Multipole contributions to the effective dielectric constant of suspensions of spheres

We study multipole contributions to the effective dielectric constant of dilute suspensions of uniform spheres. It is shown that for frequencies near the plasma resoance multipole contributions are negligible in comparison with the dipole contributions. Outside resoance multipolar corrections to the Clausius-Mossotti formula are of the same order of magnitude as the dipolar ones. We argue that in resonance the dipole approximation should be valid also for more complicated sphere models.     

Multipolar corrections to the Clausius-Mossotti formula for the effective dielectric constant of a polydisperse suspension of spheres

We study multipolar corrections to the Clausius-Mossotti formula for the effective dielectric constant of a polydisperse suspension of spheres with identical uniform dielectric constant embedded in a uniform background. The first few moments of the spectral density occurring in the Bergman representation are evaluated exactly to second order in the volume fraction. We present numerical results for a log-normal distribution of sphere radii.     

Spectral broadening in suspensions of metallic spheres

We study the effective dielectric constant of dilute suspensions of metallic spheres in a transparent background, e.g. glass or water. In the low density limit the effective dielectric constant as a function of frequency exhibits a strong absorption peak corresponding to the dipolar surface plasmon of isolated spheres. We investigate how the absorption peak is modified at higher density due to electrostatic interactions between spheres. We find appreciable deviations from the Clausius-Mossotti formula which may be seen most clearly in a Cole-Cole plot of the effective dielectric constant.     

The Clausius-Mossotti formula and its nonlocal generalization for a dielectric suspension of spherical inclusions

Employing a recently developed cluster expansion for the effective dielectric constant of a suspension of spherical inclusions, we show which parts of the cluster integrals give rise to the Clausius-Mossotti formula. The same selection of terms is then used to obtain an approximate expression for the wave-vector-dependent effective dielectric tensor. For a system of hard spheres with only dipole polarizability this expression is evaluated in closed form. This last result is then used to derive the form of the electrostatic potential due to a point charge in the effective medium. For physically reasonable values of the polarizability, the potential has asymptotically the form corresponding to a medium with the Clausius-Mossotti dielectric constant, while at short range it oscillates about this form. For values of the polarizability beyond the physical range critical points are found at which the oscillations become long range.     

Fluids of polarizable hard spheres with dipoles and tetrahedral quadrupoles Integral equation results with application to liquid water

The mean spherical, linearized hypernetted chain and quadratic hypernetted chain approximations are solved for a fluid of hard spheres with embedded point dipoles and tetrahedral quadrupoles and this system is shown to be quite similar to the dipole-linear quadrupole case previously studied. However, tetrahedral quadrupoles have a larger influence upon the structural and thermodynamic properties and are slightly more effective in decreasing the dielectric constant from the purely dipolar value. Also we describe a simple self-consistent mean field theory which allows molecular polarizability to be taken into account. This approximation together with the integral equation methods is applied to a polarizable dipole-tetrahedral quadrupole fluid with water-like parameters. The dielectric constant of this system is found to be in good agreement with the experimental results for liquid water for temperatures ranging from 25°C to 300°C. The influence of molecular polarizability is shown to be very large. At 25°C the mean dipole moment is ～2·56 D compared with ～1·85 D in the gas phase and the dielectric constant increases from ～25 for non-polarizable particles to ～80 for the polarizable model.     

Static dielectric properties of Stockmayer fluids

Dielectric constants for the Stockmayer fluid are computed both from the equilibrium fluctuations of the polarization and from the polarization response to an applied field in a molecular dynamics simulation with periodic boundary conditions and with the dipole interactions treated by the Ewald method. The dielectric constant at finite wavelength is obtained from a Kirkwood-like expression, while for uniform polarization fluctuations a different expression applies due to the absence of surface effects in the Ewald calculation. The results are nearly independent of the number (up to 500) of particles investigated, even at large values of the dipole moment. The dielectric constants obtained from the approximate solution of the hypernetted chain integral equation are considerably larger than the molecular dynamics results except at low dielectric constants. The external field simulation permits study of the non-linear dependence of the dielectric constant on the magnitude of the applied electric field.     

