Permittivity Of Spheres Research Articles

Local Electric Field Enhancements of Two Closely Spaced Subwavelength Spheres in Microwaves

The local electric field enhancement (LEFE) among powdered metals or dielectrics in microwaves has been widely applied in many fields, but it is still a challenge to describe the LEFE intuitively. This article presents a simple model to predict the LEFE in two closely spaced subwavelength spheres in microwaves, based on the quasistatic electric field approximation and the dipole–dipole interaction. The results show that this LEFE is related to the radius of spheres, the separation distance, and the permittivity of spheres. The proposed model is able to predict the LEFE accurately if the electric length of the two spheres is within one-tenth of a wavelength when put in free space or a waveguide. The proposed model can benefit in predicting the LEFE in subwavelength metals or dielectrics, which can benefit a wide range of applications.

Localized magnetic plasmons in all-dielectricμ<0metastructures

Metamaterials are known to exhibit a variety of electromagnetic properties non-existing in nature. We show that an all-dielectric (non-magnetic) system consisting of deep subwavelength, high permittivity resonant spheres possess effective negative magnetic permeability (dielectric permittivity being positive and small). Due to the symmetry of the electromagnetic wave equations in classical electrodynamics, localized "magnetic" plasmon resonances can be excited in a metasphere made of such metamaterial. This is theoretically demonstrated by the coupled-dipole approximation and numerically for real spheres, in full agreement with the exact analytical solution for the scattering process by the same metasphere with effective material properties predicted by effective medium theory. The emergence of this phenomenon as a function of structural order within the metastructures is also studied. Universal conditions enabling effective negative magnetic permeability relate subwavelength sphere permittivity and size with critical filling fraction. Our proposal paves the way towards (all-dielectric) magnetic plasmonics, with a wealth of fascinating applications.

The Thermal Discrete Dipole Approximation (T-DDA) for near-field radiative heat transfer simulations in three-dimensional arbitrary geometries

A novel numerical method called the Thermal Discrete Dipole Approximation (T-DDA) is proposed for modeling near-field radiative heat transfer in three-dimensional arbitrary geometries. The T-DDA is conceptually similar to the Discrete Dipole Approximation, except that the incident field originates from thermal oscillations of dipoles. The T-DDA is described in details in the paper, and the method is tested against exact results of radiative conductance between two spheres separated by a sub-wavelength vacuum gap. For all cases considered, the results calculated from the T-DDA are in good agreement with those from the analytical solution. When considering frequency-independent dielectric functions, it is observed that the number of sub-volumes required for convergence increases as the sphere permittivity increases. Additionally, simulations performed for two silica spheres of 0.5μm-diameter show that the resonant modes are predicted accurately via the T-DDA. For separation gaps of 0.5μm and 0.2μm, the relative differences between the T-DDA and the exact results are 0.35% and 6.4%, respectively, when 552 sub-volumes are used to discretize a sphere. Finally, simulations are performed for two cubes of silica separated by a sub-wavelength gap. The results revealed that faster convergence is obtained when considering cubical objects rather than curved geometries. This work suggests that the T-DDA is a robust numerical approach that can be employed for solving a wide variety of near-field thermal radiation problems in three-dimensional geometries.

Effects of parameter variations on negative effective constitutive parameters of non-metallic metamaterials

Analytical expressions describing the variability of effective constitutive parameters of non-metallic metamaterials, as a function of the constituent geometric and material parameters and their variations, have been developed from the total differential of Clausius-Mossotti expressions (using Mie dipole polarizabilities) for the effective (bulk) constitutive parameters of the metamaterial. In practice, these expressions are important for estimating the performance of a metamaterial with particular variations in the parameters of its constituents that arise during the fabrication process, and can be used to guard against extinction of desired double negative (DNG) behavior. With the derived expressions, the effects of parameter variations on effective constitutive parameters of non-metallic metamaterials have been analyzed for three types of metamaterials: (i) cubic arrays of identical magnetodielectric spheres; (ii) cubic arrays of dielectric spheres with equal radius but two different permittivities; and (iii) cubic arrays of dielectric spheres with equal permittivity but two different radii. These effects are evaluated in terms of the calculated variations in values of the effective constitutive parameters of the metamaterial in the vicinity of the DNG or single negative (SNG) band for particular geometric and material parameters and their variations. Results show that variation in the following parameters impacts DNG bandwidth. Listed in order from greatest to least influence: (i) sphere radius; (ii) sphere permittivity and permeability; (iii) lattice constant of the array; and (iv) the constitutive parameters of the array medium, all impact the width of the achievable DNG band. For particular cases studied here, results also show that the DNG behavior may be extinguished if there are 0.78%, 0.016%, and 0.016% variations in all parameters of metamaterial types (i), (ii), and (iii), respectively, as defined above. For the design of non-metallic metamaterials with inclusions, having arbitrary material parameters, in either periodic or random arrangement, the presented results can give a qualitative guide on the level of fabrication tolerances that should be achieved in order to observe the predicted SNG or DNG behavior experimentally.

