Effective Response of Nonlinear Spherical Coated Composites Under External AC and DC Electric Field

Under the external AC and DC electric field, the effective response of nonlinear spherical coated composites, which obey the constitutive relation of electric displacement and electric field, is investigated in the dilute limit by using the perturbation method. The local potentials in inclusion and host regions are derived at all harmonics. Moreover, the formulae of the effective linear and nonlinear responses are given in the dilute limit.     

The Effective AC Response of Nonlinear Composites

A perturbative approach is used to study the AC response of nonlinear compostie media,which obey a current-field relation of the form J=σE χ|E|^2E with comp[onents having nonlinear response at finite frequencies.For a sinusoidal applied field,we extend the local potential in terms of sinusoidal components at fundamental frequency and high-order harmonic frequencies to treat the nonlinear comosites.For nonlinear composite media with a low concentrations of spherical inclusions,we give the formulae of the nonlinear effective AC susceptibility χ3ω at the third harmonic frequency.     

Effective AC response of nonlinear spherical coated composite

An effective nonlinear response of a nonlinear composite with spherical coated inclusions randomly embedded in a host medium under the action of an external AC electric field, {{\bm E}}_a = {{\bm E}}_1 \sin (\omega t) + {{\bm E}}_3 \sin (3\omega t), is investigated using a perturbation method. The local potentials of the composite at higher harmonics are given both in the region of local inclusion particles and in the local host region under the external AC electric field. All effective nonlinear responses of the composite and the relationship between the effective nonlinear responses at the fundamental frequency and third harmonics are also studied for spherical coated inclusion in a dilute limit.     

Effective AC and DC Responses of Nonlinear Composites at Higher Concentration

For higher concentration of inclusions, an effective medium approximation （EMA） method is used to investigate the bulk effective response of weakly nonlinear composites, which are subject to the constitutive relation of electric displacement and electric field, Dα = εαE ＋Xα｜E｜^2 E. As an example of three dimensions, under the external AC and DC electric fields Eapp = Eα（1 ＋ sinωt）, we have derived the general effective nonh＇near response of composites by the EMA method for higher concentration of spherical inclusions. Furthermore, the effective nonlinear responses at harmonics are predicted.     

Effective Response of Nonlinear Composite under External AC and DC Electric Field

A perturbation method is used to study effective response of nonlinear Kerr composites, which are subject to the constitutive relation of electric displacement and electric field, Dα=εαE＋xα｜E｜^2E. Under the external AG and DC electric field Eapp = Eα（1 ＋ sinωt）, the effective nonlinear responses and local potentials are induced by the cubic nonlinearity of Kerr materials at all harmonics. As an example in three dimensions, we have investigated this kind of nonlinear composites with spherical inclusions embedded in a host. At all harmonic frequencies, the potentials in inclusion and host regions are derived. Furthermore, the formulae of the effective linear and nonlinear responses are given in the dilute Iimit.     

Effective Response of Nonlinear Composite under External AC and DC Electric Field

A perturbation method is used to study effective response of nonlinear Kerr composites, which are subject to the constitutive relation of electric displacement and electric field, Dα = εαE xα|E|2E. Under the external AC and DC electric field Eapp = Eα(1 sinwt), the effective nonlinear responses and local potentials are induced by the cubic nonlinearity of Kerr materials at all harmonics. As an example in three dimensions, we have investigated this kind of nonlinear composites with spherical inclusions embedded in a host. At all harmonic frequencies, the potentials in inclusion and host regions are derived. Furthermore, the formulae of the effective linear and nonlinear responses are given in the dilute limit.     

非线性柱形涂层复合介质有效的直流-交流电响应

利用摄动展开方法, 研究了由圆柱形带涂层杂质随机嵌入基质所形成的非线性复合介质在外加 的带有不同频率和振幅的混合电场E₀ + E₁ sinωt+E₃ sin3ωt作用下有效的直流-交流电响应, 分别推导了复合介质在杂质核、涂层及基质区域的电势分布, 并在低杂质浓度下给出了复合介质有效的非线性响应及它们之间的关系. 关键词： 非线性柱形涂层复合介质 有效的非线性响应 外加交直流电场     

Effective Dielectric Response of Composites with Graded Material

The effective dielectric response of linear composites containing graded material is investigated under an applied electric field E₀. For the cylindrical inclusion with gradient dielectric function, ε_i(r)=b+cr, randomly embedded in a host with dielectric constant ε_m, we have obtained the exact solution of local electric potential of the composite media regions, which obeys a linear constitutive relation D=εE, using hypergeometric function. In dilute limit, we have derived the effective dielectric response of the linear composite media. Furthermore, for larger volume fraction, the formulas of effective dielectric response of the graded composite media are given.     