Switching mechanism due to the spontaneous emission cancellation in photonic band gap materials doped with nano-particles

We have investigated the switching mechanism due to the spontaneous emission cancellation in a photonic band gap (PBG) material doped with an ensemble of four-level nano-particles. The effect of the dipole–dipole interaction has also been studied. The linear susceptibility has been calculated in the mean field theory. Numerical simulations for the imaginary susceptibility are performed for a PBG material which is made from periodic dielectric spheres. It is predicted that the system can be switched between the absorbing state and the non-absorbing state by changing the resonance energy within the energy bands of the photonic band gap material.     

C波段球体目标系的瑞利复合散射特性

在C波段研究了一对介质球体目标的瑞利复合电磁散射特性, 得到了目标复合散射截面解析式, 验证了所得结果的正确性; 研究了入射波极化状态、目标距离、目标大小、介电常数等因素对复合散射截面的影响, 结果表明, 邻近目标对本目标散射的影响具有偶极辐射的特点, 主目标的复合散射截面是邻近目标的大小、介电常数及其位置等因素的函数; 结果为目标散射截面的准确测量、电磁相互作用等奠定了理论基础。     

Two-particle cluster integral in the expansion of the dielectric constant

We study in detail the two-particle cluster integral in the cluster expansion for the effective dielectric constant of a suspension of spherically symmetric polarizable inclusions embedded in a uniform medium. Although our form for the integrand differs from that derived earlier by Finkel'berg and by Jeffrey, we show that the integral is equivalent. The two-body dielectric problem for particles with an arbitrary radial dependence of the dielectric constant is solved by an expansion in spherical harmonics. Numerical results for some special models illustrate the importance of multipole contributions to the effective dielectric constant.     

Calculated Optical Properties of Dielectric Shell Coated Gold Nanorods

Optical absorption spectra of dielectric shell coated gold nanorods are simulated using the discrete dipole ap- proximation method. The influence of the aspect ratio, shell thickness, dielectric constant of the shell, and surrounding medium on the longitudinal resonance mode is investigated. It is found that the coated dielectric shell does not affect the trend in the dependence of resonance position on the aspect ratio, while it broadens the resonant line width and reduces the sensitivity of plasmon resonance in response to changes of the surrounding medium. F~arthermore, the difference of dielectric constants between the shell and surrounding medium plays an important role in determining the resonance position. The screening effect of the dielectric shell tends to be less apparent for a thicker shell thickness.Optical absorption spectra of dielectric shell coated gold nanorods are simulated using the discrete dipole ap- proximation method. The influence of the aspect ratio, shell thickness, dielectric constant of the shell, and surrounding medium on the longitudinal resonance mode is investigated. It is found that the coated dielectric shell does not affect the trend in the dependence of resonance position on the aspect ratio, while it broadens the resonant line width and reduces the sensitivity of plasmon resonance in response to changes of the surrounding medium. F~urthermore, the difference of dielectric constants between the shell and surrounding medium plays an important role in determining the resonance position. The screening effect of the dielectric shell tends to be less apparent for a thicker shell thickness.     

Cluster expansion for the dielectric constant of a polarizable suspension

We derive a cluster expansion for the electric susceptibility kernel of a dielectric suspension of spherically symmetric inclusions in a uniform background. This also leads to a cluster expansion for the effective dielectric constant. It is shown that the cluster integrals of any order are absolutely convergent, so that the dielectric constant is well defined and independent of the shape of the sample in the limit of a large system. We compare with virial expansions derived earlier in statistical mechanics for the dielectric constant of a nonpolar gas. In these expansions the virial coefficients are given by integrals which are only conditionally convergent.     

Influence on SERS enhancement factor of the components of an artificial opal loaded with metal NPs: A systematic study

We have inquired about the influence of composite artificial opal components on its SERS enhancement factor (EF). Particularly, we considered metal (100 nm) and dielectric spheres (290 nm), and an excitation wavelength of 632 nm. We show that the electric field of a SiO₂ sphere is weaker and more uniform as its porosity increases. Additionally, a porous sphere promotes a lower EF compared to that of a non-porous sphere. The optical response of the composite opal is insensitive to the polarization state of the incident field. A SERS EF of 10⁴ is reachable with an opal loaded with Au or Ag NPs. In general, the dielectric spheres affect the SERS EF intensity of the metal NPs. From the optical spectra, we observed that with a 632 nm wavelength, the composite opal is out of resonance.     

