Numerical simulations of negative-index refraction in a lamellar composite with alternating single negative layers

Negative-index refraction is demonstrated in a lamellar composite with epsilon-negative (ENG) and mu-negative (MNG) materials stacked alternatively. Based on the effective medium approximation, simultaneously negative effective permittivity and permeability of such a lamellar composite are obtained theoretically and further proven by full-wave simulations. Consequently, the renowned left-handed metamaterial comprising split ring resonators and wires is interpreted as an analogy of such ENG--MNG layers. In addition, beyond the effective medium approximation, the propagating field squeezed near the ENG/MNG interface is demonstrated to be left-handed surface waves with backward phase velocity.     

Effective permittivity of periodic composite materials: Numerical modeling by the finite element method

The effective properties of composite materials are closely related to the composition and arrangement of its constituents. Many studies and articles are actively studying the dielectric properties of heterogeneous structures with random and periodic arrangement. In the quasistatic limit, we use the finite element method as a numerical tool to evaluate the effective permittivity of two and three component composites. Two heterostructures are investigated; the first is formed by crossed dielectric cylinders in permanent contact and arranged in three layers. The cylinders are immersed in a dielectric host medium. The second structure is similar to the first except that the tubes are covered by an interphase layer. The numerical tool used to extract the exact value of the effective permittivity takes into account all internal multipolar interactions which contribute to the polarization of the material medium. The impacts of the relative permittivity and volume fraction of cylinders, the thickness of interphase and its dielectric constant are reported. The Maxwell–Garnett theory fails to predict the effective permittivity of the studied structures for high volume fraction and permittivity contrast. To overcome this problem, an amendment was made to the McLachlan equation McQ also termed the Two Exponent Single Percolation Equation TESPE. The first exponent t is held equal to 1 and the other exponent s is depending on the volume fraction. s is calculated so that the whole values of the effective permittivity obtained by the McQ rule are exactly the same values obtained by the simulations. Finally, we obtained a chart and a model to find the values of s, a fast way that is very useful for practitioners and design engineers of composite materials.     

Validation of the effective-medium approximation for the dielectric permittivity of oriented nanoparticle-filled materials: effective permittivity for dielectric nanoparticles in multilayer photonic composites

A formula for the effective permittivity for two-dimensional particles embedded in a host matrix is derived and a method for its numerical evaluation is described. The method is applied to specific cases of circular, square, rectangular and triangular particles. Shapes are assumed for the inclusion particles. Data for obtaining the effective permittivity is provided for a wide range of filling fractions, geometries and dielectric contrasts between the particles and the matrix under the assumption of the quasi-static approximation, that is, the wavelength of the electric field is assumed to be much larger than the particle size. Metallic particles with complex and frequency-dependent dielectric constants are treated, as well as no-loss dielectric inclusions. Calculations are validated by comparing the results of the reflectivity obtained for a composite layer using the transfer-matrix method, assuming the layer to be an effective medium, to those using the finite-element method and accounting for the heterogeneous material. PACS 78.20.-e; 78.20.Bh; 78.20.Ci; 78.66.Sq; 78.66.Vs     

高浓度纤维增强材料介电特性计算方法

针对复合材料的微观结构非均匀和各向异性特点带来的数值方法计算慢、内存消耗大的问题,利用均匀化方法计算纤维增强复合材料的等效电磁参数.采用了纤维低体积添加比至高体积添加比的迭代方法,同时提出了一个描述材料微观结构的修正的特征长度,将现有的均匀化方法推广至非准静态(微波频段)条件下高纤维浓度情况.提出的修正的均匀化模型可直接用于反射系数、屏蔽效能等计算,其屏蔽效能与实际微观结构复合材料的数值仿真结果进行了对比,验证了提出的等效电磁参数计算公式的有效性和频率适用范围.     

Modeling of ferrite-based materials for shielding enclosures

An analytical model for a magneto-dielectric composite material is presented based on the Maxwell Garnett rule for a dielectric mixture, and on Bruggeman's effective medium theory for permeability of a ferrite powder embedded in a dielectric. In order to simultaneously treat frequency-dispersive permittivity and permeability of a composite in a full-wave FDTD code, a new algorithm based on discretized auxiliary differential equations has been implemented. In this paper, numerical examples of modeling structures containing different magneto-dielectric mixtures are presented.     