Effects of Particle Shape and Microstructure on Effective Nonlinear Response

We consider a binary granular composite medium, in which two materials have high-order nonlinearities. The effect of particle shape on effective nonlinear response (ENR) is investigated by assuming all the particles to be shaped as uniaxial ellipsoid. We discuss two types of arrangements of particles: 1) parallel axes (Case I); 2) random axes (Case II). During the process of numerical calculation, one component material is assumed to be linear, and two kinds of conductors are assumed to be at high conducting contrast. We find that: 1) the shape effect on ENR is possibly strong; 2) the enhanced ENR can even be obtained by choosing particles of appropriate ellipsoidal shapes; 3) the ENR enhancement predicted by Case I is much stronger than that by Case II.     

Effective response in nonlinear spherical coated composites under external AC and DC electric fields

By using the perturbation method,effective nonlinear direct current(DC) and alternating current(AC) responses of nonlinear composites with spherical coated inclusions randomly embedded in a host medium are studied under the action of an external electric field E a = E 0 + E 1 sin ωt + E 3 sin 3ωt with different amplitudes and frequencies.The local potentials of composites at all harmonics are given in the inclusion particles and the host regions.All effective nonlinear responses to composites and the relationship between the effective nonlinear responses at all harmonics are also deduced for the spherical coated inclusions in a dilute limit.     

Effective Nonlinear Response of the Nonlinear Random Mixed Composites

A simple self-consistent mean-field theory is used to study the nonlinear composites consisting of linear and strongly nonlinear materials or strongly nonlinear materials with different nonlinear exponents. The effective nonlinear response obtained is compared with simulation data. Good agreement is found. Meanwhile, we study the effect of granular shapes (depolarization factor g) in different external applied fields on the nonlinear response of nonlinear random composites. It is found that the factor g affects the effective nonlinear response greatly in certain conditions.     

Effective response in nonlinear spherical coated composites under external AC and DC electric field

By using the perturbation method, effective nonlinear direct current (DC) and alternating current (AC) responses of nonlinear composites with spherical coated inclusions randomly embedded in a host medium are studied under the action of external electric field E_a =E₀ +E₁ sin ωt+E₃ sin 3ωt with different amplitudes and frequencies. The local potentials of composites at all harmonics are given in the inclusion particles and the host regions. All effective nonlinear responses to composites and the relationship between the effective nonlinear responses at all harmonics are also deduced for the spherical coated inclusions in a dilute limit.     

Effective Dielectric Response of Nonlinear Composites of Coated Metal Inclusions

The effective dielectric response of the composites in which nondilute coated metal particles are randomly embedded in a linear host is investigated. Two types of coated particles are considered, one is that the core is nonlinear, the other is that the shell is nonlinear. We derive general expressions for the effective linear dielectric function and the effective third-order nonlinear susceptibility, and take one step forward to perform numerical calculations on the coated metal/dielectric composites. Numerical results show that the effective linear and nonlinear dielectric responses can be greatly enhanced near the surface plasmon resonant frequency. Moreover, the resonant peaks are found within a range from 0.46ωp to 0.57ωp for spherical particles and from 0.59ωp to 0.70ωp for cylindrical inclusions. In the frequency region, the resonant peak can achieve the maximum, according to an optimal structural parameter and volume fraction. The resonant frequency exhibits a redshift with the increasing structural parameter k or volume fraction f or dimensionality factor D.     

Effective Anisotropic Dielectric Properties of Crystal Composites

Transformation fieM method （TFM） is developed to estimate the anisotropic dielectric properties of crystal composites having arbitrary shapes and dielectric properties of crystal inclusions, whose principal dielectric axis are different from those of anisotropic crystal matrix. The complicated boundary-value problem caused by inclusion shapes is circumvented by introducing a transformation electric field into the crystal composites regions, and the effective anisotropic dielectric responses are formulated in terms of the transformation field. Furthermore, the numerical results show that the effective anisotropie dielectric responses of crystal composites periodically vary as a function of the rotating angle between the principal dielectric axes of inclusion and matrix crystal materials. It is found that at larger inclusion volume fraction the inclusion shapes induce profound effect on the effective anisotropic dielectric responses.     