Preparation and microwave absorption properties of Ni–Fe 3O 4 hollow spheres

Nickel–magnetite hollow spheres with the diameter about 150 nm were prepared by an autocatalytic reduction method. The effect of Fe 3O 4 content in hollow spheres on microwave absorption properties has been investigated. With an increase of magnetite content, permittivity of sphere–wax composite decreased, while permeability increased. For composite layers, a minimum reflection loss (RL, −38.4 dB) was predicted at 10.8 GHz with a thickness of 2.5 mm. In addition, the increasing content of magnetite resulted in the peak of RL moves to higher frequency and the minimal reflection loss increases obviously.

Electromagnetic and microwave absorption properties of Fe 3O 4 magnetic films plated on hollow glass spheres

Magnetic hollow spheres of low density were prepared by plating Fe 3O 4 magnetic films on hollow glass spheres using ferrite plating. The complex permeability and permittivity of spheres–wax composites were measured in the range of 2–18 GHz. The complex permeability and permittivity increased, and the dielectric and magnetic losses were improved as the volume fraction of the magnetic spheres in the composites increased from 60% to 80%, which also resulted in a great improvement of microwave absorption properties. For composites with volume fraction 80%, its magnetic resonance frequency was at about 13 GHz and it appeared three loss peaks in the calculated reflection loss curves; the bandwidth less than −10 dB was almost 4 GHz which was just in the Ku-band frequencies (12–18 GHz) and a minimum reflection loss of −20 dB was obtained when the thickness was 2.6 mm; the microwave absorbing properties were mainly due to the magnetic loss. The results showed that the magnetic spheres composites were good and light microwave absorbers in the Ku-band frequencies.

Isotropic artificial media with simultaneously negative permittivity and permeability

AbstractA 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 in the frequency range where resonance oscillations of H111 mode in one kind of particles and E111 mode in another kind of particles are excited simultaneously. The E111 resonance and the H111 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 reveals the negative permittivity and permeability. Distribution of the electromagnetic wave outside the sphere was calculated. Influence of dispersion of the sphere permittivity and size on the effective parameters was estimated. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 2553–2556, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22002

Traveling Electromagnetic Waves on Linear Periodic Arrays of Lossless Penetrable Spheres

Traveling electromagnetic waves on infinite linear periodic arrays of lossless penetrable spheres can be conveniently analyzed using the source scattering-matrix framework and vector spherical wave functions. It is assumed that either the spheres are sufficiently small, or the frequency such, that the sphere scattering can be treated using only electric and magnetic dipole vector spherical waves, the electric and magnetic dipoles being orthogonal to each other and to the array axis. The analysis simplifies because there is no cross-coupling of the modes in the scattering matrix equations. However, the electric and magnetic dipoles in the array are coupled through the fields scattered by the spheres. The assumption that a dipolar traveling wave along the array axis can be supported by the array of spheres yields a pair of equations for determining the traveling wave propagation constant as a function of the sphere size, inter-sphere separation distance, the sphere permittivity and permeability, and the free-space wave number. These equations are obtained by equating the electric (magnetic) field incident on any sphere of the array with the sum of the electric (magnetic) fields scattered from all the other spheres in the array. Both equations include a parameter equal to the ratio of the unknown normalized coefficients of the electric and magnetic dipole fields. By eliminating this parameter between the two equations, a single transcendental equation is obtained that can be easily solved numerically for the traveling wave propagation constant. Plots of the k - β diagram for different types and sizes of spheres are shown. Interestingly, for certain spheres and separations it is possible to have multiple traveling waves supported by the array. Backward traveling waves are also shown to exist in narrow frequency bands for arrays of spheres with suitable permittivity and permeability.