弱非线性复合体中的高阶非线性响应

利用谱表示理论和微扰展开法，从理论上给出了适合于一般微结构复合体系的有效非线性响 应的一般表示式，并结合有效媒质近似（EMA），在弱非线性条件下研究了由三阶非线性组 分（体积分数为p）和线性组分构成的非线性复合体系的有效非线性响应，讨论了复合 体系的有效介电常数ε～e=εe+χe|E0|2+ηe|E0| 4中的有效三次非线性响应χe和有效高次非线性响应ηe与体积分数p和 退极化因子L之间的关系，分析了非线性组分的介电常数为复数情形时体系的有效高阶非线 性响应，从理论上说明了组分的高次非线性响应对整个复合体系的有效介电常数的影响.  关键词： 非线性复合介质 有效非线性响应 谱表示理论     

金属/电介质颗粒复合介质光学双稳的温度效应

应用有效媒质近似，结合自洽平均场理论和谱表示方法，研究了金属电介质颗粒复合介质的光学双稳行为与温度的关系.数值计算了不同的入射频率、体积分数和形状因子下光学双稳的温度效应，结果发现，温度对光学双稳的产生、双稳阈值及阈值宽度有很大影响. 关键词： 复合介质 光学双稳 谱表示 温度     

Inverse Spectral Problem and Peakons of an Integrable Two-component Camassa-Holm System

In this paper, we are concerned with the explicit construction of peakon solutions of the integrable twocomponent system with cubic non-linearity. We establish the spectral and inverse spectral problem associated to the Lax pairs of the system. The inverse problem is solved by the classical results of Stieltjes continued fractions, which also contributes a lot to the spectral problem. The explicit formulas are obtained from solutions of the inverse problem. The positivity of the spectral measures is implied by J. Moser's work on the Jacobi spectral problem.     

Application of Bruggeman and Maxwell Garnett homogenization formalisms to random composite materials containing dimers

The homogenization of a composite material comprising three isotropic dielectric materials was investigated. The component materials were randomly distributed as spherical particles, with the particles of two of the component materials being coupled to form dimers. The Bruggeman and Maxwell Garnett formalisms were developed to estimate the permittivity dyadic of the homogenized composite material (HCM), under the quasi-electrostatic approximation. Both randomly oriented and identically oriented dimers were accommodated; in the former case the HCM is isotropic, whereas in the latter case the HCM is uniaxial. Representative numerical results for composite materials containing dielectric–dielectric dimers demonstrate close agreement between the estimates delivered by the Bruggeman and Maxwell Garnett formalisms. For composite materials containing metal–dielectric dimers and metal–metal dimers with moderate degrees of dissipation, the estimates of the two formalisms are in broad agreement, provided that the dimer volume fractions are relatively low. In general, the effects of intradimer coupling on the estimates of the HCM’s permittivity are relatively modest but not insignificant, these effects being pronounced by anisotropy when all dimers are identically oriented.     

Nanocomposite-based ultrathin polarization beamsplitter

In terms of the effective medium approximation, the optical properties of heterogeneous composite materials with disordered nanosized metal inclusions of spheroidal shape with plasmon resonances lying in the visible spectral range are studied. The conditions are analyzed under which the optical characteristics of the composite with axial symmetry of the inclusion orientation distribution with respect to a certain preferential direction significantly depends on the electric field direction in the electromagnetic wave. It is shown that, in the vicinity of the plasmon resonance of inclusions, the composite layer of subwavelength thickness may exhibit a high polarization selectivity in both reflection and transmission with moderate absorption. The effect of the orientational disorder of inclusions on the optical characteristics of a polarization splitter of this kind is discussed. The predictions based on equations of quasi-electrostatic effective-medium model agree well with the results of exact numerical solution of the Maxwell equations.     

电磁诱导下Y型四能级原子系统的左手效应

采用了一个闭合的Y型四能级原子系统,在多模光场的作用下,利用量子相干技术使其实现介质的左手效应,使介质具备左手材料特性. 在相互作用表象下,考虑偶极近似和旋转波近似,利用密度矩阵方程并结合相关条件下的有关公式进行理论计算. 数值模拟结果显示：在合适的参量条件下,介质的相对介电常量和相对磁导率可以同时出现负值,产生了左手效应,相应的介质转化为左手材料.在弱探测场条件下,当探测光的拉比频率增加时,介质实现左手效应的频率范围减小并且与之相对应的折射率和吸收系数也发生变化. 通过讨论在左手效应成立的条件下介质对光场的吸收和增益问题,结果表明：在弱探测场条件下,利用电磁诱导的方法也可以实现介质的左手效应,使得左手材料在实验上的实现也得到了进一步的扩展,同时也扩展了电磁诱导的应用领域.     

An integral representation and bounds on the effective diffusivity in passive advection by laminar and turbulent flows

Precise necessary and sufficient conditions on the velocity statistics for mean field behavior in advection-diffusion by a steady incompressible velocity field are developed here. Under these conditions, a rigorous Stieltjes integral representation for effective diffusivity in turbulent transport is derived. This representation is valid for all Péclet numbers and provides a rigorous resummation of the divergent perturbation expansion in powers of the Péclet number. One consequence of this representation is that convergent upper and lower bounds on effective diffusivity for all Peclet numbers can be obtained utilizing a prescribed finite number of terms in the perturbation series. Explicit rigorous examples of steady incompressible velocity fields are constructed which have effective diffusivities realizing the simplest upper or lower bounds for all Péclet numbers. A nonlocal variational principle for effective diffusivity is developed along with applications to advection-diffusion by random arrays of vortices. A new class of rigorous examples is introduced. These examples have an explicit Stieltjes measure for the effective diffusivity; furthermore, the effective diffusivity behaves likek ₀(Pe)^1/2 in the limit of large Péclet numbers wherek ₀ is the molecular diffusivity. Formal analogies with the theory of composite materials are exploited systematically.Research partially supported by NSF DMS 90-05799 and ARO DAAL 03-89-K-0039 and AFOSR-90-0090Research partially supported by NSF DMS 87-02864, ARO DAAL 03-89-K-0013 and ONR N 00014-89-J-1044     

