A retrieval method for nonlinear metamaterials

Metamaterials are engineered periodic structures for which it is possible to assign effective homogenized constitutive properties. In recent years, metamaterials in which the constituent elements are integrated with inherently nonlinear materials or electronic components have been considered for their potential impact on nonlinear wave propagation. As is the case with their linear counterparts, nonlinear metamaterials can also be assigned homogenized effective properties. The effective constitutive parameters of a metamaterial can be determined by a retrieval method applied to full-wave numerical simulations of a single layer of the structure. In this work, we present a transfer matrix approach that extends the retrieval of metamaterial properties to include the effective nonlinear susceptibilities. Comparisons with time-domain finite element simulations of continuous nonlinear slabs confirm the validity of this approach. The proposed approach is also applied to determine the nonlinear susceptibility of a simple nonlinear metamaterial.     

Trapping of electromagnetic wave in single-negative metamaterial waveguides

We study the trapping properties of transverse magnetic (TM) waves in single-negative metamaterial waveguides including epsilon-negative (ENG) metamaterial and mu-negative (MNG) metamaterial. The relationship between effective refractive index and reduced core width is analyzed when the permittivities of ENG and MNG metamaterials are different, and the inflection on this curve can be regarded as the trapping point. Simulation results show that the properties in an ENG–MNG–ENG metamaterial waveguide are contrary to that in a MNG–ENG–MNG metamaterial waveguide. The sensitivity of trapping point to the change of permittivity makes the single-negative metamaterial waveguides to be an effective method to detect the permittivity variation and can be used as a new kind of waveguide sensor.     

Hybridization effect in coupled metamaterials

Although the invention of the metamaterials has stimulated the interest of many researchers and possesses many important applications, the basic design idea is very simple: composing effective media from many small structured elements and controlling its artificial EM properties. According to the effective-media model, the coupling interactions between the elements in metamaterials are somewhat ignored; therefore, the effective properties of metamaterials can be viewed as the “averaged effect” of the resonance property of the individual elements. However, the coupling interaction between elements should always exist when they are arranged into metamaterials. Sometimes, especially when the elements are very close, this coupling effect is not negligible and will have a substantial effect on the metamaterials’ properties. In recent years, it has been shown that the interaction between resonance elements in metamaterials could lead to some novel phenomena and interesting applications that do not exist in conventional uncoupled metamaterials. In this paper, we will give a review of these recent developments in coupled metamaterials. For the “metamolecule” composed of several identical resonators, the coupling between these units produces multiple discrete resonance modes due to hybridization. In the case of a “metacrystal” comprising an infinite number of resonators, these multiple discrete resonances can be extended to form a continuous frequency band by strong coupling. This kind of broadband and tunable coupled metamaterial may have interesting applications. Many novel metamaterials and nanophotonic devices could be developed from coupled resonator systems in the future.     

Design of an acoustic bending waveguide with acoustic metamaterials via transformation acoustics

Transformation acoustics is employed to design an acoustic bending waveguide. A two-dimensional square area with anisotropic and homogeneous material properties is transformed into a fan-shaped area with anisotropic and inhomogeneous material properties to rotate the direction of beam propagation. An alternating layered structure is considered to approximate a medium with anisotropic material properties. From the calculation results, the transformation medium can be realized by an alternating layered structure consisting of water and fluid with negative mass density. We propose that an acoustic metamaterial composed of three layers in water background can be designed to replace negative mass density fluid. The effective mass density and bulk modulus of the system that is composed of the acoustic metamaterial and water are dependent on the incident frequency and the geometric size of the acoustic metamaterial. We tune the geometric size of the acoustic metamaterial to approach the corresponding mass density distribution of the negative mass density fluid at a specific frequency. Thereby, the acoustic bending waveguide designed by using transformation acoustics can be achieved by the acoustic metamaterials.     

