative imaginary permittivity can occur for the natural passive materials near the Fabry–Perot resonances. We reveal the nature of negative imaginary permittivity, which is correlated with the magnetoelectric coupling. The anti-resonance of permittivity is a non-inherent feature for passive materials, while it can be inherent for devices or metamaterials. Our finding validates that the negative imaginary part of effective permittivity does not contradict the second law of thermodynamics for metamaterials owing to the magnetoelectric coupling.

Steady method to retrieve effective electromagnetic parameters of bianisotropic metamaterials at one incident direction in the terahertz region

We propose a steady method to extract the effective constitutive parameters of a slab of bianisotropic split-ring resonator metamaterial from reflection and transmission coefficients. The effective permittivity, permeability and magnetoelectric coupling coefficient of bianisotropic metamaterial can be simply retrieved by our derived analytical inversion equations. In our retrieval method, the transmission and reflection coefficients in only one direction of wave propagation were applied. The method was verified by the retrieval constitutive parameters for different metamaterials, among which one is isotropic structure and the other one is bianisotropic metamaterial. The intrinsic difference between the normal isotropic metamaterial and the bianisotropic metamaterial was evidently revealed. The resonant characteristic of the split ring resonator metamaterial including electric coupling to magnetic resonance was verified by the extracted effective constitutive parameters. The proposed method can be effectively applied in investigation of bianisotropic performance of metamaterials.

Closed Form Kramers–Kronig Relations to Extract the Refractive Index of Metamaterials

Closed form expressions of the Kramers–Kronig and of the multiply subtractive Kramers–Kronig relations are derived to predict the real part of the refractive index from the imaginary part, which is given in discrete frequency points. The accuracy and the convergence rate of the closed form expressions are investigated by calculating the refractive index of a hypothetical double negative metamaterial with predefined parameters. Then, a two-step procedure is presented, which utilizes the subtractive Kramers–Kronig relation to uniquely retrieve the effective refractive index of metamaterials even when the Kramers–Kronig relation fails. The developed procedure is demonstrated by extracting the effective parameters of multilayer fishnet metamaterials.