梯度圆柱颗粒复合介质的有效非线性响应

应用非线性微分有效偶极近似方法,导出了关于非线性梯度圆柱颗粒的等效线性介电常数和三阶非线性极化率的微分式,研究了稀释极限下,圆柱形梯度颗粒无规置入线性介质中组成的复合介质的有效线性介电常数和三阶非线性极化率.作为应用,数值计算了具有幂指数梯度分布的介电常数的颗粒复合介质的有效非线性响应,及梯度金属电介质颗粒复合介质的表面plasmon共振效应.     

金属/电介质颗粒复合介质的非线性交流响应

推广T矩阵法来研究二组分颗粒复合介质的非线性交流响应，解析推导出基频、三次及五次谐波频率下的有效线性介电常数及三阶和五阶非线性极化率的解析表达式.当组分颗粒的介电常数为实数时，表达式同以前微扰理论完全一致.进一步数值计算了金属-电介质复合介质的有效非线性交流响应，数值结果表明，体系的三阶、五阶非线性极化率在表面等离子共振频率附近有明显增强，而且，随着体积分数提高，共振峰增强且伴随着共振频率红移现象.还进一步讨论了维度效应对体系非线性交流响应的影响. 关键词： T矩阵方法 复合介质 非线性交流响应     

Effective response of nonlinear cylindrical coated composites under external AC and DC electric field

This paper uses the perturbation method to study effective response of nonlinear cylindrical coated composites. Under the external AC and DC electric field E_a(1 + sinωt), the local potentials of composites at all harmonic frequencies are induced. An effective nonlinear response to composite is given for the cylindrical coated inclusions in the dilute limit.     

Electric field distribution and effective nonlinear AC and DC responses of graded cylindrical composites

The perturbation method is used to study the localization of electric field distribution and the effective nonlinear response of graded composites under an external alternating-current (AC) and direct-current (DC) electric field E_app = E₀ (1+sin ωt). The dielectric profile of the cylindrical inclusions is modeled by function ε_i (r) = C_k r^k (r ≤ a), where r is the radius of the cylindrical inclusion, and C_k, k, a are parameters. In the dilute limit, the local potentials and the effective nonlinear responses at all harmonics are derived. Meanwhile, the general effective nonlinear responses are also derived and compared with the effective nonlinear responses at harmonics under the AC and DC external field. It is found that the effective nonlinear AC and DC responses at harmonics can be calculated by those of the general effective nonlinear of the graded composites under the external DC electric field. Moreover, the obtained local electrical fields show that the electrical field distribution in the cylindrical inclusions is controllable, and the maximum of the electric field inside the cylinder is at its center.     

Nonlinear Dependence of Response Rateon Intensity in Doped KNSBN Crystals

l.IntroductionThephotorefractiveresponserateisacritica1issuebecauseitdirectlydeterminestheprocessingsPeedofphotorefractivedevices[1]-TherelationshipbetweentheresPonserateandthelightintensitycanprovideusefuIinformationaboutthedefectlevels,theprocessofchargeCarriersexcited,transportedaMdtrapPed["'].Conventionalsing]elevelmod-e1s[4jpredictthatthephotorefractiveresponserateislinearlydePendentonthelightinten-sity.However,experimentaldatashowedthatthephotorefractiveresponserateofsomecrystalsvarie…     

梯度分布球颗粒复合介质的介电特性和光吸收特性

研究球形颗粒复合介质沿颗粒半径方向有梯度分布的有效介电响应和光吸收性质,利用微分有效偶极距近似方法计算有梯度分布球颗粒的等效介电常数.数值计算结果表明,对于一般的球形粒子,介电常数随半径按幂指数规律变化时,系统的有效介电常数随指数n的增大而减小;而对金属球形粒子,则存在等离子体共振吸收峰,且随参数mw和mv的增大,其位置将发生红移.这为复合材料的制备提供了一种新的理论依据.