Material parameters of metamaterials (a Review)

A theory of the homogenization of a certain class of metamaterials is stated. These metamaterials are volume lattices of electric and magnetic dipoles that are resonant with frequencies that are considerably lower than that of the first Bragg resonance of the lattice. It was shown that, for plates of a metamaterial, which are described by bulk material parameters, transition layers play an important role, and the known Drude notion of transition layers is significantly revised. The paper also discusses a more widespread method of determining the material parameters of metamaterials based on the extraction of the refractive index and the characteristic impedance from the scattering matrix of the plate of the metamaterial. The physical meaning of the material parameters obtained in this way is clarified, and the concept of Bloch lattices related to it is discussed. It is shown that the bulk material parameters and the parameters of transition layers can also be extracted from components of the scattering matrix of plates.     

基于声学超材料的低频可调吸收器

在当今社会,噪声污染已经成为人类健康的一大威胁,如何有效地控制和消除噪声污染一直是科研领域的一个重要话题.本文以开口环嵌套结构为模型,设计并制备了一种声学超材料.通过理论分析、数值模拟和实验测试,发现由于模型内部空腔的强烈耦合共振效应,该超材料可以在低频区域实现接近完美的吸声效应.此外,通过简单地绕轴旋转其内腔开口方向,即可改变该超材料的相对阻抗值,进而在较宽的频带范围内实现对吸收峰位置的可调控制.由于该超材料具有深亚波长的尺寸,因此非常有利于低频吸声器件的小型化和集成化,同时该模型也为宽带吸收器的设计奠定了基础.     

Absorption and dispersion in metamaterials: Feasibility of device applications

We present a quantitative study of the effects of losses in layered media with a metamaterial layer as the constituent. The metamaterial is modelled by a causal isotropic effective medium (Lorentz-type) response. The parameters for the model are picked from a recent experiment. Two specific examples, namely, that of resonant tunnelling (RT) and imaging are chosen to demonstrate the devastating effects of losses in the present day metamaterials. It is then shown how large delays in RT, as well as near perfect imaging can be restored in gain-doped metamaterials. We also point out yet another use of metamaterials for achieving near perfect absorption, and its use for probing strong atom-field interaction.     

电磁编码超材料的理论与应用

本文系统地对编码超材料、数字超材料及现场可编程超材料的新进展进行了综述,讨论其对电磁波的实时调控和构造多功能器件的能力。首先,引入1-bit编码超材料,由"0"和"1"两种编码单元构成,分别对应于相位相反的电磁响应。通过控制不同的"0"和"1"编码序列,可以调控电磁波,并实现不同功能。这种1-bit编码超材料可以扩展到2-bit,甚至更高比特。其次,介绍了一种由开关二极管来控制的数字编码超材料,每个编码单元可通过二极管的开和关来获得不同的相位响应,进而获得不同的数字态。结合现场可编程门阵列(FPGA)控制系统,实现了对数字超材料的实时可编程设计,构造出现场可编程超材料。最后,研究了编码超材料对太赫兹波的调控,包括太赫兹波宽带漫散射及其对目标雷达散射截面(RCS)的缩减、各向异性编码超材料对太赫兹波的极化调控和波束调控等。数值仿真和实验测试结果吻合很好,验证了编码超材料的出色性能,展示了编码超材料调控电磁波的多功能性。编码超材料对微波及太赫兹波的实时控制可用于制作波束分离、波束偏折、极化转换等功能器件,也可在宽带范围内有效缩减目标RCS。     

Double-negative dynamic properties in one-dimensional multi-phase metamaterial based on the symmetrical equivalent layer

Acoustic metamaterials have important potential applications in engineering by their unusual properties. Based on the concept of symmetrical equivalent layer, it is found that layered acoustic metamaterial which exhibits simultaneously negative effective modulus and density can be existed. By using the transfer matrix method, the continuous double-negative dynamic properties can be achieved through a multi-phase microstructure considering viscous damping, and the left-handed wave propagation property appears during the double-negative frequency regions. This will be a reference for the design of 1D acoustic negative refraction metamaterials.     