Dielectric properties of microcomposite ferroelectrics

The dielectric response in two-phase composites of ferroelectric and dielectric materials was studied within the quasistatic approximation. Using different effective medium theories (Maxwell-Garnet theory, the effective medium approximation and the Bergman representation) the dielectric function was represented as a distribution of polar modes. One of the main results concerns the existence of modes due to geometric resonances which among other effects can lead to new low-frequency absorption peaks near the percolation threshold of the ferroelectric material. These peaks appear always higher than the transverse polar mode frequencies of the bulk components but below their corresponding longitudinal mode frequencies. The soft mode with renormalized mode strength but unchanged frequency exists only in the composite with percolated ferroelectric clusters. When the ferroelectric clusters are only finite the soft mode does not soften completely.     

基于稀疏表示模型和自回归模型的高光谱分类

针对高光谱分类中对光谱信息和空间信息利用不足的问题,提出了一种基于稀疏表示模型和自回归模型相结合的分类算法。该算法利用稀疏表示模型和自回归模型,设计联合字典:在光谱维上,利用稀疏表示模型将高光谱的每个光谱向量表示为字典中训练样本的稀疏线性组合;在空间维上,利用自回归模型对每个光谱向量的8邻域进行约束。针对不同样本分别构造一个字典,在减少计算量的同时减小重构误差,最后在最小重构误差和邻域相关性的约束下求解稀疏表示问题,以最小重构误差为准则实现高光谱数据的分类。仿真结果表明,该方法能够有效地提高高光谱数据的分类精度。     

Effective medium approximation for optical bistability in nonlinear metal-dielectric composites

A general theory based on the spectral representation method and effective medium approximation is adopted to investigate the optical bistable behavior in a nonlinear two-phase composite with symmetrical microstructure, in which the metal particles of the volume fraction p and the dielectric particles of the volume fraction 1−p are randomly dispersed but oriented with respect to one another. The relation between the spatial average of local field squared and the external applied field is established through the spectral density function m(x), obtained from the modified Bruggeman effective medium approximation. We find that the optical bistability (OB) is dependent on the depolarization factor L of the components and the volume fraction p. For a given p, we predict that OB can be observed only when L is larger than the critical value L_c, and bistable behavior is more pronounced at large L. Moreover, numerical results show that both the upper threshold field and the width of OB region increase monotonically as L increases. The field-dependent reflectance at normal incidence R in random composites is also investigated.     

Electrical characteristics of three-component dielectric media

We study the effective parameters of a three-component plane dielectric medium with a doubly periodic arrangement of circular inclusions. The problem is solved in the one-dipole approximation. The computational results are compared with a two-component Rayleigh model. The general structure of the formulas for the effective parameters is discussed and the reciprocity relations for a three-component matrix system are determined. Explicit expressions are given for the dielectric permittivity when the concentration of circular inclusions is low, and their domain of applicability is determined. Under certain polarization conditions, the effective conductivity in a three-component medium is exactly equal to the dielectric permittivity of the matrix. Zh. éksp. Teor. Fiz. 114, 1121–1136 (September 1998)     

Perturbation Expansion Method and Effective Medium Approximation for Effective Conductivity of Nonlinear Composite Media

In this paper, we establish an effective medium approximation (EMA) for effective conductivity of nonlinear composite media. As an example, we consider a two-dimensional composite medium with a cylindrical inclusion embedded in a homogeneous host, both the host and the inclusion having nonlinear current-voltage constitutive relations, and apply the perturbation expansion method to derive its analytic series solution. Using the nonlinear EMA we derive the formulae of the first, the third and the fifth-order effective conductivities, which are valid for nonlinear composite media with middle concentration of inclusion.     

Effective thermal conduction in composite materials

The problem of determining the bounds and/or estimating the effective thermal conductivity (λ _eff) of a composite (multiphase) system given the volume fractions and the conductivities of the components has been investigated. A comparison between the measured data and the results predicted by theoretical models has been made for seven heterogeneous samples. The tested models include those of the effective medium theory (EMT), Hashin and Shtrikman (HS) bounds, and Wiener bounds. These models can be used to characterize macroscopic homogeneous and isotropic multiphase composite materials either by determining the bounds for the effective thermal conductivity and/or by estimating the overall conductivity of the random mixture. It turns out that the most suitable one of these models to estimate λ _eff is the EMT model. This model is a mathematical model based on the homogeneity condition which satisfies the existence of a statistically homogeneous medium that encloses inclusions of different phases. Numerical values of thermal conductivity for the samples that satisfy the homogeneity condition imposed by the effective medium theory are in best agreement with the experimentally measured ones.