首页/论文/physics/0402018

arXiv physics/04020182004-02-04physics.opticsphysics.class-ph

A limitation of the Bruggeman formalism for homogenization

T. G. Mackay, A. Lakhtakia

发表信息：: Optics Communications 234, 35-42 (2004)
DOI：: 10.1016/j.optcom.2004.02.007

英文摘要：

The Bruggeman formalism provides an estimate of the effective permittivity of a particulate composite medium comprising two component mediums. The Bruggeman estimate is required to lie within the Wiener bounds and the Hashin-Shtrikman bounds. Considering the homogenization of weakly dissipative component mediums characterized by relative permittivities with real parts of opposite signs, we show that the Bruggeman estimate may not be not physically reasonable when the component mediums are weakly dissipative; furthermore, both the Wiener bounds and the Hashin-Shtrikman bounds exhibit strong resonances.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

On limitations of the Bruggeman formalism for inverse homogenization

The Bruggeman formalism provides an estimate $\eps^{Br}_{hcm}$ of the relative permittivity of a homogenized composite material (HCM), arising from two component materials with relative permittivities $\eps_a$ and $\eps_b$. It can be inverted to provide an estimate of $\eps_a$, from a knowledge of $\eps^{Br}_{hcm}$ and $\eps_b$. Numerical studies show that the inverse Bruggeman estimate $\eps_a$ can be physically implausible when (i) $Re\{\eps^{Br}_{hcm}\}/Re\{\eps_b\} > 0 $ and the degree of HCM dissipation is moderate or greater; or (ii) $Re\{\eps^{Br}_{hcm}\}/Re\{\eps_b\} < 0 $ regardless o…

2010-04-29physics.optics

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 HC…

2015-02-16physics.optics

On the application of homogenization formalisms to active dielectric composite materials

The Maxwell Garnett and Bruggeman formalisms were applied to estimate the effective permittivity dyadic of active dielectric composite materials. The active nature of the homogenized composite materials (HCMs) arises from one of the component materials which takes the form of InAs/GaAs quantum dots. Provided that the real parts of the permittivities of the component materials have the same sign, the Maxwell Garnett and Bruggeman formalisms give physically plausible estimates of the HCM permittivity dyadic that are in close agreement. However, if the real parts of the permittivities of the comp…

2009-02-05physics.optics

Bruggeman formalism vs. `Bruggeman formalism': Particulate composite materials comprising oriented ellipsoidal particles

Two different formalisms for the homogenization of composite materials containing oriented ellipsoidal particles of isotropic dielectric materials are being named after Bruggeman. Numerical studies reveal clear differences between the two formalisms which may be exacerbated: (i) if the component particles become more aspherical, (ii) at mid-range values of the volume fractions, and (iii) if the homogenized component material is dissipative. The correct Bruggeman formalism uses the correct polarizability density dyadics of the component particles, but the other formalism does not.

2012-01-27physics.optics

Bruggeman Approach for Isotropic Chiral Mixtures Revisited

Two interpretations of the Bruggeman approach for the homogenization of isotropic chiral mixtures are shown to lead to different results. Whereas the standard interpretation is shown to yield the average-polarizability-density approach, a recent interpretation turns out to deliver a null-excess-polarization approach. The difference between the two interpretations arises from differing treatments of the local field

2019-06-03physics.optics

On extended homogenization formalisms for nanocomposites

In a long wavelength regime, the effective properties of particulate composites, including nanocomposites, may be estimated using one of various homogenization formalisms, such as the Bruggeman and Maxwell Garnett formalisms, and the approach of the strong--property--fluctuation theory (SPFT). In the conventional implementations of these formalisms, the constituent particles are treated as point--like scattering centres. However, extended formalisms have been established--which involve integral formulations--that take account of the spatial extent of the constituent particles. In particular, t…

2008-07-21physics.optics

更多相关论文收起更多论文

Geometrically-Derived Anisotropy in Cubically Nonlinear Dielectric Composites

We consider an anisotropic homogenized composite medium (HCM) arising from isotropic particulate component phases based on ellipsoidal geometries. For cubically nonlinear component phases, the corresponding zeroth-order strong-permittivity-fluctuation theory (SPFT) (which is equivalent to the Bruggeman homogenization formalism) and second-order SPFT are established and used to estimate the constitutive properties of the HCM. The relationship between the component phase particulate geometry and the HCM constitutive properties is explored. Significant differences are highlighted between the esti…

2004-08-09physics.optics

Negative phase velocity in isotropic dielectric-magnetic mediums via homogenization

We report on a strategy for achieving negative phase velocity (NPV) in a homogenized composite medium (HCM) conceptualized using the Bruggeman formalism. The constituent material phases of the HCM do not support NPV propagation. The HCM and its constituent phases are isotropic dielectric-magnetic mediums; the real parts of their permittivities/permeabilities are negative-valued whereas the real parts of their permeabilities/permittivities are positive-valued.