Tuning the resonance in high-temperature superconducting terahertz metamaterials

In this Letter, we present resonance properties in terahertz metamaterials consisting of a split-ring resonator array made from high-temperature superconducting films. By varying the temperature, we observe efficient metamaterial resonance switching and frequency tuning. The results are well reproduced by numerical simulations of metamaterial resonance using the experimentally measured complex conductivity of the superconducting film. We develop a theoretical model that explains the tuning features, which takes into account the resistive resonance damping and additional split-ring inductance contributed from both the real and imaginary parts of the temperature-dependent complex conductivity. The theoretical model further predicts more efficient resonance tuning in metamaterials consisting of a thinner superconducting split-ring resonator array, which are also verified in subsequent experiments.     

Effect of metamaterial layer on optical surface plasmon resonance sensor

In this paper an optical surface plasmon resonance (SPR) sensor with metamaterial for four and five layered structure is studied. The numerical results presented in this paper leads to a significant properties of metamaterials in sensing field. Computed results of SPR sensors using metamaterial are compared with conventional optical SPR sensors for four and five layered structure. It is seen that wider dynamic range or effective range of measurable refractive index increases when metamaterial layer is used. It is also verified that SPR sensor with metamaterial layer can dramatically enhance the resolution and reduce the reflectivity compared with conventional SPR. Validity of the magnetic field results is proved on the basis of smooth match of the fields in the different layers of the proposed optical SPR sensor.     

Acoustic absorbers at low frequency based on split-tube metamaterials

The remarkable properties of acoustic metamaterials have attracted massive researches and applications, especially on low-frequency sound absorptions. Currently, most of the acoustic metamaterial absorbers employ resonances in plastic cavities, and their structural strengths are important in many circumstances, especially in harsh environment. However, studies of metamaterials including this point are very scarce. Here, we propose an acoustic metamaterial for low-frequency (<500 Hz) absorptions, composed of three nested square split tubes with inverted opening directions. The efficiency of the absorber is investigated both numerically and experimentally, and absorptions at the peeks are found to exceed 90% and the frequency can be effectively adjusted by tuning its geometric parameters. We further test its yield strength under compression and confirm its buckling behavior happens from the outmost layer. This tunable acoustic metamaterial with a fairly good mechanical strength may lead to broad applications in noise reduction.     

Metamaterials and their application in microwaves: A review

A metamaterial is a composite material that has attracted the attention of researchers since the late 1990s-early 2000s. This material contains an artificial periodic structure, which modifies its permittivity and permeability and, thereby, makes it possible to control the dispersion, refraction, and reflection of electromagnetic waves in the metamaterial. Analytical and experimental studies of the properties of metamaterials, as well as their applications, cover a wide frequency range from radio waves to the visible range. In recent years, considerable progress has been made toward the application of these materials in the microwave range (1–100 GHz). Works on development and application of metamaterials in the microwave range published over the last 8–10 years are reviewed. Artificial transmission lines as 1D metamaterials are discussed. Resonators, filters, and phase shifters based on the “metamaterial philosophy” are considered. Special attention is given to the application of metamaterials in the antenna technology.     

磁电耦合超材料本构矩阵获取方法的研究

单负(仅介电常数或仅磁导率小于零)超材料以及由导线-开口谐振环组成的双负超材料本构参数的提取通常采用传统的S参数方法. 由于磁电耦合超材料存在交叉极化现象, 仅用介电常数和磁导率两个本构参数无法准确描述其电磁特性. 传统的S参数提取方法一开始就假定超材料仅具有介电常数和磁导率两个本构参数, 所以采用该方法提取磁电耦合超材料本构参数存在明显局限性. 将磁电耦合超材料中的电元件和磁元件分别等效为面电流和面磁流, 通过推导平均电通密度和磁通密度与外加电磁场的相互关系, 从理论上获取了磁电耦合超材料2×2 的本构参数矩阵, 确定了磁电耦合超材料这四个本构参数与磁元件的磁导率、电元件的介电常数、空间色散项和耦合系数之间的关系解析公式, 进而获得了折射率理论计算公式. 利用该折射率公式对折射率提取值进行了非线性拟合, 发现提取值和理论值之间的误差很小, 这个结果很好地验证了所给出的本构矩阵解析式和折射率公式的正确性. 根据拟合结果, 获得了磁电耦合超材料本构矩阵中四个电磁参数的频率响应曲线. 所提出的磁电耦合超材料本构矩阵参数获取方法将为研究磁电超材料中电元件和磁元件的耦合现象提供重要的理论参考.     