Tunneling mechanism of light transmission through metallic films

A mechanism of light transmission through metallic films is proposed, assisted by tunneling between resonating buried dielectric inclusions. This is illustrated by arrays of Si spheres embedded in Ag. Strong transmission peaks are observed near the Mie resonances of the spheres. The interaction among various planes of spheres and interference effects between these resonances and the surface plasmons of Ag lead to mixing and splitting of the resonances. Transmission is proved to be limited only by absorption. For small spheres, the effective dielectric constant of the resulting material can be tuned to values close to unity, and a method is proposed to turn the resulting materials invisible.     

含有偏心球形微粒介质球的有效介电常量

对于处在均匀外电场中含有偏心球形微粒的介质球,利用分离变量法求出球内外的电场,给出了球外电偶极矩和电四极矩的近似表达式.首次引入含有偏心球形微粒介质球的有效介电常量,它不同于同心多层介质球的等效介电常量,不仅与介质球内的介质有关,而且与球外介质有关.数值结果显示了有效介电量数随偏心距和球外介质介电常量的变化情况.     

基于介质谐振器原理的左手材料设计

本文通过对高介电常数介质基于介质谐振器理论进行分析,明确了利用高介电常数介质产生负介电常数或负磁导率的途径在于介质中产生具有Lorentz谐振形式的电磁响应的电偶极子或磁偶极子,指出了这种偶极子的产生来源于电磁波在介质中形成的驻波,而左手通带的形成正是由于电偶极子和磁偶极子之间的相互影响,破坏了驻波形成的条件所实现的. 模拟结果表明,通过将尺寸相同,介电常数不同的介质进行组合,使二者电谐振和磁谐振的频率点重合从而实现左手通带,最后利用高介电常数,低损耗的陶瓷进行样品制作并测试,测试结果证实了基于这一原理实 关键词： 全介质左手材料 介质谐振器 磁偶极子 电偶极子     

Simulation of two dimensional systems with two dimensional electrostatics

Some of the problems associated with Monte Carlo and molecular dynamics simulations of three dimensional ionic and dipolar systems are discussed, with emphasis on the use of periodic boundary conditions (PBC). It is shown that analogous problems may arise in two dimensional systems provided that the interactions are two dimensional electrostatic interactions, that is, interactions derived from the two dimensional Laplace equation. The PBC hamiltonian is evaluated by considering the appropriate two dimensional lattice sums, and a computable form for the effective pair interactions in PBC developed. The idea of an external dielectric constant is introduced and its effects included in the PBC hamiltonian. Formulae for evaluating the dielectric constant from a simulation with any external dielectric constant are given. Perturbation formulae showing the effects on the structure and mean square dipole moment of a dipolar system which are caused by a change in external dielectric constant are derived. A formula for the shift in mean square dipole moment of an ionic system is also developed. The problem of interpreting results from such simulations is discussed briefly.     

Modelling of isotropic double negative media for microwave applications

A composite medium consisting of two sublattices of dielectric spherical particles of high permittivity and different radii embedded in a dielectric matrix of smaller permittivity are considered. It has been shown that such a composite medium reveals properties of an isotropic double negative media (DNG) in a limited frequency range, when resonance oscillations of H_III mode in one kind of particles and E_III mode in another kind of particles are excited simultaneously. The E_III resonance and the H_III resonance give rise to the magnetic dipole momentum and the electric dipole momentum correspondingly. Averaging the magnetic momentum and the electric momentum over the cells belonging to the appropriate spherical particles gives the negative permittivity and permeability. The model of diffraction of a plane electromagnetic wave on a dielectric sphere is presented and compared with the mixing rule based consideration. The results obtained are rather close. Distribution of the electromagnetic wave outside the sphere is calculated. Influence of the dispersion of the sphere size and the dielectric permittivity on the effective parameters of the DNG material is estimated.     

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.     

A comparative study of the effective dielectric constant of a medium containing randomly distributed dielectric spheres embedded in a homogeneous background medium

The effective dielectric constant ∈_eff of a medium containing randomly distributed dielectric particles has been analysed by conventional methods: Foldy's approximation, the quasi-crystalline approximation (QCA) and the QCA with coherent potential. These conventional methods, however, have been indicated to become invalid for particles with a high dielectric constant; we have thus presented a new method that is valid for them. This paper compares ∈_eff of our method with those of the conventional methods by changing the volume fraction and the dielectric constant of spheres. As a result, our method is shown to be more powerful for the analysis of ∈_eff than the conventional methods.