2005-04-30physics.optics

包含具有取向分布的球体和截球体的颗粒复合材料的电磁均匀化

Electromagnetic homogenization of particulate composite materials comprising spheroids and truncated spheroids with orientational distribution

University of Edinburgh（爱丁堡大学）；The Pennsylvania State University（宾夕法尼亚州立大学）

本研究开发Bruggeman与Maxwell Garnett均匀化形式的实现方案，探究含取向分布球体及截球体颗粒的复合材料介电各向异性与取向分布标准差的关系，对比两种形式的预测差异。

2025-04-04physics.optics

Anisotropic Bruggeman Effective Medium Approaches for Slanted Columnar Thin Films

Two different formalisms for the homogenization of composite materials containing ellipsoidal inclusions based on Bruggeman's original formula for spherical inclusions can be found in the literature. Both approximations determine the effective macroscopic permittivity of such an idealized composite assuming randomly distributed dielectric particles of equal shape and differ only in the definition of the depolarization factors. The two approaches are applied to analyze ellipsometric Mueller matrix spectra acquired in the visible and near-infrared spectral region from metal and semiconductor sla…

2013-09-11cond-mat.mtrl-sciphysics.optics

A simple construction for a cylindrical cloak via inverse homogenization

An effective cylindrical cloak may be conceptualized as an assembly of adjacent local neighbourhoods, each of which is made from a homogenized composite material (HCM). The HCM is required to be a certain uniaxial dielectric-magnetic material, characterized by positive-definite constitutive dyadics. It can arise from the homogenization of remarkably simple component materials, such as two isotropic dielectric-magnetic materials, randomly distributed as oriented spheroidal particles. By carefully controlling the spheroidal shape of the component particles, a high degree of HCM anisotropy may be…

2011-08-30physics.optics

Towards an experimental realization of affinely transformed linearized QED vacuum via inverse homogenization

Within the framework of quantum electrodynamics (QED), vacuum is a nonlinear medium which can be linearized for a rapidly time-varying electromagnetic field with a small amplitude subjected to a magnetostatic field. The linearized QED vacuum is a uniaxial dielectric-magnetic medium for which the degree of anisotropy is exceedingly small. By implementing an affine transformation of the spatial coordinates, the degree of anisotropy may become sufficiently large as to be readily perceivable. The inverse Bruggeman formalism can be implemented to specify a homogenized composite material (HCM) which…

2011-09-09physics.optics

Towards a piecewise-homogeneous metamaterial model of the collision of two linearly polarized gravitational plane waves

We considered the experimental realization of a Tamm medium that is optically equivalent to the collision of two linearly polarized gravitational plane waves as a piecewise homogeneous metamaterial. Our formulation was based on the homogenization of remarkably simple arrangements of oriented ellipsoidal nanoparticles of isotropic dielectric-magnetic mediums. The inverse Bruggeman homogenization was used to estimate the constitutive parameters, volume fractions, and shape parameters for the component mediums. The presented formulation is appropriate for the regions of spacetime where the two gr…

2014-08-04physics.optics

On the effective permittivity of silver-insulator nanocomposites

The Bruggeman formalism provides an estimate of the effective permittivity of a composite material comprising two constituent materials, with each constituent material being composed of electrically small particles. When one of the constituent materials is silver and the other is an insulating material, the Bruggeman estimate of the effective permittivity of the composite exhibits resonances with respect to volume fraction that are not physically plausible.

2006-11-08physics.optics

Enhanced group velocity in metamaterials

The Bruggeman formalism is implemented to estimate the refractive index of an isotropic, dielectric, homogenized composite medium (HCM). Invoking the well--known Hashin--Shtrikman bounds, we demonstrate that the group velocity in certain HCMs can exceed the group velocities in their component materials. Such HCMs should therefore be considered as metamaterials.

2004-02-06physics.class-phphysics.optics

Anisotropic enhancement of group velocity in a homogenized dielectric composite medium

Under certain circumstances, the group velocity in a homogenized composite medium (HCM) can exceed the group velocity in its component material phases. We explore this phenomenon for a uniaxial dielectric HCM comprising isotropic component material phases distributed as oriented spheroidal particles. The theoretical approach is based upon the Bruggeman homogenization formalism. Enhancement in group velocity in the HCM with respect to the component material phases is shown to be sensitively dependent upon the shape of the component spheroids and their alignment relative to the direction of prop…

2005-08-09physics.optics

On Direct and Indirect Scattering Approaches for Homogenization of Particulate Composites

Theoretical formalisms for the homogenization of particulate composites are identified as following either the direct scattering approach (DSA) or the indirect scattering approach (ISA). Both approaches can take inclusion size-dependence and distribution statistics into account. However, the DSA is generally limited to mediums with direction-independent constitutive properties and inclusions with simple shapes, but the ISA is not hobbled thus.

2019-10-07physics.optics

The homogenization of orthorhombic piezoelectric composites by the strong-property-fluctuation theory

The linear strong--property--fluctuation theory (SPFT) was developed in order to estimate the constitutive parameters of certain homogenized composite materials (HCMs) in the long--wavelength regime. The component materials of the HCM were generally orthorhombic $mm2$ piezoelectric materials, which were randomly distributed as oriented ellipsoidal particles. At the second--order level of approximation, wherein a two--point correlation function and its associated correlation length characterize the component material distributions, the SPFT estimates of the HCM constitutive parameters were expr…

2008-11-14physics.optics

源于截断球体、椭球体和椭球体的各向异性均匀化复合介质

Anisotropic homogenized composite mediums arising from truncated spheres, spheroids, and ellipsoids

基于截断球体、球体和椭球体去极化并矢的闭式表达式，实现了 Maxwell Garnett 均匀化形式体系，揭示了复合介质各向异性程度随包含物形状偏离球体而增大的规律。

2024-04-27physics.optics