Exploring electromagnetic response of tellurium dielectric resonator metamaterial at the infrared wavelengths

We numerically investigate the electromagnetic properties of tellurium dielectric resonator metamaterial at the infrared wavelengths. The transmission spectra, effective permittivity and permeability of the periodic tellurium metamaterial structure are investigated in detail. The linewidth of the structure in the direction of magnetic field W x has effects on the position and strength of the electric resonance and magnetic resonance modes. With appropriately optimizing the geometric dimensions of the designed structure, the proposed tellurium metamaterial structure can provide electric resonance mode and high order magnetic resonance mode in the same frequency band. This would be helpful to analyze and design low-loss negative refraction index metamaterials at the infrared wavelengths.     

Effective electromagnetic response of nanostructured metal-dielectric metamaterials

The optical properties of metamaterial layers have been analyzed by the scattering matrix method. The properties of effective ɛ and μ, reconstructed from the transmittance and reflectance of metamaterial layers of finite thickness using the inverse Fresnel formulas, are discussed. It is shown that the optical response of nanostructured metal-dielectric metamaterials is strongly nonlocal and dissipative. Original Russian Text ? S.G. Tikhodeev, 2009, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2009, Vol. 73, No. 1, pp. 95–97.     

Dielectric substrate effect on the metamaterial resonances in terahertz frequency range

We report on the effect of dielectric substrate on the resonance shift of metallic metamaterials operating in the terahertz frequency region. The resonance frequencies for various metamaterials obtained by time-domain spectroscopy agree well with calculations based on the finite-difference time-domain method. The dependencies of the resonance frequency to substrate index are studied, and are systematically determined by introducing an effective substrate index. The relative contributions of the substrate index for various metamaterials are obtained by fitting the numerically obtained effective refractive indices as a function of substrate index, which is found to be ∼0.63 regardless of the metamaterial geometry.     

Temperature-controlled tunable acoustic metamaterial with active band gap and negative bulk modulus

The local resonant band gap and the negative bulk modulus of the acoustic metamaterial with Helmholtz resonators are strongly affected by the temperature of water. In this paper, the acoustic transmission line method (ATLM) is introduced to investigate the influences of the temperature of water on the local resonant band gap and the negative bulk modulus of the acoustic metamaterial. Results show that the relative variations of the local resonant band gap and the negative effective bulk modulus suffering from the change of the temperature of water are approximately equivalent and are up to about 11%. The reason is that the local resonant frequency is proportional to the sound speed of fluid which is strongly effects by the temperature of water. By achieving the unambiguous relationships between these unusual properties of the acoustic metamaterial and the temperature of water, we find that the temperature-controlled acoustic metamaterial with the active band gap and the active negative bulk modulus can be realized in theory. This idea opens a new avenue for the design of the tunable acoustic metamaterial that can modulate the acoustic wave propagation.     

Dual-band polarization-independent sub-terahertz fishnet metamaterial

A dual-band and polarization-independent fishnet metamaterial for the sub-THz frequency range is proposed and investigated. Dual-band modes have two resonances in which the first one is fixed as a left-handed mode and the second one can be arranged as a left-handed or single-negative mode. We select the character of second resonance by the choice of substrate properties. The metamaterial features of the structure are analyzed using the scattering data and confirmed by applying Kramers-Kronig relations. The characteristic features are also verified by the current distribution at the inner metallic surfaces of the structure. The influence of substrate modifications is studied and the effect of this change on resonances is discussed. The design of a dual-band and polarization-independent sub-THz metamaterial presented here can serve as a model and guide to realize tunable fishnet metamaterials for other frequency regimes.